JPH08204766A - Frequency analysis detection method for time-limited waveforms - Google Patents

Abstract

(57) [Summary] [Objective] Without decreasing the detection output of the target signal to be detected, as compared with the noise power detected by the correlation detection technique that has been widely used in the conventional modulation methods such as FSK and PSK. , It aims at suppressing the detection noise power. In a system for analyzing frequency / phase components included in an input time waveform time-limited to a frame time length T ₀ seconds, an arbitrary frequency interval smaller than f _d (= 1 / T ₀ ) is provided. Under the condition of permitting that, an arbitrary number N of element frequencies f _j (j = 0, 1, 2, ... N-1) are provided,
A pair of orthogonal waveform components C _j and S having this element frequency f _j
A frequency analysis and detection method for a time-limited waveform, characterized in that the input time waveform is analyzed and expressed by a combination of _j .

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a synchronous detection receiving system in a band pass type data transmission system capable of improving the detection accuracy of the frequency and phase of a sinusoidal waveform whose time is limited.

[0002]

2. Description of the Related Art The band-pass type data transmission system is a basic technology of digital radio transmission, and its modulation system is
Frequency shift keying modulation (FSK), phase shift keying modulation (PSK), quadrature amplitude modulation (QAM)
and so on. Of these, the former two are important and fundamental modulation schemes, and the present invention is directly related to them. 2 is F
The operation in the receiver TX, which is a block diagram of the SK transmission system, will be described.

In the modulator (MOD), the binary signals D _S to be received are made to correspond to the shift frequencies f ₀ and f ₁ , and either one is obtained as an output. This output modulates the carrier wave f _c and sends it to the transmission line. Next, the receiver RX receives the signal to which the noise n (t) has been added on the transmission path. This received signal is demodulated by f _c , and only the low frequency component is extracted by the reduction filter (LPF). This component is subjected to correlation detection with f ₀ and f ₁ in the demodulator, and this detection output is applied to the decision circuit and compared with a preset threshold value to become a demodulation binary output D _R.

The time waveform of the period T having two different shift frequencies used here is expressed by the following equation. v ₀ (t) = Asin {n2πf _D t} (0 ≦ t ≦ T) (1) v ₁ (t) = Asin {(n + 1) 2πf _D t} (0 ≦ t ≦ T) (2) where f _D = 1 / T, n = 1, 2, 3, ... T is a frame time width, which is a bit period in the case of binary transmission. FIG. 3 shows a time waveform when the binary series 1, 0, 1, 1 is transmitted when n = 3. The demodulator of FIG. 4 inputs the same waveform as the signal waveform v _i (t) (i = 0,1) to be detected by the correlator e _i (t) = 2 sin {(n + i) 2πf _D t} (3) into r ( It is composed of a circuit that multiplies with t) and a circuit that integrates its output. The time T of the output v _i (t) of this correlator
The value at is

[0005]

[Equation 2] Becomes Generally, if white noise n (t) is included in the received input, it is expressed as r (t) = v _i (t) + n (t) (5) and multiplied by n (t) and e _i (t). The product output integrated value is

[0006]

(Equation 3) Becomes Here, η is the one-sided noise power density (/ Hz). From this, the SN ratio in the integrated output is given by the following equation.

SNR = (A ² T) / η = (2E _b ) / η (7) Here, E _b (= A ² T / 2) is the signal energy for one frame T seconds and is called bit energy. From now on S
The N ratio was constrained to 4E _b / η due to the intrinsic performance of the correlator and no further improvement was possible using conventional techniques. Let's obtain the frequency characteristic of the integrated output based on the noise of equation (6). Assuming that the input noise is a single frequency n ^* (t) = Asin (2πft + θ) (8), the integrated value of the product output of n ^* (t) and e ₀ (t) shown in equation (3) is obtained. When,

[0008]

[Equation 4] Given in. Here, ω = 2πf and ω _D = 2πf _D. Now, when v _in (T) is averaged with respect to θ in Expression (9) and the power of the integrated output with respect to the noise of the input frequency f is calculated, the following expression is obtained. _{N M (f) = [(} 2Anω D) / {τ (ω 2 -n 2 ω 2 D)}] 2 (1-cos ωT) (10) = 1/2 {(AT) / τ} 2 (ω = Nω _D ) (11) FIG. 5 shows the characteristics of N _i (f) when n = 4, A = 1, and τ = T. As can be seen from the figure, the output mainly occurs in the frequency band 3f _{D to} 5f _D. This bandwidth B
= 2f _D is a bandwidth required to transmit a signal without substantial distortion, which corresponds to twice the signal transmission rate.
(B corresponds to four times the Nyquist bandwidth.) When the power of FIG. 5 and the equation (10) is integrated from f = 0 to ∞, it becomes the noise power for the white noise shown in the equation (6). Now, when the white noise power coming into the bandwidth B = 2f _D is P _N (B) = 2ηf _D = 1 (W) (12), the power generated on the output side of the integrator by this white noise is When τ = T and A = 1 are calculated, N _M (∞) = ηf _D /2=0.25w N _M (B) = 0.226w (B = 2f _D ) (13) from the formula (6). . Noise power of about 90% is f = (3-5) f _D
Than occurs at (n = 4 case), the total noise power 1w applied to the band 2f _D, 0.25 w (actually 0.22
6w) is detected. That is, the main band (bandwidth B)
About 1/4 of the noise added to is detected.

On the other hand, if a correct signal waveform v _i (t) is received and demodulated by e _i (t) and it is 1 (w), then A = 1, τ = T in equation (4) , Its detection output is also 1w
Becomes Therefore, according to the above-described correlation detection method, the input signal and the noise component are preliminarily B
The reference SNR when limited to Hz is limited to about 4 (6 dB). It is an object of the present invention to provide a technique for reducing the noise power detected by such correlation detection.

On the other hand, as is clear from the characteristics of FIG. 5, when a sine waveform is sent using a frame with a time width of T seconds (= 1 / f _D ), when k is an integer, f _k = kf _D When expressed as (14), the correlation between the signals f _{k having} different _k is

[0011]

(Equation 5) And both are orthogonal. That is, for example, kf _D ,
When two waveforms of (k + 1) f _D are sent simultaneously in the same frame, or when either one of them is sent in a different frame, the output side of the correlator that detects the waveform of kf _D is (k
The influence of the waveform of +1) f _D does not appear, and no interference occurs.

[0012] Especially when using only the case for example a sine wave of FSK, since becomes zero if _{ω = nω 0 + ω 0/} 2 in equation (9), f = k ( f D / 2) (16) However, signals having different k are orthogonal to each other. However, the orthogonal condition of the method using both PSK and FSK such that the sine waveform and the cosine waveform are used at the same frequency is the equation (14).
That is, in the correlation detection method, the minimum value of the frequency intervals at which signals can be detected without interference with each other is f _D / 2, and an interval of f _D is usually required.

It is an object of the present invention to provide a technique capable of narrowing the interval of frequencies which can be identified without interference from these values. First, the frame time length ^* (frame period)
Let T define the frequency of T (= f _D ^-1 ). Single frequency continuous sinusoidal waveform v (t) = sin2πf ₀ t (f ≠ kf
_{If D} , k = 0, 1, 2, ...) Is limited within the frame period as shown in FIG. 1 to form an isolated waveform, its frequency component is f
Infinitely spreads around, and if the frequency axis is standardized by f _D , then E (f) = (2 / f _D ) [Sinc (f−f ₀ ) + Sinc (f + f ₀ )] (17) It is expressed and contains infinite frequency components. If a repetitive waveform of a frame of period T is assumed, then D
By FT analysis,

[0014]

(Equation 6) Is expressed as FIG. 6A shows a sine waveform in the case of f = 3.875f _D , and FIG. 6B shows the spectrum absolute value C _n = √ (a _n ² + b _n ² ) of the DFT analysis output. from now on,
It can be seen that the analysis result of v (t) spreads infinitely over the frequency band. Either method makes it difficult to identify the original frequency f ₀ .

Here, it is assumed that the waveform elements of a single frequency forming the frame signal are continuous as shown in FIG. 6A, and the frequency of the continuous waveform is set to the original frequency (Orig).
inal Frequency-OF, in the case of the figure OF
= 3.875f _D ). The following discussion will be developed focusing on this original frequency OF. That is, FIG.
As shown in (b), the goal is to represent the spread frequency component with one frequency, but a method of actually expressing with a small number of element frequencies to be described later is derived. An object of the present invention is to provide a technique for accurately detecting a time waveform component having a frequency component that does not match an integral multiple of f _D.

[0016]

The object of the present invention is to detect the detected noise power without reducing the detected output of the target signal to be detected, as compared with the noise power detected by the correlation detection technique widely used in the modulation schemes such as FSK and PSK. The purpose is to suppress. Conventionally, in the FSK system with the frame period T (= 1 / f _D ), the frequency interval of signals that can be detected without interfering with each other was (f _D / 2 or f _D ), but this interval is γ f _D (γ Is a real number). Also,
When the occupied bandwidth of the signal group included in the frame period (received signal bandwidth before detection) is BHz, this BHz
It is an object of the present invention to provide a technique capable of detecting a plurality of (M) signals of an arbitrary frequency OF included in the above (1) without interfering with each other. Conventionally, the frequency component of the time waveform whose time is limited to the frame period T is analyzed at a frequency that is an integral multiple of f _D. However, here, it is necessary to provide a technique for analyzing the phase component with a frequency accuracy of f _D or less. To aim.

[0017]

SUMMARY OF THE INVENTION In order to achieve the above object, the invention according to claim 1 is a system for analyzing a frequency / phase component included in an input time waveform time-limited to a frame time length T ₀ seconds. The element frequency f under the condition that it is possible to have an arbitrary frequency interval smaller than f _d (= 1 / T ₀ ).
_{j (j = 0,1,2 ... N-} 1) to provided any number of N, the orthogonal waveform components C _j and S _j of the pair with the component frequency f _j
It is characterized in that the input time waveform is analyzed and expressed by a combination of.

According to a second aspect of the present invention, in the first aspect, one of the element frequencies included in the input time waveform is included.
Under the condition of maintaining the continuity of the waveform of arbitrary phase having the number of components f _j , T _j becomes an integral multiple of the period of f _j by duplicating or deleting a part of the input frame. So that the input frame length T ₀ is T _j =
A modified frame is created by changing to k (1 / f _j ), and the cosine wave and sine wave components of the frequency f _j included in the input time waveform are
The feature is that extraction is performed by performing correlation analysis with T _j as the integral frame length.

According to a third aspect of the invention, in the first aspect, the element frequencies f _i (i =
0,1,2 ... N-1) for a cosine waveform C _i and a sine waveform S _i , to create an enlarged or reduced frame having a frame time T _j of claim 2 corresponding to another element frequency f _j. To generate a modified cosine waveform C _ij and a modified sine waveform S _ij , and the correlation _coefficients α _ij and α with C _ij with T _j as an integration frame length for the input cosine waveform component C _i and the input sine waveform component S _i . _ij is obtained, and the two input waveforms C _i and S _i are similarly obtained.
Previously determined correlation system number beta _ij with S _ij, and a beta _ij hand, by correlation analysis by C _ij and S _ij to this modified frame input waveform, obtains the analysis output U _j, V _j, these values and 2N former simultaneous linear equations hold when the unknown amplitude y _j of amplitude x _j and sinusoidal components of the cosine wave component in f _j component contained in the input time waveform (described in the claim 3) satisfying such (x _i, y _i), characterized in that can be analyzed detected by the N sets of the set of the N frequency and phase contained in the input time waveform by obtaining a set of (x _i, y _i) And

According to a fourth aspect of the present invention, in the first aspect, one or more of the element frequencies f _j are the element frequencies for detailed analysis, the remainder is the element frequency for main analysis, and all the former frequencies are used. While shifting by the frequency interval Δf, the analysis result (x
_i , y _i ) is obtained, and the detailed frequency characteristics of the input frame signal are obtained by obtaining the cosine waveform and sine waveform of the line spectrum in steps of Δf and the power spectrum density from this set. And

According to a fifth aspect of the present invention, when the desired attenuation coefficient is γ in one or more of the cosine waveform and the sine waveform of the line spectrum obtained in Δf steps in the fourth aspect, (1-γ) It is characterized in that a desired filter characteristic is realized with accuracy close to Δf by multiplying the multiplied amplitude value and then subtracting it from the input waveform.

According to a sixth aspect of the present invention, in 2N kinds of signals consisting of a cosine waveform and a sine waveform of the element frequency f _j (j = 0,1,2 ... N-1) in the first to fourth aspects. A feature is that multi-level transmission of a maximum of 2N values is performed by associating any one of the transmission frame signals with each other and detecting these signals on the receiving side without mutual interference. According to a seventh aspect of the present invention, in the sixth aspect, the 2N types are set to 1 × N sets, and each type of signal is associated with a transmission frame signal, so that the maximum number of N channels is 2. It is characterized by performing value transmission.

[0023]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Prior to the description of the embodiments of the present invention, the basic principle of the present invention will be described. Now, assume that the frequency component of the received signal v (t) includes the following range D (f) in D (f): 3.75f _{D to} 4.25f _D. Here, the frequency component of f refers to a component in which a sine wave and a cosine wave having a frequency f (OF) that continue for a long time are limited by a frame. N element frequencies f _j when analyzing and detecting such a received signal
(J = 0,1,2 ... N-1), where N = 3
The case will be described as an example.

F _j : f ₀ = 4.0f _D f ₁ = 3.75f _D f ₂ = 4.25f _D (19) Let the original frame period of the received signal be T = T ₀ = 1 / f _D ,
The waveforms of the cosine wave C _j and the sine wave S _j corresponding to N = 3 are defined by the following equation, where the left end of the original frame is t = 0. C _j (t) = cos 2πf _j t (0 ≦ t ≦ T) (20) S _j (t) = sin 2πf _j t (0 ≦ t ≦ T) (21) The sine waveform shown by the above equation is shown in FIG. Shown in. The waveform of S ₀ (t) includes a waveform of 4 cycles within the period T ₀ , but S ₁
The waveforms of (t) and S ₂ (t) include a non-integer number of cycles. In order to convert the non-integer number of cycles into an integer, the waveforms of these waveforms are framed as shown on the right side of FIG. Extend the cycle. First, T ₁ and T ₂ are defined by the following equation. T ₁ = 1 / f _D1 = α ₁ T ₀ (α ₁ = 4.0 / 3.75) T ₂ = 1 / f _D2 = α ₂ T ₀ (α ₂ = 5.0 / 4.25) (22 ) Here, α ₁ (≧ 1) is a frame period extension coefficient.
In general, T ₀ , T ₁ , and T ₂ are represented by T _j (j = ₀ , ₁ , 2). The cosine waveform and the sine waveform of the element frequency f _j (= T _j ⁻¹ ) used in the analysis based on T _j are C _jj and S _jj, and are given by the following equation. C _jj (t) = cos (2πf _j t) (0 ≦ t ≦ T _j ) S _jj (t) = sin (2πf _j t) (0 ≦ t ≦ T _j ) (23) Next, to extend the frame period. Accordingly, the element sine wave S _i0 (t) based on the original frame T ₀ is modified to _obtain S _ij (t)
The method of obtaining FIG. 7 (b) shows that when the period extension [T ₀ → T ₁ ] for defining S _ii (t) is applied, the 3 of FIG.
The changes that occur in the element sine waveform S _i0 (t) are shown. Figure 7
Suppose that the input v (t) contains a signal component having exactly the same waveform as S _i (t) in (a). In order to use this component to generate S _ij (t) shown in the first stage of FIG. 7 (b) having an integer cycle in the length T _i , in order to create a part of S _i (t) indicated by a dotted line, It is sufficient to use ΔS _i (t), shift it by time (T ₀ −t ₀ ), and add it to the end of S _i (t). This is defined by the following formula.

S _ii (t) = S _i (t) + ΔS _i {t− (T−t ₀ )} (24) That is, ΔS _i (t) is a waveform shorter than one cycle of the waveform S _i (t), Generally, there are multiple equal waveforms in S _i (t). Therefore, if any one of them is taken out, the time is shifted and added to the end of the extension frame, the waveform S _ii (t) of a complete integer cycle is obtained. In this case, the sine wave S _ii (t) is a continuous waveform having a frame length T _i and consists of 4 cycles. The figure shows the case where a part of the waveform included in the first cycle of the frame is extracted and added to the last. This process will be described as COV (T ₀ → T ₁ ). When the same process is applied to S ₀ (t) of FIG. 7A, S ₀₁ (t) of the second stage of FIG. 7B is obtained. When applied to the waveform of S ₂ (t) in FIG. 7A, the S in the third stage of FIG.
₂₁ (t) is obtained. These two waveforms include a discontinuity at the end. The waveforms involved in the T ₁ -based analysis are generally denoted as S _ii (t), where i (= 0,1,2) is the number indicating the frequency component contained in the input. T ₀ and S ₀₀
For the same processing focusing on (t), since S ₀ (t) is already an integer cycle, there is no partial waveform to be added, and the waveform S ₁₀ (t) matches S _i (t). , These correspond to waveforms in which the cycle of S _jj (t) is limited to T ₀ .

Next, if attention is paid to T ₂ and S ₂₂ (t) and similar processing is performed, S _i2 (t) is obtained. Further, similar processing is performed on the cosine wave component C _i (t) to obtain the continuous waveform C ₀₀ (t), C ₁₁ (t), C ₂₂ (t) and the discontinuous waveform C.
₁₀ (t), C ₂₀ (t), C ₀₁ (t), C ₂₁ (t), C ₀₂
(T) and C ₁₂ (t) are obtained. (In the display of C _ij and S _ij , i is the number of the element frequency f _j included in the input signal, and j is the number of the analysis period T _j .) The 18 element waveforms defined by the above method Is used to analyze the input signal v (t). frequency f _v included in v (t)
The amplitude of the cosine waveform component of x _i and the amplitude of the sine wave component of y _i
Let's express v (t) by the combination of both. Input signal

[0027]

(Equation 7) Assuming that, let us consider a case where the analysis is performed by focusing on the period T ₀ . In this case, C _{00 is applied} to v (t) without changing the original frame.
Correlation is performed with (t) and S ₀₀ (t). The correlation value is obtained by digital signal processing (DSP) using the sample value of the signal of the original frame, and the value is U
_0, suppose V _0. Then, the following equation holds.

Α ₀₀ x ₀ + α _{00 ′} y ₀ + α ₁₀ x ₁ + α _{10 ′} y ₁ + α ₂₀ x ₂ + α _{20 ′} y ₂ = U ₀ (27) β ₀₀ x ₀ + β _{00 ′} y ₀ + β ₁₀ x ₁ + β _{10'y 1 + β 20 x 2} + β 20'y 2 = V 0 (28) _{where, α ij, α ij ',} β ij, β ij' is the correlation coefficient,

[0029]

(Equation 8) Given in. In the analysis based on the periods T ₁ and T ₂ , α _i1 , α _i1 ′, β _i1 , ...
_i2 , α _i2 ′, β _i2 , ... _Are used. The cross-correlation symbols between the input and analysis waveforms are shown in FIG. The specific values of this table corresponding to equation (19) are shown in the matrix on the left side of FIG. 8 described below.

Next, let us consider a case where the analysis is conducted by focusing on the period T ₁ . In this case, for the input signal v (t), the expression (2
4) and the conversion process COV (T ₀ → T shown in FIG. 7B).
₁ ) in advance to obtain the waveform v ₁ (t) of the enlarged frame T ₁ . For this v ₁ (t), C ₁₁ (t), S ₁₁ (t)
When the correlation analysis is performed using, the processing results U ₁ and V ₁ are obtained, and the same expressions as the expressions (27) and (28) are established. Further, in the case of an analysis focusing on the cycle T ₂ , after v (t) is subjected to the conversion process COV (T ₀ → T ₂ ) in advance, U ₂ and V ₂ are obtained, and equations (27) and (28) are obtained. A formula similar to is obtained.

Rewriting these expressions,

[0032]

[Equation 9] This is represented by the following matrix.

[0033]

[Equation 10] The above equation is a six-dimensional linear equation, and the matrix on the left side [α,
The value of β] is calculated in advance by the method described above as shown in FIG. Therefore, by solving the above equation using U _i and V _i obtained by the correlation processing, six values (x _i , y _i ) can be obtained. The process of changing the cycle of the input frame signal and performing the above processing to obtain (x _i , y _i ) is as shown in the block diagram of FIG. If v (t) satisfies the equation (25), v (t) can be completely expressed. That is, three frequencies having a frequency interval smaller than f _D and their phases enable complete analysis, and the following equation holds for the restored waveform v _a (t) using the analysis result.

[0034]

[Equation 11] When v (t) does not satisfy the equation (25), an analysis error ε shown in the following equation occurs. _{ε = v a (t) -v} (t) (33) in accordance with the principles of the above equation, v (t) = cos ( 2πf 0 t-π / 6) (34)

[0035]

(Equation 12) When the input is, the analysis result [U,
V] and the solution [x, y] of the simultaneous equations are shown in FIGS.
Shown in The figure shows that since the input satisfies the equation (25), an accurate result is obtained under this condition. Now, the parameter for N = 3 similar to the case shown in the examples of FIGS. α, β] and v (t)
Sine wave n ^* (t) A of single frequency (f) shown in equation (8)
= √2, θ = 0), the detection output (x _j , y)
_j ). The value when x is changed by this method (x
_j , y _j ) is obtained and shown in FIG. 9A, and its analysis error voltage ε is shown in FIG. 9B.

In this case, the equation (25) is satisfied, or at least for v (t), when f is the original frequency OF, then f ₁ ≤f≤f ₂ (36) is satisfied. It is assumed. Generally, the frequency band of the received signal is limited in advance by a filter that passes only the desired signal component to be demodulated, and the out-of-band noise component is removed. Therefore, the pass band of this filter is given by the equation (3
You can choose like 6). However, when a waveform whose time is limited to one frame period is filtered, the waveform is disturbed, so that the target signal component may be attenuated and another frequency component may be generated. To suppress such waveform deterioration to a small extent, it is necessary to slightly widen the pass band. As an example, when the target frequency to be detected is assumed to be kf _D, consider the pass band of the following formula. (K-1) f _D <f <(k + 1) f _D (37) B = 2f _D (38) This corresponds to four times the Nyquist rate. To accurately analyze the signal components contained in this band, the number N of element frequencies may be increased. Therefore, the parameters [α, β] for N = 5 are obtained in advance, and attention is paid to the power P _j = (x _j ² + y _j ² ) / 2 (39) of the j-th element frequency, and the frequency characteristic of P _j is determined. Is obtained as shown in FIG. The analysis error power Pε = ε ² in this case is shown in FIG.
It is shown in 0 (b). From FIGS. 9 and 10, when v (t) is composed of only the waveform component of the element frequency f _j , f = f
components _{P j '(j' ≠ j} ) in the _j by only 0 completely component frequency components v (t) is represented. Also, it can be seen that the error power for other input frequencies is considerably small. This result shows that when a plurality of signals are made to correspond to element frequencies, even if the intervals are smaller than f _D , orthogonal detection can be performed without mutual interference, as if they were orthogonal in the detection process. .

Further increasing N, N = 9 and k = 4, and the input signal is n ^* (t) in the equation (8), A = √2,
Among the component frequency component when analyzed output assuming theta = 0, the power P of the 4f _D component ^{_{0X = x 0 2/2,}} P 0y = y 0 2/2
Is obtained, the analysis error power P is obtained.
ε is shown in FIG. Pε≈0, which indicates that accurate analysis can be performed when N is large.

Next, under the same conditions as in FIG. 11, θ is 0 to 2π.
4f of the analysis output when it changed in _D Sine wave power P₀ 
Focusing on γ, the average power (P _0y) Ask
Then, FIG. 12 is obtained. The figure shows a conventional matched filter
The correlation analysis characteristic of FIG. 5 is shown by a wavy line. Compare both
Then, the generation bandwidth of the method of the present invention is narrowed. So
The reason is that among the input frequency components, f≈f_i (F_i ≠ 4f
_D ), Most of the components of_i As a result of being absorbed by
This is because they can be separated closely. The above average power
(P _0y)of(P) Is originally a mark with (~) immediately above P
Although it is a code that you want to express as an issue, it is used in electronic applications.
Due to the limitation of usable codes, it is unavoidable (P)
There is. The band B is used as input and L frequencies and θ of each frequency are input.
Is divided into L ', each signal is equal power, and total power is
Let's assume 1w as in (12). L, L '→ ∞
Then this is a white noise model. The size of L and L '
ValueP _0yTotal power N_E (B) is from FIG.
In this example, as a value corresponding to Expression (13), N_E (B) ≈0.0869 (40) is obtained. From now on, increase of SN ratio for white noise
Solving for the minutes for the matched filter yields: ρ = N_M (B) / N_E (B) = 0.2261 / 0.0869 = 2.60 (41) This is the case of N = 9, and if N → large, the SN ratio
The improvement amount ρ further increases. Therefore, as shown in FIG.
Compared to a normal matched filter, the detection noise is suppressed, and the value of ρ
Can improve the SN ratio only.

In the above description, the case where the original frame is expanded is shown with reference to FIG. 7. However, by reducing the original frame to T _j ′, the period of the element frequency f _j is reduced as shown in FIG. It can also be an integer multiple match. T ₁ → T ₁ ′
To the original element sine waveform S ₁ (t) [with period T ₀
7 (b) including the part of the broken line], S ′ ₁₁ (t) is obtained, and as shown in the first stage of FIG. 17 (b), the waveform of frequency f ₁ is included for 3 cycles. In this case, for the sine waves of the other element frequencies f ₀ and f ₂ , S ′ ₀₁ (t) and S ′ ₂₁ (t) can be easily created by using a part of the original waveform as shown. In this case, the frame period corresponding to the equation (22) is: T ′ ₁ = 1 / f _D1 = α ′ ₁ T ₀ (α ′ ₁ = 3.0 / 3.75) T ′ _a = 1 / f _D2 = α ′ ₂ T ₀ (α ′ ₂ = 4.0 / 4.25 ... (22) ′. C _ij ′ (t), C _jj ′ thus created
Similar results can be obtained by performing the same processing as described above using (t), S _ij ′ (t), and S _jj ′ (t). However,
7 (a) is equal to FIG. 7 (a), resulting in C _i0 ′ (t)
= C _i0 (t), S _i0 ′ (t) = S _i0 (t). Next, specific examples of the present invention will be described. FIG. 1 is a block diagram of a receiver high-sensitivity demodulation circuit according to an embodiment of the present invention. This circuit has a function of suppressing in-band noise that has passed through a receiver filter and a frequency interval narrower than a frame rate f _0. It has a function of identifying the element frequencies and phases of the plurality of frame signals. In this example, the number of element frequencies is N = 3, and the parameters shown in FIGS. 7 and 13 are assumed. The received signal in the wireless band is demodulated by the local carrier into a baseband signal, and the frame signal v (t) whose bandwidth is limited to B through an appropriate filter.
And added to this circuit.

First, v (t) is the encoder (1) (A / D).
The sampled value is represented by a digital quantity. Therefore, the following demodulation processing is performed by the DSP (digital signal processing) method. V of digital quantity
(T) is three frame period expansion circuits (2, 2 ',
2 ″), the frame signal v _j having three types of frame periods (T _j , j = 0, 1, 2) by the method of FIG.
Converted to (t). COV (T _j ) is a circuit for expanding an original frame signal having a time length of T ₀ to T _j by the method of FIG. Therefore, in COV (T ₀ ), it is actually unnecessary to perform any particular processing.

These v _j (t) are transmitted to three post-valued correlators COR _j (3, 3 ', 3 "). The element frequency waveforms C _ij and C shown in FIG. The sampled value of _ij (i = j) is stored in advance in the arithmetic coefficient memory (MEM) COR _j by using these waveform information and v _j (t).
Performs correlation processing to obtain calculation results U _j and V _j . For example, in COR ₀ , correlation calculation between V ₀ (t) and C ₀₀ and between V ₀ (t) and S ₀₀ is performed, and calculation results U ₀ and V _{0 are obtained.}
Get.

On the other hand, the cross-correlation coefficient shown in FIG. 13 is calculated in advance and stored in the arithmetic coefficient memory (MEM). Using these coefficients and (U _j , V _j ) the simultaneous equations shown in equation (31) are solved in the computing units (4) and (QS),
Get three unions of unknowns (x _j , y _j ). as a result,
If, for example, the C ₀₀ component is present in the received signal, its power is detected as x ₀ without being attenuated. On the other hand, if the band of v (t) is limited so as to satisfy the equation (32), noise of an arbitrary frequency passing through the band becomes a combined output of (x _j , y _j ). The frequency characteristic is as shown in FIG. Among noise detection powers assuming white noise, for example, y ₀ is reduced as described above as compared with the conventional matched filter. Therefore, if (x _j , y _j ) is sent to the decision circuit (see FIG. 2), a high SN is obtained. It can be judged by the ratio. Particularly, if the number N of element frequencies is increased, the SN ratio is further improved as described above.

The matched filter shown in FIG. 4 has been used for the receiving side demodulator of a transmission system using a conventional modulation method such as FSK, PSK, QAM, etc. Instead of this matched filter, the circuit of FIG. 1 is used. With, it is possible to demodulate and detect a signal with a high SN ratio. For example, when PSK is used, C ₀ (cosine waveform similar to S _{0 in} FIG. 7) and S ₀ are transmitted corresponding to the binary input D _S , and the receiving side detects x ₀ and y ₀ and outputs a binary value. Get D _R. Here, the values of x ₀ and y ₀ generated due to transmission line noise can be made significantly smaller than in the system using a matched filter.

Here, as shown in FIG. 10, the bandwidth required to send signals such as C ₀ and S ₀ is extremely narrow as compared with FIG. When using FSK, FSK and PS
When K is also used, the frequency interval between adjacent signals can be narrowed. Therefore, the frequency utilization efficiency can be improved.
FIG. 14 is an explanatory diagram of a multiplex transmission system according to another embodiment of the present invention. FIG. 14 (a), dividing the Satoshi transmission band to block the band B = 2f _D each plurality, allocates five information frequency _{f s (s = 0,1 ... 4} ) in each, BH ₂ per FIG. 3 is a frequency allocation diagram for realizing 5-channel (ch) PSK transmission. FIG. 14B, in which the group of f _s is represented as SFG, is a block diagram of the receiving side demodulation circuit of this system.

In the figure, the case where the entire band is divided into three and the input signal is separated on the demodulation side by using three counterband filters BPF _n (n = 0.1, −1) is shown. The band-separated input signals are subjected to the above-described element frequency analysis processing, and x _s and y _s are detected and output corresponding to the transmission waveforms C _S and S _S as shown in FIG. Get as. Here, in addition to SFG, f ₋ and f ₊ are added on both sides as element frequencies. This whole is called an element frequency group (EFG). f _-
And f ₊ play a role of absorbing noise near f ₀ and f ₄ and improving the reception SN ratio. The specific arrangement of each frequency may be determined so that the value based on the noise component generated in the analysis outputs x _s and y _s is minimized.

A system in which the entire band 6f ₀ is separated by only one BPF and, for example, 15 SFGs are transmitted therein can also be realized, but in this case, it is necessary to solve simultaneous equations of 30 elements, and the circuit by the DSP is required. It is a little difficult to realize the function.
However, since the band leakage function becomes simple, it can be used as a method for realizing wideband multi-channel transmission depending on the purpose and design conditions such as when the DSP processing time is sufficiently allowable. In the case of this method, the interference between the SFG signals (f
The advantage is that there is no interference from the _s component to the f _s ′ component. In the above description, 5 frequencies are used as SFG,
The case of performing binary transmission of 5 ch has been described, but C _s , S _s
It can also be used as a multilevel transmission method in which one of the 10 waveforms (s = 0, 1, ... 4) is selected and transmitted.

FIG. 15 is an explanatory diagram of an embodiment of the continuous frequency analysis system. FIG. 15A is an element frequency allocation diagram, and FIG. 15B is a configuration circuit block diagram. Here, from the viewpoint of avoiding the deterioration of the waveform of the input signal, a system in which a low-frequency wave breaker LPF that allows a component of 4f _D or less to pass therethrough is placed in front is taken as an example. However, in general, a wave breaker that passes only the frequency component of interest may be placed in front. Since there can be any frequency OF components of f <4f _{D in} the input frame signal, at least f _k to analyze them by DFT
= Kf _D (k = 0,1,2 ... 4 + h). (4+
h) Several groups (MEFG) are required in the main elements. Here, h is set to a value corresponding to the spread of the DFT analysis component when the input signal of f ≠ kf ₀ is analyzed as shown in FIG. Here, h = 3. (In theory, h = ∞ is generally required, but here, from the analytical theory of 4,1 the fixed auxiliary element frequency (FAEF), f ₃ = 6.5f
By adding _D , the value of h can be reduced to a finite value under the condition that the analysis error does not increase.

In this embodiment, in addition to MEFG and FAEF,
As a detailed analysis element frequency group (PEFG), f _j (j =
0, 1, 2) are defined as shown in the figure. The mutual frequency interval of f _j is expressed by the following equation. Δf = f ₀ −f ₁ = f ₂ −f ₀ (42) f _j represents most of the input frequency components included in the frequency range ΔF = 3Δf ranging from (f ₁ −Δf / 2) to (f ₂ + Δf). It plays a role of analyzing and displaying electric power.

Consider shifting the absolute value to the left or right while keeping the mutual relationship of the PEFG frequencies constant. f
₀ of the absolute value _{λ [= 0,1,2 ... (f D} / Δf) -1]
Is defined by the following equation. f ₀ (k, λ) = kf ₀ + λΔf (43) Then, the other frequencies of PEFG are: f ₁ (k, λ) = f ₀ (k, λ) −Δf (44) f ₂ (k, λ) = F ₀ (k, λ) + Δf (45). When (k, λ) is fixed, there are 11 element frequencies including DC in total. v (t) is this 1
Analysis with a cosine wave and a sine wave of one frequency, output x
Calculate ₁ (k, λ) and y _j (k, λ). Then (k,
Similar output is obtained as λ + 1). By repeating this, a set of (x _j , y _j ) can be obtained in steps of Δf. From now on f ₀
The peak amplitude components of the cosine wave and the sine wave of approximate frequency components per band of ± (Δf / 2) centered on (k, λ) are given by the following equations.

[0050]

(Equation 13) If C (k, λ) and S (k, λ) are obtained and plotted while changing λ and k, the power component per Δf can be obtained. Here, C 1 and S 2 mean a code in which the code ∧ shown in the above equation is added to the position directly above C and S, respectively.
Due to the limitation of usable codes, they are expressed as C and S , respectively.

[0051]

[Equation 14] FIG. 1B is a block diagram of a constituent circuit that specifically implements the above principle. In the figure, the received signal r (t) is leaked by the LPF and becomes the input signal v (t). The sampled value (digital amount) of v (t) is stored in the input side storage circuit I-ST. [R (t) sampling and A / D conversion are LPF or I-
Although it is performed in the first stage of ST, it is not shown in the figure. The analytical element generator E-Gen corresponds to the initial value of (k, λ), and the cosine waves of all element frequencies are sine waveforms C (t) and S.
(T) Further, the parameters α and β shown in FIG. 13 are sent to the demodulator DEM. The DEM analyzes the input signal using these parameters, obtains the output (x ₁ , y ₁ ) and sends it to the output side storage circuit O-ST. Upon completion of this analysis, a control command SH (Δf) for shifting each frequency of DEFG to the right (or left) by Δf is set to OS.
T sends to E-Gen. As a result, E-Gen is (k, λ
The analysis element corresponding to +1) is sent to the DEM, and the analysis of the next stage is started.

The plotter PLT is from O-ST to (k, λ).
(X _j , y _j ) corresponding to the above are received, and using these, the frequency phase characteristic of the substantially continuous input signal is obtained by the equation (48) and the output F (f) thereof is obtained. Here, if Δf << f _D , detailed frequency characteristics are obtained. Further, the number of frequencies used as PEFG may be one, but if the number is increased, the analysis accuracy is increased. The method for obtaining the approximate values C (k, λ) and S (k, λ) is a method other than the equations (46) and (47), for example, an average value calculation method by weighted addition and an output generated at each Δf shift. There is a method of using a differential value of (x _j , y _j ). By using the method of this embodiment, it is possible to analyze the system of equations (22 elements in the case of FIG. 15) without making it too large even for a wide band input. Compared with the conventional analysis method having a spread of f _D units, a dramatic improvement in analysis accuracy is expressed.

FIG. 16 is an explanatory view of a high precision filter according to the embodiment of the present invention. FIG. 16A shows a part of the output obtained by analyzing the input signal v (t) using the method shown in FIG. That is, depending on the value of λ, the line spectrum output C λ, S of Δf Hz
λ is given. If Δf << f _D , these values can approximate the frequency and phase included in the input with high accuracy. Therefore, the desired frequency band is now (k
f _D + λ ₁ Δf) to {(k + 1) f _D + λ ₂ Δf}, a plurality [f _D of C λ and S λ included in this band {f _D −λ ₁ −1 −λ ₂ ) Δf} / Δf−λ + 1 + λ ₂ ] can be used to modify this in-band component in the input signal.
For example, a band elimination filter that removes this in-band component can be realized with high frequency accuracy.

FIG. 16B is a block diagram of a constituent circuit that realizes this filter function.

The received signal r (t) is leaked to a v (t) by a wide-band reduction leaky wave breaker. (Display of sampling and A / D conversion is omitted.) V (t) is stored in I-ST. The frequency analyzer FA is the circuit described in FIG.
The outputs x _j (k, λ) and y _j (k, λ) are sent to a waveform generator WG, where a plurality of cosine and sine waveforms of the target band, C _ki (t) and S _ki (t). ), And the combined wave and v (t) are added. [In this case, since the target band component is decided to be removed, the target band component is actually subtracted. ] The addition result is the band rejection output v _F (t).

In the case of a general filter, the attenuation parameter α
Set _k γ and β _k γ, and output the WG as

[0057]

(Equation 15) Assuming that, the attenuation phase characteristics corresponding to α _k γ and β _k γ can be given to the components of the target band. The method of the present invention is characterized in that a filter having a high accuracy with respect to the frequency OF can be configured for a frame signal.

[0058]

The present invention is characterized in that the frequency analysis accuracy of a time waveform whose time is limited can be dramatically improved as compared with the conventional method, and the noise component contained in a signal can be suppressed effectively. Because it has, it can be applied to various fields to achieve excellent results.

[Brief description of drawings]

FIG. 1 is a block diagram of a receiving side high sensitivity demodulation circuit showing an embodiment of the present invention.

FIG. 2 is a block diagram of an FSK transmission system.

FIG. 3 is a diagram showing a time waveform when sending a binary series 1, 0, 1, 1 when n = 3.

FIG. 4 is a binary signal detection circuit.

FIG. 5 is a characteristic diagram.

6 (a) and 6 (b) are sine waveform diagrams in the case of f = 3.875f _D , and diagrams showing the spectrum absolute value of the DFT analysis output thereof.

7A and 7B are diagrams showing sinusoidal waveforms represented by Expressions 20 and 21, and diagrams showing changes occurring in the three iodine sinusoidal waveforms in FIG. 7A.

8A and 8B are diagrams showing analysis results using the values in the table shown in FIG. 13 and solutions of simultaneous equations.

9 (a) is a value (x _j , y _j ) when f is changed by a method of obtaining a detection output when a single frequency sine wave shown in Expression (8) is added as v (t). ), (B) shows the analysis error voltage.

10A is a diagram showing a result of _obtaining a frequency characteristic of P _j , and FIG. 10B is a diagram showing an analysis error power in this case.

11A is a diagram showing a value of electric power obtained in element frequency components of an analysis output, and FIG. 11B is a diagram showing an analysis error power thereof.

FIG. 12A is a diagram showing the value of electric power obtained in the element frequency components of the analysis output, and FIG. 12B is a diagram showing the analysis error power thereof.

FIG. 13 is a table showing cross-correlation symbols between an input waveform and an analysis waveform.

14 (a) and (b) are other embodiments of the present invention, FIG.
Explanatory drawing of a multiplex transmission system.

15A and 15B are explanatory diagrams of an embodiment of a continuous frequency analysis system, in which FIG. 15A is an element frequency allocation diagram, and FIG. 15B is a block diagram of a constituent circuit.

16 (a) and 16 (b) are explanatory views of a high precision filter according to an embodiment of the present invention.

17 (a) and (b) are principle diagrams of frame period extension.

FIG. 18 is a system diagram of frame enlargement processing.

[Explanation of symbols]

1 a demodulator when a modulation method such as FSK, PSK or QAM is used in the data transmission method, 2 an improvement in the SN ratio in the data transmission method, 3 an improvement in the frequency utilization efficiency, 4 an increase in the transmission capacity of the multilevel transmission method Improvement, 5 High-accuracy waveform frequency measuring instrument, 6 Filter with high frequency accuracy, 7 Analysis of reflected waveform such as ultrasonic diagnosis, 8
Waveform analysis of electromagnetic waves received by a patient in astronomical observation, 9 Analysis of detected waveforms in memory, 10 Waveform discriminator on receiving side in PCM transmission.

─────────────────────────────────────────────────── ─── Continuation of front page (51) Int.Cl. ⁶ Identification number Office reference number FI Technical display location G01S 15/89 H04L 27/00 27/22 // G01S 5/02 Z H04L 27/00 A 27 / 22 Z (72) Inventor Naoki Suehiro 3-6-305-103 Takezono, Tsukuba-shi, Ibaraki (72) Inventor Toshikatsu Naito 2-1-1 Kotani, Samukawa-cho, Takaza-gun, Kanagawa Toyo Communication Equipment Co., Ltd.

Claims (7)

[Claims] 1. An arbitrary frequency interval smaller than f _d (= 1 / T ₀ ) in a system for analyzing frequency / phase components included in an input time waveform time-limited to a frame time length T ₀ seconds. component frequency f _j under conditions which permit to have (j = 0,1,2 ... N-1 ) to provided any number of N, the orthogonal waveform components C _j a pair with the component frequency f _j
A frequency analysis and detection method for a time-limited waveform, characterized in that the input time waveform is analyzed and expressed by a combination of S and S _j . 2. The input frame 1 according to claim 1, under the condition that the continuity of the waveform of an arbitrary phase having one component f _j in the element frequency included in the input time waveform is maintained. By duplicating or deleting parts,
T _j is made a _{T j = k (1 / f} j) changes to deform the frame using the integer k the input frame length T ₀ to be an integral multiple of the period of f _j, included in the input time waveform A frequency analysis detection method for a time-limited waveform, characterized in that a cosine wave component and a sine wave component of a frequency f _j to be extracted are extracted by performing a correlation analysis with T _j as an integral frame length. 3. The cosine waveform C _i and the sine waveform S _i of the element frequency f _i (i = 0, 1, 2, ... N-1) included in the input frame according to claim 1, and other elements. Frequency f
_A modified cosine waveform C _ij and a modified sine waveform S _ij are created by creating an enlarged or reduced frame having the frame time T _j of claim 2 corresponding to _j , and the input cosine waveform component C _i and the input sine waveform component S _{i are} generated. Correlation _coefficients α _ij and α _ij with C _ij are calculated with T _j as the integration frame length for _i , and
Correlation _coefficient β _ij with S _ij for one input waveform C _i , S _i ,
β _ij is obtained in advance, and C is applied to this modified frame input waveform.
Analysis output U is obtained by _performing correlation analysis with _ij and S _ij.
j, obtains the V _j, 2N source under formula holds when an unknown amplitude y _j of amplitude x _j and sinusoidal components of the cosine wave component in f _j components contained in these values and the input time waveform Simultaneous linear equations [Equation 1] By obtaining a set of (x _i , y _i ) that satisfies the following, the N frequencies and phases included in the input time waveform are calculated as (x
_i , y _i ) A frequency analysis and detection method for time-limited waveforms, which is capable of being analyzed and detected by a set of N sets. 4. The element frequency f _{j according to} claim 1, wherein one or more of the element frequencies are used as a detailed analysis element frequency, the rest is used as a main analysis element frequency, and all of the former frequencies are shifted in frequency intervals Δf. While each time, the set of analysis results (x _i , y _i ) is obtained by the method of claim 2 and claim 3,
A frequency analysis detection method for a time-limited waveform characterized in that a detailed frequency characteristic of an input frame signal is obtained by obtaining a cosine waveform, a sine waveform, and a power spectrum density of a line spectrum in steps of Δf from this set. . 5. The method according to claim 4, wherein one or more of the cosine waveform and the sine waveform of the line spectrum obtained in steps of Δf are multiplied by an amplitude value multiplied by (1-γ) when a desired attenuation coefficient is γ. After that, the frequency analysis and detection method of the time-limited waveform is characterized in that desired filter characteristics are realized with accuracy close to Δf step by subtracting from the input waveform. 6. Any of 2N kinds of signals consisting of a cosine waveform and a sine waveform of the element frequency f _j (j = 0, 1, 2, ... N-1) according to claim 1, 2, 3 or 4. A frequency-analysis detection method for a time-limited waveform, characterized in that one transmission frame signal is associated with each other, and the reception side detects these signals without mutual interference to perform multi-value transmission of maximum 2N values. 7. The binary transmission of maximum N channels according to claim 6, wherein 2N types are set to 1 ×× N sets, and one type of signal is associated with a transmission frame signal for each set. A frequency analysis and detection method for time-limited waveforms characterized by being performed.