JPH084214B2 - Transversal filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Outline] In a binary transversal filter,
It is characterized in that the tap coefficient obtained by the inverse Fourier transform of the expanded integration range is used to reduce the error between the frequency characteristic of the binary transversal filter having a small number of tap stages and the desired frequency characteristic.

[Industrial applications]

The present invention relates to an equalizer in a digital data transmission system, and more particularly to a transversal filter.

The importance of digital data transmission is increasing year by year due to the expansion of use of computers, and a high-speed and error-free transmission system is desired. When digital data is transmitted using a transmission line, it is distorted according to the transfer characteristics of the transmission line. For example, when the data transmission rate is high or the transmission line length is large, the attenuation in the high frequency region cannot be ignored, the waveform becomes smooth gradually, and one waveform affects even its adjacent waveform. Such waveform distortion is also caused by the cutoff characteristic in the low frequency range. These are collectively called waveform distortion. Particularly in data transmission, the influence on adjacent waveforms, that is, intersymbol interference becomes a problem.

In order to reduce such waveform distortion and intersymbol interference, an equalizer is inserted in the transmission line. Although various types of equalizers have been proposed, a transversal filter is often used as an equalizer that can be easily digitized.

[Conventional technology]

FIG. 5 is a diagram showing an example of a conventional transversal filter. In FIG. 5, reference numeral 51 is a delay line with a tap, which is composed of a shift register when digitized. 52 is a multiplier for multiplying the tap coefficient. The multiplier is used to multiply the input value from each tap stage by its tap coefficient. An adder 53 adds the outputs of the tap stages multiplied by the tap coefficient. When digitized, the tap coefficient, the multiplier and the adder can be composed of a ROM.

In the transversal filter thus configured, the input signal X (t) applied to the input terminal 55 is
It is added to a tapped delay line consisting of a shift register, and is obtained as each tap, in the illustrated example, as each tap output of 13 stages. The output of each tap is RO that stores the tap coefficient.
A multiplier 52 including M multiplies each tap coefficient. Then, each tap output multiplied by the tap coefficient is added by the adder 53.
Are added to produce an output Y (t). In practice, this output is converted back to an analog value through the low pass filter and sent to the next stage.

The tap coefficients C _{1 to} C ₁₃ are set so that the intersymbol interference is as small as possible. For example, when an NRZ signal X (f) having a characteristic shown in FIG. 3 is used as an input and an output Y (f) having a root roll-off characteristic shown in FIG. 4 is obtained, H (f) = Y As (f) / X (f), Where n is the number of tap stages, f _{N is the} Nyquist frequency T is the sampling period (generally T = 1 / 2f _N · N, N> 2) f _{P is the} stop frequency, Here, f _N ; Nyquist frequency f _P ; (1-α) f _N α; roll-off rate tap coefficient Cn has been obtained.

The equalizer using this transversal filter is
It is used for the modulator on the transmitter side and the demodulator on the receiver side of the data transmitter / receiver on the transmission path. The roll-off characteristic needs to be the characteristic at the output of the equalizer on the receiving side. The reason for inserting an equalizer on the transmission side is that if the NRZ signal is output from the transmitter as it is, unwanted waves will collide with other signals, so it is necessary to limit the band. Also, the reason for inserting an equalizer at the receiving side is to remove noise. At that time, what kind of band limitation should be performed is to install equal equalizers on both the transmitting side and the receiving side, and therefore the root roll-off characteristic is adopted.

The reason for setting the tap coefficient Cn in the integration range shown in the equation (1) is that the frequency range in which the output Y (f) exists is
Since it was designed to exist only in (2f _N -f _P ) to (2f _N -f _P ), the calculation range is this range.

If a binary transversal filter is constructed using the tap coefficient obtained by this method,
As long as the number of tap stages is finite, the ideal frequency characteristic as shown in FIG. 2 (a) cannot be obtained. For example, in a binary transversal filter with about 13 tap stages, as shown in Fig. 2 (b), it rises and falls sharply at a position close to 2f _N -f _P, and the frequency range beyond that. There are some peaks at.

When the NRZ signal shown in FIG. 6A is input, the output Y (t) shown in FIG. 6B is obtained.

[Problems to be solved by the invention]

When the transversal filter is constructed according to the conventional design method as described above, if the number of tap stages is reduced in order to reduce the circuit scale and the number of elements in order to reduce the size of the device, for example, the number of tap stages is about 13. In that case, there is a problem that desired characteristics as a filter cannot be obtained.

The present invention has been made in view of the above points, and an object of the present invention is to provide a binary transversal filter in which the number of tap stages can be at least desired.

[Means for solving problems]

In order to solve the above problems, in the present invention, a transversal filter is provided for each of a delay line that sequentially delays an input signal and n tap outputs of the delay line. H (f) = Y (f) / X (f) X (f); NRZ input signal, Y (f); output signal However, Y (f) has frequency f of | f | 2f _N -f in function of the root roll-off characteristics in the range of _{P, 2f n -f P | f} | 2f n of the function of root roll-off characteristics in a range | 2f _n -f _P | continuous function folded in n; taps stages , F _N ; Nyquist frequency T; sampling period (generally f _P : Stopping frequency Δf; Optimal tap coefficient deriving variable frequency (f _P Δf> 0) is composed of a multiplier that multiplies n coefficients Cn and an adder that adds the outputs of the multipliers.

[Action]

As a result, the frequency characteristic of the filter having at least the number of tap stages close to the ideal characteristic can be obtained, which facilitates downsizing of the device.

〔Example〕

Examples of the present invention will be described below. Figure 1 (a) is an example of a binary transversal filter, and
Is a shift register forming a delay line, 12 is a coefficient unit composed of ROM, and 13 is an adder. The input signal X (t) is applied to the terminal 15, and the output signal Y is output from the output terminal 14 of the adder 13.
(T) is obtained.

In the present invention, the tap coefficient is calculated from the following equation.

Here, H (f) = Y (f) / X (f).

Next, the transfer coefficient H (f) of the transversal filter
The method of obtaining is described with reference to FIG. Input signal is NRZ signal and cycle And Where f _N is the Nyquist frequency. The input signal X (f) is shown as follows.

When this input signal X (f) is processed by the sampling processor 21 by, for example, double sampling, X (f) becomes X ′.
(F).

Also, the aperture effect A (f) obtained by converting the output of the transversal filter 22 into an analog signal by the D / A converter 23 is output with a double sampling width,
It becomes as follows.

The smoothing filter 24 removes the aliasing component outside the band.

If the output signal Y (f) (ideal characteristic) is to output the spectrum of the root roll-off characteristic, it can be expressed as follows. However, the roll-off rate is α
Then f _P = (1−α) f _N.

That is, the output Y (f) becomes 1 in the range of | f | f _P and becomes the above value displayed as a square root in the range of f _P | f | 2f _N −f _P , and 2f _N −f _P | f | It becomes 0 in the range.

Under these assumptions, the transversal filter 22
The frequency characteristic H (f) of is obtained as follows.

Y (f) = X ′ (f) × H (f) × A (f) When H (f) is an ideal characteristic, integration of the region about Δf is meaningless in the region where f is larger than | 2f _N −f _P | In order to obtain the characteristics, the transversal filter must have an infinite number of taps, and it is impossible to downsize the filter.

The present invention considers that the functional system H (f) when the number of taps is finite is not zero in a region somewhat larger than | 2f _N -f _P |, and minimizes its cumulative squared error. It was done. For example, when an input signal characteristic as shown in FIG. 2D is input, for example, when the roll-off rate is 0.5, the output signal characteristic as shown in FIG. (F) is obtained to minimize the cumulative squared error from the theoretical value. Figure 2 (e) here
The output signal Y (f) shown in can be expressed as follows.

As is clear from the above formula (2), in the present invention, Y (f) is a function of the root roll-off characteristic in the frequency f range of | f | 2f _N -f _P , and 2f _N -f _P | In the f | 2f _N range, a root roll-off characteristic function is folded back with | 2f _N −f _P | to extend the integration range by Δf.

Ideally, Y (f) is defined only in a range smaller than | 2f _N -f _P |, but in the present invention, as described above, | 2f
_In order to consider a functional system in which Y (f) is not zero even in a range larger than _N −f _P |, the above equation (3) is defined to be extended to 2f _N. The reason for expanding to the front of 2f _N is that there is a folding error at 2f _N in the case of double sampling, so there is no point in expanding it further, and when expanding to 2f _N , the error from the ideal characteristic is large. .

For folding back, 2f for double sample processing
Think even before _N. Further, when processing 4 times as many samples, it is sufficient to consider up to 4f _N. However, even if you think more than that, for example, if you think about 2f _N or more when processing twice the sample,
Since spurious outside the band becomes large, it is meaningless, and it is desirable to gradually increase Δf as 2f _N −f _P + Δf as in the present invention.

At the same time, the root roll-off rate is slightly changed from the desired characteristic value. For example, when a tap number 13, the integration range expanded from 1.5f _N to 1.78F _N, the roll-off factor of 0.5
When set to 0.6, the cumulative squared error is about 10 to 0.19 from the conventional value.
I was able to reduce to. The frequency characteristic of the filter when the sampling period at this time is 1 / 4f _N is shown in FIG. In this case, the downward curve from approximately f _N point is cos
The function is faithfully reproduced, and the height of the waveform generated before the 2f _N -f _P point can be reduced.

Generally, the ratio of Δf and f _{N at} which the cumulative square error is minimized varies depending on various conditions such as H (f) and f _P, but can be obtained by repeating experiments or calculations. The cumulative squared error is the cumulative square of the difference between the frequency characteristic with a finite number of tap stages and the desired frequency.

In the conventional case, when the tap coefficient is obtained, the output Y (f)
The frequency range in which is present is-(2f _N -f _P )-(2f _N-
Since it was designed to exist only in f _P ), the calculation range was limited to this range. On the other hand, in the present invention, by expanding the integration range as described above, what is conventionally discontinuous at the point of | 2f _N -f _P | is treated as the presence of further frequency components. Therefore, the error can be reduced without increasing the number of stages of the transversal filter.

Further, the value of Δf may be determined by appropriately determining the frequency width.

〔The invention's effect〕

As described above, according to the present invention, the cumulative square error can be reduced without increasing the number of stages of the transversal filter, and therefore, the transversal filter can be downsized and the performance can be improved. It will be possible.

[Brief description of drawings]

FIG. 1 (a) is an example of a binary transversal filter, FIG. 1 (b) is the frequency characteristic of the filter when the tap coefficient is obtained by expanding the integration range according to the present invention, and FIG. 2 is the frequency of the filter. Characteristics (a) are ideal characteristic diagrams, (b) characteristic diagrams of filters having tap coefficients obtained by the conventional method, (c) H (f) explanatory diagram, (d) input signal characteristic, (E) shows output signal characteristics, Fig. 3 shows input signal diagram, Fig. 4 shows output signal diagram, and Fig. 5 shows transversal.
FIG. 6 is a diagram showing a filter, and FIG. 6 is an explanatory diagram of input / output signals of the transversal filter. 51 ... Delay line with tap (shift register), 52 ... Multiplier, 53 ... Adder, 54 ... Output signal (Y (t)), 55 ...
... Input signal (X (t).

Claims (1)

[Claims] 1. A delay line (11) for sequentially delaying an input signal.
And for each of the n tap outputs of the delay line, H (f) = Y (f) / X (f) X (f); NRZ input signal, Y (f); output signal However, Y (f) has frequency f of | f | 2f _N -f It is a function of the root roll-off characteristic in the range of _P , and is a continuous function obtained by folding back the function of the root roll-off characteristic in the range of 2f _N ‐f _P | f | 2f _N by ｜ 2f _N ‐f _P ｜ the number of tap steps. , F _N ; Nyquist frequency T; sampling period (generally f _P : Stopping frequency Δf; Multiplier (12) that multiplies the n coefficients Cn obtained at the variable frequency for deriving the optimum tap coefficient (f _P Δf> 0), and addition that adds the output of the multiplier (12) A transversal filter comprising a container (13).