JPH0444425A - D/a converter - Google Patents

Abstract

PURPOSE:To devise the way of interpolation of the D/A converter such that an interpolation function passes through sampling points without fail and smooth interpolation is attained by applying direct interpolation to adjacent sampling points with the interpolation function in response to a data change, allowing the interpolation function to take over a gradient of the interpolation function caused by one preceding data group and using a new data group so as to decide the interpolation function for a new block. CONSTITUTION:An interpolation function generating section 13 decides an interpolation function interpolating a data between a noted digital data D(0) and a digital data D(1) after one sampling time by using a function decision section 13a while taking the noted digital data D(0), digital data before and after the noted digital data and its gradient GO into account, is provided with coefficient arithmetic sections 13b-l-13b-5 deciding each degree of coefficient for each decided function and a function generating section 13c generates the said decided interpolation function by using the calculated coefficient. As a result, the interpolation function between data is revised in response to a data change and a reproduction field corresponding to the data change is created and a data between digital data is interpolated smoothly without causing spurious oscillation.

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial Application Field> The present invention relates to a DA converter, and more particularly to a DA converter that generates an analog signal that smoothly interpolates between discrete digital data.

<Prior art> The conversion theory of a DA converter using a conventional digital converter is to replace each discrete digital data with a sampling time ΔT interval with a predetermined function, and then add the function values of each digital data on the time axis. It is used for interpolation. In addition, the function according to the digital value n is the unit data (
= 1) (referred to as a unit interpolation function) is determined and obtained as the product of the unit interpolation function and n. Furthermore, in practice, data values are compressed with full scale (FS) set to 1, and then function values on the time axis are added together to interpolate between each digital data.

Figures 11 to 13 are examples of unit interpolation functions for unit data. Figure 11 is an example where the interpolation function is expressed as a quadratic function, Figure 12 is an example where the interpolation function is expressed as a cubic function, and Figure 12 is an example where the interpolation function is expressed as a cubic function. Figure 13 shows the interpolation function as 5in(π・fs-t)/π・fs
This is an example expressed as -t. Incidentally, the third-order interval number F in FIG. 12 is expressed by the following formula.

Figure 14 shows digital data D(1), D(0), D(~1
), D(-2) functions IF(1) , IF(0) , I
It is a relationship diagram of F(-1), IF(-2), and an analog signal AS obtained by adding each function value on the time axis.

<Invention tries to solve! Problem I> Since the sum of quadratic functions is a quadratic function, the sum of three time numbers is a cubic function, and the sum of sine waves is a sine wave, the interpolated output (analog signal) produced by the conventional method is.

It inherits the unique properties of the interpolation function used and creates a single, unique playback space. However, this modulates data recorded in various spaces into a single unique space. This means that the original sound field cannot be reproduced.

Furthermore, when digital data obtained by sampling a 20 KHz sine wave at 44.1 KHz is converted into an analog signal using the conventional method (using the unit interpolation function as the cubic function shown in Fig. 12), 0 in Fig. 15 is obtained. As shown by mark C, an unnatural waveform is generated when viewed from the data group. This occurs because all digital data is interpolated using only a cubic function, and the unique properties of the interpolation function come to light.

Furthermore, if a group of digital data whose values change linearly is converted into an analog signal using the conventional method (the unit interpolation function is a cubic function as shown in Figure 12), the points connected by straight lines are sampling points as shown in Figure 16. It undulates with a cubic function every time Ts, making it impossible to obtain an accurate analog signal.

Incidentally, these problems in FIGS. 15 and 16 also occur when the unit interpolation function is the quadratic function in FIG. 11.

On the other hand, if the unit interpolation function is the sinusoidal waveform shown in FIG. 13, the original analog signal can be accurately reproduced if the data changes in a continuous sinusoidal manner.

However, when data changes impulsively, unnecessary vibrations occur. For this reason, for example, a digital data group in which the data value changes linearly in the middle is processed using the conventional method (the unit complement l!lrM number is a sine wave as shown in Fig. 13).
When converted into an analog signal, as shown in Figure 17,
The parts connected by a straight line undulate with a sine wave every sampling time Ts, making it impossible to obtain an accurate analog signal.

From the above, an object of the present invention is to provide a DA converter that can smoothly interpolate between digital data and does not generate unnecessary vibrations.

Another object of the present invention is to provide a DA converter that can change an interpolation function according to changes in digital data, thereby creating a playback space that corresponds to changes in data.

Means for Solving the Problems The present invention solves the above problems by providing a digital data output section that outputs the digital data of interest and some digital data before and after it, and a digital data output section that outputs the digital data of interest and some digital data before and after the data of interest and the digital data of one sampling time before. A calculation unit that calculates the slope of an interpolation function that interpolates between data, and an interpolation function that interpolates between the first data and the digital data after one sampling time by considering the data of interest, the digital data before and after it, and the slope. This is achieved by an interpolation function determining section.

Function> Calculates the slope at the position of the data of interest of an interpolation function that interpolates between the digital data of interest and the digital data of one sampling time before, and takes into consideration the slope, the data of interest, and the digital data before and after it. , an interpolation function for interpolating between the data of interest and digital data after one sampling time is determined, and the interpolation functions between each digital data are connected to generate an analog signal. As a result, it is possible to change the interpolation function between data according to changes in data, and create a playback space that corresponds to changes in data.In addition, it is possible to smoothly move between each digital data without causing unnecessary vibrations. Can be interpolated.

<Embodiment> The complete structure of the DA converter of the present invention FIG. 1 is a block diagram of the DA converter according to the present invention. In the figure, 11 indicates discrete data D(N+1), D(N),...D(0)...D(1-) at each sampling time Ts.
M), a digital data output section that generates D(-M), 1
2 is a slope calculation unit that calculates the slope GO at the data position of interest of an interpolation function that interpolates between the digital data D(0) of interest and the digital data D(−1) of one sampling time before; 13 is the gradient calculation unit of interest; Digital data 0 (0)
and an interpolation function FOI that interpolates between digital data D(0) and digital data D(1) after one sampling time, taking into account the digital data before and after that and the slope GO.
This is an interpolation function generation unit that determines (t).

The digital data output unit 11 includes a large number of delay circuits Z (
N+1), Z (N), ・・Z (0) −−Z (
1-M).

Z (-M), which are connected in series. Each delay circuit consists of a latch circuit that uses LCKI as a latch clock for each sampling when the input data is parallel data, and a shift register that uses WBICK as a pit clock for sending data when it is serial data. be done. Delay circuit Z (N+1
) is sequentially inputted with digital data every sampling time Ts from a digital data generating section (not shown), and the data stored in each delay circuit is shifted to the right every l sampling times. Therefore, if the digital data of interest is D(0), some digital data generated before the digital data D(-1)=D(-
M) and some digital data D(1)=D(N+1) generated after digital data D(0) are output from each delay circuit.

The interpolation function generator 13 generates the digital data D of interest.
(0), the digital data before and after it, and the slope GO, and determines an interpolation numerical value for interpolating between digital data 0 (0) and digital data D (1) after one sampling time; , coefficient calculation units 13b-1 to 13 that are provided for each function to be determined and determine coefficients of each order.
b-5, and a function generating section 13c that generates the determined interpolation function using the calculated coefficients.

Hereinafter, the function determining unit 13a and the coefficient calculating unit 13b-i (i
=1.2. ), function generation section 13c, slope calculation section 12
The configuration of is explained below.

(a) Function determination unit (a-1) Function determination method Using the digital data D(N+1)=D(-1'l), the current digital data D(0) of interest and the digital data after one sampling time are An interpolation function FOI(t) for interpolating between data D(1) is determined according to the following selection criteria 1) to 12).

ID1=DO=D-1 (see Figure 2 (a)), F
OI(t)=D(0) (0≦t×1)...(1)2
Di ≠D O=D −1=D −2D 4 =
D (3) = D 2 Kusougi (see Figure 2 (b)) F 01 (t) is a cubic polynomial, and 1 = 0.1 = 1
The slope at is O.

F 01 (t) = 2(D(0)-D(1))t'
+3(D(1)-D(0))t”+o(o) (0≦
tku1)...(2)3) D O#D1=D3
=D2=D-1=D-2 (see Figure 2 (C)) FOI(t) is a third-order polynomial, and the slope at 1=0.1=1 is O.

F 01(t) =2(D(0)-D(1))t”+3
(D(1)-D(0))t2÷D(0) (0≦t〈
1)...(2)4) D 3 = D 2 = D I≠D
O=D-1=D-2 (see Fig. 2(d)) FOI(t) is a third-order polynomial, and the slope at t=o and t=1 is O.

F 01 (t) = 2(D(0)-D(1))t”
+3(D(1)-D(0))t”÷D(0) (0≦
tku1)...(2)5) D2-DI=D
1-D OD O=D -1=D -2 Summer survey (2nd
! ii! (See I(e)) Let F 01 (t) be a first-order polynomial.

pol(t)=(o(t)-D(0))t+o(0)
(0≦t×1)...(3) 6) D3=02=DI [+1-DO=GO AC Figure 2 (f))], however, GO is the data one sampling time before the current time. Function F- that interpolates between current data
10(t) at the data position of interest.

Note that before l sampling time, F-10(t) is FO
I(1), therefore the slope GO is t of F-10(t)
= 1.

FOI(t) is a first-order polynomial, and FOI(t) = (D(1)-D(0))t+D(0)
(0≦tku1)・(3)・・(4) D 3 =02 =01 (see Figure 2 (g))F
OI(t) is a third-order polynomial, and the slope at t=1 is O.

F 01(t) = K3・t"ten to 2・t"+GO・t
+D(0)(0≦t<1) However, K3=2(D(0)−
D(1))+GOK2=3(D(1)-D(0))-2
GO8) GO is set and D(1=+FS (full scale) mail (see Fig. 2 (h)) FOI(t) is a third-order polynomial, and the slope at t=1 is 0.

FOI(t) = 3・t”+ 2・t” +GO・t+
D (0) (0≦tku1)...(4) However, K3=2(D(0)-D(1))+GOK2=3
(El(1)-D(0))-2GO9) DO, ±F
Let AGO=O in the case of S full scale.

10) Go is activated, ON = fFSteD N-
1-D IL operator fork l...Truncation (see Figure 2 (i)) FO
I(t) is an (N+2) degree polynomial, and the slope at t=N is 0. Finding FOI(t) in the case of N:2 is F
01(t) = to 4-t'+ to 3・t3+ to 2-t2+G
o-t+D(0) (0≦t×1)...(5) However,
K4=(-2-DC2)+4-D(1)-2-D(0)
-Go)/4)[3, (7-D(2)-16-D(1)
+9-D(0)+5-Go)/4 to 2=(-5-D(2
)+16-D(1)-11-D(0)-8・Go)/4
becomes. Also, the function F12 after l sampling time Ts
(t), in other words, the function po1(t) after one sampling time has elapsed (see Figure 2 (j)) is determined by the condition 8), and F 01 (t) = K3・t3+ 2− t"+GO
-t+D(0) (o≦tku1)...(4) However, K3=2(D(0)-D(1))4GOK2=3
(D(1)-D(0))-2GO.

In addition, in the case of Ni3, FOI(t) becomes a 5th order polynomial, and the following formula Fol(t)=5・t'+4・t'+3・t1◆
2・t3+GO・t+D(0) (0≦t<1)
...(6), however.

K5=(-13・D(3)+27・D(2)−27・D
(1)+13-D(0)+6-Go)/108 to 4=(
2g・D(3)−63・D(2)+72・D(1)=3
7・D(0)−18・GO)/36 to 3=(−161・
D(3)+405・D(2)−567・D(1)+32
3・D(0)+174・Go)/108 to 2=(10・
D(3)-27・D(2)+54・D(1)-37・D
(0)-26・Go)/12F 01 (t) is (Ni
1) It is a degree polynomial, and in the case of Ni3, F 01 (t)
= to 4・t'+ to 3-t3+ to 2-t" +GO-t+
D (0) (0≦tku1) ... (7) However, K4=(2-D(3)-9-D(2)+18-D(1)
-11-D(0)-6-GO)/36 to 3=(-D(3
)+6-D(2)-15・D(1)+1O-D(0)+
6-Go) 76 to 2=(4-D(3)-27-D(2)
+108・D(1)-85・D(0)-66・Go)/
In the case of the function FOI(t) above 3612), the absolute value of (F 01(t))wax may exceed the full scale and overflow may occur depending on the large sword data group.

In order to prevent such overflow, the tachi data,
Or safety factor A≦FS/(
F 01 (t)) Multiply by a+ax.

(a-'2) Structure of Function Determining Unit FIG. 3 is a block diagram of the function determining unit 13a, where SBC is a subtracter, and LG is a high level ("
1”), otherwise low level (“0”)
) logic circuit that outputs a signal, AG is an AND gate, O
This is RG or gate. In the figure, where the force a is at a high level, satisfies the condition 1), and (1)
If the interpolation function (F01(t)=D(0)) shown in the formula is selected, the first-order interpolation function shown in the formula (3), which is at a high level, satisfies the conditions 5) or 6). Function Fo1(t)=(D
Select (1) - D (0)) t + D (0), when the force C is at a high level, are: 2) , 3) , 4) ,
7), 8), and select the cubic interpolation function shown in equation (2).When the force d is at a high level, the condition of 10) (however, N=2
) and select the fourth-order interpolation function shown in equation (5). When the force e is at a high level, the condition of 10) (however, N: 3) is satisfied.
) is satisfied and the 5th order interpolation function shown in equation (6) is selected.If the output abcde is all low level, the condition 11) is satisfied and the 4th order function shown in equation 7) is selected.

(b) Coefficient calculation unit FIGS. 4 to 8 are block diagrams of the coefficient calculation unit that determines the coefficients for each order of the function determined by the function determination unit.

(b-1) Coefficient calculation unit for linear function (Equation (3)) The coefficient calculation unit 13b-1 for linear function is ±1 as shown in FIG.
The multiplier MLP and the output of each multiplier are added to obtain the first-order coefficient K1.
Adder AD that outputs 1 (=(D(1)-D(0)))
D, and a gate circuit GTC that outputs the calculated linear coefficient Kll when a is at a low level and b is at a high level.

(b-2) Coefficient calculation section for cubic function (Equation (2) or (4)) The coefficient calculation section 13b-2 for cubic function is as shown in FIG. ±2. Five multipliers MLP multiply the input signal by ±3, and the multiplier outputs are added to give a cubic coefficient of 32 (=
Adder A outputs 2(D(0)-D(1))+GO)
DDI and the multiplier output are added to give a quadratic coefficient of 22 (=3
Adder A that outputs (D(1)-D(0))-2GO)
32. to the third and second order coefficients calculated when DD2, a and b are at low level and C is at high level. It is composed of gate circuits GTCI and GTC2 which output 22 signals.

(b-3) Coefficient calculation unit for the quartic function (Equation (5)) The coefficient calculation unit 13b-3 for the quartic function (Equation (5)) multiplies the input signal by a predetermined value, as shown in FIG. 12 multipliers M
Adding LP and the multiplier output gives the fourth-order coefficient 43=(-2・D(2)+4・D(1)−2・D(
0)-Go)/4 and the output of the 1 multiplier are added to give the cubic coefficient 33=(7・D(2)−16・D(1)+9・D(0
)+5・GO)/4 and adds the multiplier output to the quadratic coefficient 23=(−5・D(2)+16・D(1)−11−D
an adder ADD3 that outputs (0)-8・GO)/4;
4th order calculated when a, b, c are low level and d is high level.

43. for cubic and quadratic coefficients. 33. It is composed of gate circuits GTCI, GTC2, and GTC3 that output 23 signals respectively.

(b-4) Coefficient calculation unit for the quartic function (formula (7)) The coefficient calculation unit 13b-4 for the quartic function (formula (7)) multiplies the input signal by a predetermined value, as shown in FIG. 15 multipliers M
Adding LP and 1 multiplier output gives the 4th order coefficient 44=(2・D(3)−9・D(2)418・D(1
)-11・D(0)-6・Go)/36 is added to the adder ADDl that outputs 1 multiplier output, and the third-order coefficient is 34=(-D(3)+6・D(2)-15・D(1)
Adder A that outputs +10・D(0)+6・GO)/6
Adding DD2 and the multiplier output gives the quadratic coefficient 24=(4・D(3)−27・D(2)+108・D
When the adder ADD3 that outputs (1)-85・D(0)-66・Go)/36 and Bet)ycod9e are all at low level, the calculated 4th, 3rd, and 2nd order The coefficient is 44. 34. It is composed of gate circuits GTCL, GTC2, and GTC3 that output 24 signals respectively.

(b-5) Coefficient calculation unit for the 5th order function (Equation (6)) The coefficient calculation unit 13b-5 for the 5th order function (Equation (6)) multiplies the input signal by a predetermined value, as shown in FIG. 20 multipliers M
Adding LP and the multiplier output gives the fifth-order coefficient 55=(-13・D(3)+27・D(2)−27・
The adder ADD1 outputs D(1)+13・D(0)÷6・Go)/108, and the multiplier output is added to give the fourth-order coefficient 45=(28・D(3)−63・D( 2) +72・D
Adder ADD2 outputs (1)-37・D(0)-18・Go)/36 and the multiplier output is added to give the cubic coefficient 35=(-161・D(3)+405・D( 2)-5
67・D(1)+323・D(0)+174・Go)/
The adder ADD3 outputs 108 and the multiplier output is added to give a quadratic coefficient of 25=(10・D(3)−27・D(2)+54・D
(1) When the adder ADD4 which outputs -37.D(0)-26.GO)/12 and -at by at d are at low level and e is at high level, the calculated 5th order, 4th order, 3
It is composed of gate circuits GTCI, GTC2, GTC3, and GTC4 that output 55 to 25 as the next and second-order coefficients, respectively.

(e) Function generation section FIG. 9 is a block diagram of the function generation section 13c and the slope calculation section 12. In the function generating section 13c, 21 to 25 select and output the first, second, third, fourth, and fifth coefficients of the interpolation function determined by the function determining section 13a, respectively, based on the logical value of a'=e. Coefficient selection units 30 to 35 select coefficients Kl of each order by latch clock LCK2. 3. to 4
．． A latch circuit that latches 5 for one sampling time, 4
0 to 45 are each composed of 5 multipliers, and t (1,
t 1 t X t Jt't' constant Ko,
A time multiplier that multiplies the 1st, 2nd, 3rd, 4th, and 5th coefficients by 1 to 5, and 51 is an adder that adds the outputs of each multiplier. 61 is an addition unit that uses latch clock LCK3. Vessel 5
This is a latch circuit that latches the output of 1 and stabilizes the data. Note that the latch clock LCK2 is synchronized with the data-delayed latch clock LCKI (see FIG. 1), and is generated with a delay of Td relative to the latch clock LCKI. Now, assume that the time required for function determination, coefficient calculation, and selection is Tp.

Td must satisfy Tp<Td<Ts.

Each time multiplier 40 to 45 divides the time t (0<t≦1 or 0≦t (period of 1)) into S steps to multiply the coefficient KO- by 5, and divides the time t (0<t≦1 or 0≦t (period of 1) into S steps,・→(S-1)/
S→S/S or 0/S→1/S→・→・→(S-2)
/S→(S-1)/S and multiplies it by the corresponding coefficient, the adder 51 adds the signals output from each multiplier, and the latch circuit 61 once latches the adder output with LCK3. and output it. Note that LCK3 is a latch pulse that is generated every Ts/S and is generated with a delay of Tf from LCK2. 5Tm<Tf (Tm is the calculation time of the multiplier) Therefore, the output signal of the latch circuit 61 is
The signal waveform is obtained by approximating the interpolation function determined in step a by a broken line at S steps per sampling time, and becomes a smooth interpolation function by passing it through a filter circuit, for example.

(d) Slope calculation unit The slope generation unit 12 calculates the digital data D (0
) and the digital data immediately before one sampling time -1) The slope Go of the interpolation function F-10(t) at the data position of interest is calculated. The slope Go is the interpolation function F-
This is the value when t=1 in the differential function of 1o(t). Therefore, the slope generating section 12 multiplies the 5th coefficient by 5 times, 4
It is composed of a multiplier MLP that quadruples a first-order coefficient, three times a third-order coefficient, doubles a second-order coefficient, and multiplies a first-order coefficient by one, and an adder ADD that adds the results of each multiplication.

Figure 10 shows an example in which digital data obtained by sampling a 20KHz sine wave at 44.1KH2 is converted into an analog signal using the present invention.A smooth sine waveform is obtained everywhere, and unlike the conventional example, the digital data is converted into an analog signal. No natural waveform will occur.

<Effects of the Invention> According to the present invention, instead of replacing each discrete data with an interpolation function and superimposing each interpolation function on the time axis to obtain an analog signal as in the conventional method, is directly interpolated using an interpolation function according to data changes, so unnecessary vibrations do not occur as in conventional methods.

Furthermore, according to the present invention, the most suitable function is selected probabilistically for each change in discrete data, the most suitable coefficients are determined, and direct interpolation is performed. You can create a playback space that suits your needs.

Furthermore, according to the present invention, since the slope of the function generated by the previous data group is inherited and a new interval function is determined by the new data group, it is possible to always pass through the sampling points and perform smooth interpolation. .

[Brief explanation of the drawing]

Fig. 1 is a block diagram of the DA converter according to the present invention, Figs. 2(a) to (k) are explanatory diagrams of the interpolation function determination method, and Fig. 3
The figure is a block diagram of the function determining unit, Figures 4 to 8 are block diagrams of the coefficient calculating unit, Figure 9 is a block diagram of the function generating unit and slope calculating unit, and Figure 10 is an example of analog signal conversion according to the present invention. , FIGS. 11 to 13 are waveform diagrams showing interpolation functions in the conventional method. FIG. 14 is a waveform diagram for explaining the conventional method, and FIGS. 15 to 17 are diagrams for explaining the drawbacks of the conventional method. 11...Digital data output unit 12...Slope calculation unit 13...Interpolation function generation unit 13a...Function determination unit 13b-i (i=:1.2....)...Coefficient calculation unit 13c...Function generation Fig. 2 Fig. 1 Fig. 2 Fig. 4 Fig. Fig. 6 Fig. cda

Claims (1)

[Claims] In a DA converter that converts digital data into an analog signal by interpolating between digital data generated at predetermined sampling time intervals using an interpolation function, some data generated before the digital data of interest is A digital data output unit that outputs digital data and some digital data generated after the digital data of interest, and an interpolation function that interpolates between the digital data of interest and digital data one sampling time before. A calculation unit that calculates the slope at the data position, the digital data of interest, the digital data before and after it, and the interpolation that interpolates between the digital data of interest and the digital data after one sampling time based on the calculated slope. A DA converter comprising: an interpolation function generation section that determines a function, connects an interpolation function, and outputs an analog signal.