JP2672691B2 - DA converter - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a DA converter, and in particular, generates an analog signal for smoothly interpolating between discrete digital data.
About DA converter.

<Prior Art> In the conversion theory of a DA converter using a conventional digital filter, discrete digital data with sampling time ΔT intervals are replaced with predetermined functions, and the function values of the respective digital data are added on the time axis. It is to interpolate. The function corresponding to the digital value n is obtained as a product of the unit interpolation function and n by defining a function for the unit data (= 1) (referred to as a unit interpolation function). or,
Actually, the full scale (FS) is set to 1 and compressed from the data value, and then the function values on the time axis are added together to interpolate between the respective digital data.

11 to 13 are examples of the unit interpolation function for unit data. FIG. 11 shows an example in which the interpolation function is expressed by a quadratic function, and FIG. 12 shows an example in which the interpolation function is expressed by a cubic function. FIG. 13 is an example in which the interpolation function is expressed by sin (π · fs · t) / π · fs · t. The cubic function F in FIG. 12 is expressed by the following equation F (t) = 0 −1.5 ≦ t ≦ −1 F (t) = − 2 (t + 1) ³ +3 (t + 1) ² −1 ≦
t <0 F (t) = 2t ³ −3t ² +1 0 ≦ t <1 F (t) = 0 1 ≦ t ≦ 1.5.

FIG. 14 shows digital data D (1), D (0), D (-1), D when the unit interpolation function is the quadratic function waveform of FIG.
Functions of (-2) IF (1), IF (0), IF (-1), IF (-
FIG. 2 is a relationship diagram between 2) and an analog signal AS obtained by adding each function value on a time axis.

<Problems to be Solved by the Invention> The sum of quadratic functions is a quadratic function, the sum of cubic functions is a cubic function,
Since the sum of the sine waves is a sine wave, the interpolation output (analog signal) created by the conventional method inherits the unique property of the interpolation function used and creates a single unique playback space. However, this means that data recorded in various spaces is modulated into a single unique space, and data recorded in a sound field space that is artistic and has various personalities like music. This means that the original sound field cannot be reproduced.

In addition, the digital data obtained by sampling a 20 KHz sine wave at 44.1 KHz is converted to the conventional method (the unit interpolation function is
Is converted to an analog signal by the cubic function shown in FIG.
As shown by the mark C in FIG. 15, an unnatural waveform is generated when viewed from the data group. This is because all digital data is interpolated with only a cubic function.
The intrinsic properties of the interpolation function have surfaced.

Furthermore, if a digital data group whose values change linearly is converted into an analog signal by the conventional method (the unit interpolation function is the cubic function in FIG. 12), the points connected by a straight line as shown in FIG. 16 are sampled. An accurate analog signal cannot be obtained because it is undulated with a cubic function at each time Ts.

The problems in FIGS. 15 and 16 also occur when the unit interpolation function is the quadratic function in FIG.

On the other hand, if the unit interpolation function is the sine waveform of FIG. 13, the original analog signal can be accurately reproduced when the data changes like a continuous sine wave. However, when data changes impulsely, unnecessary vibration occurs. Therefore, for example, if a digital data group that changes linearly so that the data value folds in the middle is converted into an analog signal by the conventional method (the unit interpolation function is the sine wave of FIG. 13),
As shown in FIG. 17, a portion connected by a straight line undulates with a sine wave at each sampling time Ts, and an accurate analog signal cannot be obtained.

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 vibration.

Another object of the present invention is to provide a DA converter capable of changing an interpolation function according to a change in digital data and thereby creating a reproduction space corresponding to the change in data.

<Means for Solving the Problem> In the present invention, the above-mentioned problem is achieved by a digital data output unit that outputs the digital data of interest and some digital data before and after the digital data of interest, and the digital data of interest and one sampling time before. A calculation unit that calculates the slope of an interpolation function that interpolates between data, and determines the number of interpolation functions that interpolate between the data of interest and the digital data after one sampling time in consideration of the data of interest, the digital data before and after it, and the slope. And an interpolating function determining unit.

<Operation> The inclination of the interpolation function for interpolating between the digital data of interest and the digital data of one sampling time before is calculated, and the inclination, the data of interest, and the digital data before and after that are taken into consideration. , An interpolation function for interpolating between the focused data and the digital data after one sampling time is determined, and the interpolation function between the respective digital data is connected to generate an analog signal. As a result, the interpolation function between the data can be changed according to the data change, and a reproduction space corresponding to the data change can be created. Further, interpolation can be performed smoothly between the digital data so as not to generate unnecessary vibration.

<Embodiment> Overall Configuration of DA Converter of the Present Invention FIG. 1 is a configuration diagram of a DA converter according to the present invention. In the figure, 11 indicates discrete data D (N + 1), D (N), ... D (0) ... D (1-
M), D (-M) generating digital data output unit, 12 is the data of interest of an interpolation function for interpolating between the digital data D (0) of interest and the digital data D (-1) one sampling time before A tilt calculator for calculating the tilt G0 at the position, 13 is the digital data D (0) of interest, the digital data before and after it, and the digital data D (0) and the digital after one sampling time in consideration of the tilt G0. This is an interpolation function generation unit that determines an interpolation function F01 (t) that interpolates between the data D (1).

The digital data output unit 11 includes a number of delay circuits Z (N +) for delaying digital data by one sampling time (Ts).
1), Z (N),... Z (0)... Z (1-M), Z (−
M), and these are connected in series.
When the input data is parallel data, each delay circuit
It is composed of a latch circuit that uses LCK1 as a latch clock for each sampling, and in the case of serial data, a shift register that uses WBCK as a bit clock for data transmission. Digital data is sequentially input to the delay circuit Z (N + 1) from a digital data generator (not shown) for each sampling time Ts, and the data stored in each delay circuit is shifted to the right every sampling time. Therefore, if the focused digital data is D (0), some digital data D (-) to D (-M) generated before the digital data and the digital data D (0) generated after the digital data are generated. Some digital data D
(1) to D (N + 1) are output from each delay circuit.

The interpolation function generator 13 outputs the digital data D of interest.
(0), the digital data before and after it, and the gradient G0 are taken into consideration, and a function determination unit 13a that determines an interpolation function that interpolates between the digital data D (0) and the digital data D (1) one sampling time later, Coefficient calculators 13b-1 to 13b-5 which are provided for each function to be determined and which determine the coefficient of each order,
It has a function generator 13c that generates the determined interpolation function using the calculated coefficient. Note that the digital data following the current digital data of interest becomes new digital data of interest at every sampling time, and a new interpolation function is generated at every sampling time from the interpolation function generator 13, and these interpolation functions are connected. Is output.

Hereinafter, the function determination unit 13a and the coefficient calculation unit 13b-i (i = 1, 2,
..), the configuration of the function generator 13c, and the slope calculator 12 will be described.

(A) Function determination unit (a-1) Function determination method Using digital data D (N + 1) to D (-M),
An interpolation function F01 (t) for interpolating between the current digital data D (0) of interest and the digital data D (1) after one sampling time is determined according to the following selection criteria 1) to 12).

1) When D (1) = D (0) = D (−1) (see FIG. 2 (a)), F01 (t) = D (0) (0 ≦ t ≦ 1) (1) 2 ) D (1) ≠ D (0) = D (-1) = D (-2), D
When (4) = D (3) = D (2) (see FIG. 2 (b)) F01 (t) is a cubic polynomial, and the slope at t = 0, t = 1 is 0.

F01 (t) = 2 {D (0) -D (1)} t 3 +3 {D
(1) -D (0)} t 2 + D (0) (0 ≦ t <1) ... (2) 3) D (0) ≠ D (1) = D (3) = D (2) = D ( −
1) = D (−2) (see FIG. 2 (c)) F01 (t) is a third-order polynomial, and the slope is 0 at t = 0 and t = 1.

F01 (t) = 2 {D (0) -D (1)} t 3 +3 {D
(1) -D (0)} t ² + D (0) (0 ≦ t <1) (2) 4) D (3) = D (2) = D (1) ≠ D (0) = D ( −
1) = D (−2) (see FIG. 2 (d)) F01 (t) is a third-order polynomial, and the slope is 0 at t = 0 and t = 1.

F01 (t) = 2 {D (0) -D (1)} t 3 +3 {D
(1) -D (0)} t ² + D (0) (0 ≦ t <1) (2) 5) {D (2) -D (1)} = {D (1) -D
(0)}, D (0) = D (-1) = D (-2) (see FIG. 2 (e)) F01 (t) is a first-order polynomial, and F01 (t) = {D ( 0) -D (1)} t + D (0)
(0 ≦ t <1) (3) 6) D (3) = D (2) = D (1), {D (1) −D
When (0)} = G0 (see FIG. 2 (f)). However, G0 is a function F that interpolates between the data one sampling time before the current time and the current data.
It is the inclination at the target data position of −10 (t). It should be noted that one sampling time before, F-10 (t) is F01 (t), and therefore the gradient G0 is the gradient of F-10 (t) at t = 1.

F01 (t) is a first-order polynomial, and F01 (t) = {D (1) -D (0)} t + D (0)
(0 ≦ t <1) (3) 7) The function F-01 (t) before one sampling time Ts is selected, and the gradient G0 (= F'-01 (1) at t = 1 is determined, When D (3) = D (2) = D (1) (see FIG. 2 (g)) F01 (t) is a cubic polynomial, and the slope at t = 1 is 0.

F01 (t) = K3 · t 3 + K2 · t 2 + G0 · t + D (0) (0 ≦
t <1) (4) where K3 = 2 {D (0) -D (1)} + G0 K2 = 3 {D (1) -D (0)}-2G0 8) G0 is determined and D ( 1) = ± FS (full scale) (see FIG. 2 (h)) F01 (t) is a cubic polynomial, and the slope at t = 1 is 0.

F01 (t) = K3 · t 3 + K2 · t 2 + G0 · t + D (0) (0 ≦
t <1) (4) where K3 = 2 {D (0) -D (1)} + G0 K2 = 3 {D (1) -D (0)}-2G0 9) D (0) = ± FS In case of (full scale), it is G0.

10) G0 is determined, and D (N) = ± FS and D (N-1) to D
When (1) is not ± FS (see FIG. 2 (i)), F01 (t) is a (N + 2) degree polynomial, and the slope at t = N is 0. When F01 (t) when N = 2 is calculated, F01 (t) = K4 · t ⁴ + K3 · t ³ + K2 · t ² + G0 · t + D
(0) (0 ≦ t <1) (5) where K4 = {− 2 · D (2) + 4 · D (1) −2 · D (0) −
G0} / 4 K3 = {7 ・ D (2) -16 ・ D (1) +9 ・ D (0) +5
・ G0} / 4 K2 = {-5 ・ D (2) +16 ・ D (1) -11 ・ D (0)-
8.G0} / 4. In addition, the function F12 after one sampling time Ts
(T), in other words one sampling time elapsed function after F01 (t) (see FIG. 2 (j)) is defined by the condition 8), F01 (t) = K3 · t 3 + K2 · t ² + G0t + D (0) (0≤
t <1) (4) However, K3 = 2 {D (0) -D (1)} + G0 K2 = 3 {D (1) -D (0)} + 2G0.

In the case of N = 3 is, F01 (t) becomes a fifth order polynomial, the following equation F01 (t) = K5 · t 5 + K4 · t 4 + K3 · t 3 · K2 · t 2 + G0 · t
+ D (0) (0 ≦ t <1) (6) However, K5 = {-13D (3) + 27D (2) -27D (1) +
13 ・ D (0) +6 ・ G0} / 108 K4 = {28 ・ D (3) -63 ・ D (2) +72 ・ D (1) -37
・ D (0) -18 ・ G0} / 36 K3 = {-161 ・ D (3) +405 ・ D (2) -567 ・ D
(1) +323 ・ D (0) +174 ・ G0} / 108 K2 = {10 ・ D (3) -27 ・ D (2) +54 ・ D (1) -37
・ D (0) -26 ・ G0} / 12 11) When G0 is determined and D (N) to D (1) are not ± FS (see FIG. 2 (k)) F01 (t) is (N + 1) Suppose the following polynomial, N = 3 in the case of F01 (t) = K4 · t 4 + K3 · t 3 + K2 · t 2 + G0 + t + D
(0) (0 ≦ t <1) (7) However, K4 = {2D (3) -9D (2) + 18D (1) -11
・ D (0) -6 ・ G0} / 36 K3 = {-D (3) +6 ・ D (2) -15 ・ D (1) +10 ・
D (0) +6 ・ G0} / 6 K2 = {4 ・ D (3) -27 ・ D (2) +108 ・ D (1) -8
In the case of function F01 (t) of 5 · D (0) −66 · G0} / 36 12) or more, the absolute value of {F01 (t)} max exceeds the full scale depending on the input data group, and overflow occurs. There are cases. In order to prevent such overflow, it is advisable to multiply the input data or all the obtained coefficients by the safety coefficient A ≦ FS {F01 (t)} max.

(A-2) Configuration of function determining unit FIG. 3 is a configuration diagram of the function determining unit 13a. SBC is a subtractor, LG is a high level (“1”) when the subtraction result is 0 (zero).
Is a logic circuit that outputs a low-level (“0”) signal in other cases, and AG is an AND gate and an ORG OR gate. In the figure, when the output a is at a high level, the condition 1) is satisfied,
The interpolation function (F01 (t) = D (0)) shown in equation (1) is selected. When the output b is at high level, the condition of 5) or 6) is satisfied, and 1 shown in equation (3) is satisfied. Select the next interpolation function F01 (t) = {D (1) -D (0)} t + D (0). When output c is high level, 2), 3), 4), 7), 8 ) Is satisfied, and the cubic interpolation function shown in equation (2) is selected. When the output d is high level, the condition of 10) (however, N =
If the output e is at a high level, the condition (10) is satisfied (where N =
If the condition (3) is satisfied and the fifth-order interpolation function shown in the expression (6) is selected, and the outputs a, b, c, d, and e are all at low level, the condition of 11) is satisfied and the expression (7) is satisfied. Is selected.

(B) Coefficient Calculation Unit FIGS. 4 to 8 are block diagrams of the coefficient calculation unit that determines the coefficient in each order of the function determined by the function determination unit.

(B-1) Coefficient calculation unit of linear function (equation (3)) The coefficient calculation unit 13b-1 of the linear function adds ± 1 multiplier MLP and each multiplier output as shown in FIG. And outputs a first-order coefficient K11 (= {D (1) -D (0)})
It is composed of DD and a gate circuit GTC which outputs the calculated primary coefficient K11 when a is low level and b is high level.

(B-2) Coefficient calculation unit of cubic function (equation (2) or (4)) The coefficient calculation unit 13b-1 of cubic function inputs 1, ± 2, ± 3 as shown in FIG. 5 multipliers MLP for multiplying signals
And the output of the multiplier are added, and the third-order coefficient K32 (= 2 {D
Adder ADD1 that outputs (0) -D (1)} + D0 and the output of the multiplier are added to each other to obtain a quadratic coefficient K22 (= 3 {D (1) -D).
(0)} − 2G0) output adder ADD2, and gate circuits GTC1 and GTC2 that output the calculated third and second order coefficients K32 and K22 when a and b are at low level and c is at high level. Composed of.

(B-3) Coefficient operation unit of quartic function (Equation (5)) The coefficient operation unit 13b-1 of quartic function (Equation (5)) multiplies an input signal by a predetermined value as shown in FIG. Twelve multipliers MLP to be added and the multiplier output are added to obtain a fourth-order coefficient K43 = {-2 · D (2) + 4 · D (1) -2 · D (0)
Adder ADD1 that outputs −G0} / 4 and the output of the multiplier are added to add a cubic coefficient K33 = {7 · D (2) −16 · D (1) + 9 · D (0) +
Adder ADD2 that outputs 5 · G0} / 4 and the multiplier output are added to obtain a quadratic coefficient K23 = {− 5 · D (2) + 16 · D (1) −11 · D (0)
Adder ADD3 that outputs −8 · G0} / 4, and the fourth-, third-, and second-order coefficients K43, calculated when a, b, and c are low level and d is high level
Gate circuits GTC1, GTC2, GTC3 that output K33 and K23 respectively
It consists of.

(B-4) Coefficient operation unit of quartic function (Equation (7)) The coefficient operation unit 13b-4 of quartic function (Equation (7)) multiplies the input signal by a predetermined value, as shown in FIG. Fifteen multipliers MLP are added to the multiplier output, and the fourth order coefficient K44 = {2D (3) -9D (2) + 18D (1) -1
Adder ADD1 that outputs 1 · D (0) −6 · G0} / 36 and the output of the multiplier are added to add a cubic coefficient K34 = {− D (3) + 6 · D (2) −15 · D ( 1) +10
・ Adder ADD2 that outputs D (0) +6 ・ G0} / 6 and the multiplier output are added to obtain a quadratic coefficient K24 = {4 ・ D (3) -27 ・ D (2) +108 ・ D (1 ) −
85 ・ D (0) −66 ・ G0} / 36 adder ADD3 and a, b, c, d, e are all low level, calculated 4th, 3rd and 2nd order coefficient K44, K34, K2
It is composed of gate circuits GTC1, GTC2, and GTC3 that output 4 respectively.

(B-5) Coefficient operation unit of quintic function (Equation (6)) The coefficient operation unit 13b-5 of quintic function (Equation (6)) multiplies the input signal by a predetermined value as shown in FIG. 20 multipliers MLP and the output of the multiplier are added, and the fifth-order coefficient K55 = {− 13 · D (0) + 27 · D (2) −27 · D (1)
Adder ADD1 that outputs + 13 · D (0) + 6 · G0} / 108 and the output of the multiplier are added, and a fourth-order coefficient K45 = {28 · D (3) −63 · D (2) + 72 · D ( 1) -3
Adder ADD2 that outputs 7 · D (0) -18 · G0} / 36 and the multiplier output are added to add a third-order coefficient K35 = {− 161 · D (3) + 405 · D (2) −567 · D
(1) + 323 · D (0) + 174 · G0} / 108 output adder ADD3 and multiplier output are added to obtain a quadratic coefficient K25 = {10 · D (3) −27 · D (2) +54・ D (1) -3
7 · D (0) −26 · G0} / 12 output adder ADD4 and a, b, c, d are at low level, and e
Are high level, gate circuits GTC1, GTC2, which output the calculated fifth-order, fourth-order, third-order, and second-order coefficients K55 to K25, respectively.
It is composed of GTC3 and GTC4.

(C) Function Generator FIG. 9 is a block diagram of the function generator 13c and the slope calculator 12. In the function generator 13c, 21 to 25 are respectively a to
A coefficient selecting section for selecting and outputting first-order, second-order, third-order, fourth-order, and fifth-order coefficients of the interpolation function determined by the function determining section 13a based on the logical value of e A latch circuit for latching the order coefficients K1, K2, K3, K4, K5 for one sampling time, and 40 to 45 are composed of five multipliers, respectively, t ⁰ , t ¹ , t ² , t ³ , t ⁴ , t ⁵ is a constant K0, primary, secondary, tertiary, 4
A time multiplication unit for multiplying and outputting the 5th and 5th order coefficients K1 to K5, 51
Is an adder that adds the outputs of the multipliers, 61 is the latch clock
A latch circuit that latches the output of the adder 51 by LCK3 and stabilizes the data. The latch clock LCK2 is the data delay latch clock LCK1 (first
(See the figure) and the latch clock LCK1
It is delayed by Td. Now, if it takes Tp time for function determination, coefficient calculation and selection, Td must satisfy Tp <Td <Ts.

Each of the time multiplication units 40 to 45 divides a time t (a period of 0 <t ≦ 1 or 0 <t ≦ 1) to be multiplied by the coefficients K0 to K5 into S steps, and 1 / S → 2 / S → ・ ・ → (S-1) / S → S / S or 0
/ S → 1 / S → ・ → ・ → (S-2) / S (S-1) / S is changed to multiply the corresponding coefficient, and the adder 51 adds the signals output from the respective multiplication units. Then, the latch circuit 61 temporarily latches the adder output by the LCK3 and outputs it. LCK3 is a latch pulse generated at every Ts / S and is delayed by Tf from LCK2. 5Tm <Tf (Tm is the calculation time of the multiplier) Therefore, the output signal of the latch circuit 61 is the function determination unit 13a.
The interpolating function determined in step S1 becomes a signal waveform that is approximated by a polygonal line in S steps per sampling time, and becomes a smooth interpolating function by passing through a filter circuit, for example.

(D) Inclination calculation unit The inclination generation unit 12 determines the digital data D of interest.
(0) and digital data D (-
1) The gradient G0 at the target data position of the interpolation function F-10 (t) for interpolating between the two is calculated. The slope G0 is the interpolation function F−
It is a value when t = 1 in the differential function of 10 (t). Therefore, the slope generating unit 12 multiplies the fifth-order coefficient by 5 times, the fourth-order coefficient by four times, the third-order coefficient by three times, the second-order coefficient by two times, and the first-order coefficient by one, and each multiplication result. ADD for adding
It consists of.

DA conversion example according to the present invention FIG. 10 is an example in which digital data obtained by sampling a 20 KHz sine wave at 44.1 KHz is converted into an analog signal according to the present invention, and a smooth sine waveform is obtained everywhere. Therefore, an unnatural waveform does not occur.

<Effects of the Invention> As described above, according to the present invention, each discrete data is replaced with an interpolation function as in the conventional method, and the respective interpolation functions are not superposed on the time axis to obtain an analog signal. Since the points are directly interpolated by the interpolation function according to the data change, unnecessary vibration does not occur unlike the conventional method.

Further, according to the present invention, the most suitable function is selected stochastically for each change of discrete data, the most suitable coefficient is determined, and the interpolation is directly performed. It is possible to create a playback space according to.

Further, according to the present invention, since the slope of the function generated by the immediately preceding data group is inherited and the new interpolation function is determined by the new data group, it is possible to surely pass the sampling point and smoothly interpolate.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a DA converter according to the present invention, FIGS. 2 (a) to (k) are explanatory diagrams of an interpolation function determination method, FIG. 3 is a configuration diagram of a function determination unit, and FIGS. FIG. 9 is a block diagram of a coefficient calculation unit, FIG. 9 is a block diagram of a function generation unit and a slope calculation unit, FIG. 10 is an analog signal conversion example according to the present invention, and FIGS. 11 to 13 are interpolation functions in the conventional method. FIG. 14 is a waveform diagram for explaining the conventional method, and FIGS. 15 to 17 are explanatory diagrams of defects of the conventional method. 11: Digital data output section 12: Inclination calculation section 13: Interpolation function generation section 13a: Function determination section 13b-i (i = 1,2, ...): Coefficient calculation section 13c: Function generation section

Claims (1)

(57) [Claims] 1. A DA converter for converting digital data into an analog signal by interpolating between digital data generated at a predetermined sampling time interval by an interpolation function, and sequentially storing digital data generated at a predetermined sampling time interval. A digital data output unit that outputs one digital data as the focused digital data, outputs the focused digital data, some digital data generated before the focused digital data, and some digital data generated after the focused digital data An interpolation function determining unit that determines an interpolation function that interpolates between the digital data of interest stored in the digital data output unit and digital data after one sampling time, and digital data next to the digital data of interest for each sampling time As new digital data of interest An interpolation function generator that outputs analog signals by connecting the respective interpolation functions determined by the interpolation function determiner, and a slope calculator that calculates the slope of the interpolation function at the digital data position of interest. The section calculates the slope at the current digital data position of the interpolation function determined by the interpolation function determination section one sampling time before, and the interpolation function determination section calculates the current digital data and the digital data before and after the current digital data. Based on the generated tilt, the current digital data of interest and 1
The interpolation function for interpolating between the digital data after the sampling time is determined, and thereafter, the slope calculating unit calculates the slope and interpolates the digital data next to the current digital data of interest as new digital data of interest at every sampling time. A DA converter characterized in that the function determination unit determines an interpolation function, and the interpolation function generation unit connects the determined interpolation function and outputs an analog signal.