JPH03124110A - Digital controlled filter - Google Patents

Abstract

PURPOSE:To improve the filter characteristic and to facilitate how to use the filter by adopting a filter in which addition in a characteristic equation of an analog linear low pass filter is realized by an adder, subtraction is by subtractor, multiplication is by a multiplier and integration is realized by an accumulator and employing an insertion filter with a characteristic whose transmission gain is decreased at a frequency being a half of the sampling frequency for signal processing. CONSTITUTION:A 2nd low pass filter 5 is constituted entirely the same as unit filters 1-1, 1-2 except that a coefficient alpha of a multiplier M is set to 1/2 and its cut-off frequency fo is set nearly to fs/4. An output OUT 2 among outputs of the unit filter is inputted to a multiplier 3 via the 2nd low pass filter 5 and the multiplier 3 multiplies the input with a prescribed coefficient beta. A subtractor 4 subtracts an output of the multiplier 3 from an input sample waveform signal and inputs the result to the unit filter 2. The filter characteristic is changed by varying the coefficient beta.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a digital condrouldo filter that has characteristics and ease of use similar to analog voltage condrouldo filters.

[Prior Art] In analog music synthesizers and the like, a VCF (voltage controlled filter) as shown in FIG. 9 is widely used. Here, each unit filter 1-1
．． 1-2. ..., 1-0 is a first-order low-pass filter configured to have a variable cutoff frequency using, for example, a CR passive circuit, and its low-pass transfer function has a cutoff frequency fC of fC=□ ・・・・・・ (2)2
It is expressed as π.

Further, the feedback circuit 3 and the subtraction circuit 4 are connected to the cascade-connected unit filters 1-1. 1-2. ..., 1-n for negative feedback of the output of the final stage 1-n to the first stage.

The gain β of the feedback circuit 3 is the cutoff frequency f of vCF.
Related to resonance near C.

In digital music synthesizers and the like, FIR (finite impulse response) type or IIR (infinite impulse response) type digital filters are used as those compatible with such VCFs (digital condromed filters). .

However, these digital filters have the disadvantage that many multiplier coefficients must be set at the same time, and the relationship between these coefficients and filter characteristics is complicated, making control difficult.

In order to eliminate such drawbacks, the present inventors used a digital first-order low-pass filter as disclosed in Japanese Patent Application Laid-Open No. 18212-1983 in place of the unit filter in the analog filter shown in FIG. 9, making it possible to control its characteristics. An attempt was made to construct a digital condrol filter.

An example is shown in FIG. 10. In the same figure, the symbol "+"
is an adder or subtractor that adds the data input to the unmarked or marked input terminal and subtracts the data input to the marked input terminal, and M is a constant value for the input signal. (hereinafter referred to as a coefficient), and Z''1 is a delay circuit that delays input data by one period (sampling period) T of the sampling pulse. The symbol indicates the coefficient by which the signal is multiplied in the multiplier.

In the same figure, the digital first-order low-pass filter 1-1.1-2, which is a unit filter, uses an adder for addition, a subtracter for subtraction, a multiplier for multiplication, and an accumulation for integration in the characteristic equation of the analog first-order low-pass filter. The low-pass transfer function is α H(Z)−, −(1−CE) z−′ −°°°°°
It is expressed as (3). Moreover, the cutoff frequency fc is
If α (=aT) is sufficiently smaller than 1, it is expressed as follows (where f3 is the sampling frequency). That is, this digital first-order low-pass filter has almost the same frequency characteristics as an analog filter, and has the advantage that the relationship between the coefficient α of the multiplier and the filter characteristics is simple and is easy to handle in the same way as an analog filter.

In the digital condromed filter shown in FIG. 10, the frequency characteristics can be arbitrarily set as shown in FIG. 11 by setting the coefficient α of the multiplier M and the coefficient β of the multiplier 3.

Here, the cutoff frequency depends on the coefficient α of the multiplier M, as can be seen from equation (4). Further, the coefficient β of the multiplier 3 corresponds to the gain of the feedback circuit 3 in the analog VCF, and is related to the resonance near the cutoff frequency fc of the filter.

[Problems to be Solved by the Invention] By the way, in the digital Chorod filter shown in FIG. 10, if β is set to a large value and α approaches 1, When oscillation occurs and α is brought closer to l, the oscillation amplitude further increases. Since the filter shown in the figure is a system with a finite word length, the input signal is blocked due to this oscillation, resulting in a disadvantage that the output signal level decreases.

In other words, with respect to the input signal sample waveform as shown in FIG. 12A, the output signal sample waveform is a superimposed oscillation waveform as shown in FIG. 12B, and this amplitude is the maximum amplitude determined by the finite word length. If it exceeds , the amplitude of the part exceeding it will be limited and the waveform will be clipped.
The amplitude of the output signal will decrease.

This invention was made in view of the problems in the conventional example described above, and an object of the present invention is to provide a digital condrouldo filter that has characteristics and ease of use similar to analog voltage condrouldo filters. do.

[Means for Solving the Problems] In order to achieve the above object, the present invention connects in cascade a plurality of digital first-order low-pass filters (unit filters) each having an arbitrary but identical cutoff frequency set by digital information. In a digital condrol filter configured to feed back the output of this cascade circuit to the input terminal using a multiplier and an adder/subtractor, the addition in the characteristic equation of the analog first-order low-pass filter is added as the digital first-order low-pass filter. In addition to using a filter in which subtraction is replaced with a subtracter, multiplication is replaced with a multiplier, and integration is replaced with an accumulator, the transmission gain is reduced at a frequency that is 1/2 of the sampling frequency for signal processing. The present invention is characterized in that an insertion filter with a characteristic is inserted into a closed loop consisting of the plurality of unit filters and the feedback circuit.

As the insertion filter, a band-pass filter or another digital low-pass filter having a cut-off frequency set higher than the cut-off frequency of the first-order low-pass filter and lower than 1/2 of the sampling frequency can be used.

Here, the subtracter includes one configured to equivalently perform subtraction using an inverter and an adder.

[Operation] In the above configuration, the operation of the portion consisting of the plurality of unit filters and the feedback circuit is almost the same as that of the analog VCF shown in FIG. 10, except for the problem of fs/2 oscillation. The insertion filter has a reduced transmission gain at a frequency that is 1/2 of the sampling frequency fs at which the unit filter is operated. Therefore, the loop gain of the closed loop is reduced by the presence of the insertion filter. This prevents f5/2 oscillation or reduces the amplitude. On the other hand, the cutoff frequency of the insertion filter is set higher than the cutoff frequency of the unit filter. For this reason, an adverse effect on the characteristics of the digital condromed filter is prevented.

Further, since the present invention is configured equivalently to an analog VCF except for the insertion filter, the frequency characteristics are almost the same. That is, the cutoff frequency fC can be controlled by giving the unit filter a multiplication coefficient that replaces the control voltage of the analog VCF, and the resonance characteristics of the filter can be changed by changing the coefficient of the feedback multiplier. . Furthermore, since a digital first-order filter similar to that disclosed in JP-A-61-18212 is used as the unit filter, the relationship between the multiplier coefficients and filter characteristics, especially the cutoff frequency fc, is simple and easy to handle. easy.

Effect C] As described above, according to the present invention, it is possible to realize a digital controlled filter that has characteristics similar to those of an analog VCF and is as easy to use as an analog filter.

[Examples] Hereinafter, the present invention will be described in detail based on Examples. Note that common or corresponding parts are denoted by the same reference numerals throughout the figures.

FIG. 1 shows the configuration of a digital condrol filter according to an embodiment of the present invention.

The filter in the figure includes a unit filter 1-1.1'-2 which is a digital first-order low-pass filter, a multiplier 3 and a subtracter 4, and a second low-pass filter 5 as an insertion filter that is a feature of the present invention. .

The digital first-order low-pass filters 1-1 and 1-2 are substantially the same as those described in the embodiment of JP-A-68-18212, and have the Laplace transfer function H(S) − of the analog first-order low-pass filter. ,+8・
...Applying appropriate s-z conversion to (5), this 2
The leap number H(z) is simplified as necessary and then converted into a circuit. These Laplace transfer functions and S−
2 conversion is well known.

The s-z transformation to be adopted is "based on differential approximation < s-z transformation" which performs the transformation of
or s-aml-z-' exp(aT) and (s-a+
J b) (s-a+j b)= (s-a)2+b
2 -41-2 e"cos(b T) z-'+ e"
``Match-2 conversion'' in which conversion is performed using a conversion pair z-2 is preferred.

The simplest method is based on differential approximation and <sz transformation. In order to apply this S-Z transformation to the Laplace transfer function described above, if S is replaced by 1-z-' and aT is replaced by α, α H(z)=1-, -, +. ----(6) If this equation is expressed in a circuit using a delay circuit z-1, a multiplier α, and an adder/subtractor, the result will be as shown in FIG. In this circuit, the coefficient must be calculated by dividing 1/(1+α), which may cause a delay in processing, so it is modified as follows.

In other words, the difference 1-z"' between the current data and the data one sampling period ago means a differentiation, and the differentiation of the constant α (
1-z-') α is 0. Considering this, the above equation can be rewritten as α t −(t−a) z−′ (6). If this equation is expressed in a circuit, it will be as shown in FIGS. 1 and 3.

FIG. 4 shows a circuit example of a first-order low-pass filter obtained by matching 2 conversion.

In the filters shown in FIGS. 1 to 4, the cutoff frequency is determined according to a coefficient α given as a value in the range from 0 to α to 1.

And α! In a sufficiently smaller range, the accuracy of the conversion or approximation is high, and the cutoff frequency fC and α have a nearly proportional relationship, expressed as (where fs is the sampling frequency). Therefore, by changing this coefficient α, the cutoff frequency can be changed in the same manner as shown in FIG. 11 above. The fact that the coefficient α is almost proportional to the cutoff frequency fc means that the filter can be easily controlled.

The filter shown in Figures 2 and 3 has 0UT as the output terminal.
1 and 0UT2 which generates an output obtained by delaying this 0UTI by one sampling period by a delay circuit z-1. In FIG. 1, the output terminal of filter 1 is ou'
rt, but the output terminal of filter 2 uses 0UT2. This is because if a closed loop (delay-free loop) that does not include a delay circuit is formed, normal arithmetic operations will not be performed. This is to ensure that the closed loop consisting of the subtracter 4 and the subtracter 4 always includes the delay circuit z-1.

In FIG. 1, the second low-pass filter 5 has the unit filter 1- It is configured exactly the same as 1.12. Fifth
The figure shows the frequency characteristics of the second low-pass filter 5. This filter 5 has a frequency f3/2 of a closed loop consisting of a unit filter 1-1.1-2, a multiplier 3, and a subtracter 4.
The loop gain of the oscillation waveform is reduced to prevent oscillation at frequency f3/2, or to reduce the amplitude of the oscillation waveform.

The multiplier 3 outputs the output 0UT2 of the output of the unit filter 2.
is input through the second low-pass filter 5, and is multiplied by a predetermined coefficient β.

The subtracter 4 subtracts the output of the multiplier 3 from the input sample waveform signal and inputs the result to the unit filter 2.

By changing this coefficient β, the filter characteristics can be changed as shown in FIG. 11.

FIG. 6 shows an example of a configuration in which the digital condroldo filter of the present invention is applied to a sound source of an electronic musical instrument. In the same figure, 61 is a digital waveform sound source consisting of a memory storing sample point data of, for example, natural musical instrument sounds;
2 is a digital condominium filter of the present invention, 6
Reference numeral 3 denotes a musical tone forming means for forming musical tones based on the output of the digital condrol filter 62.

In the same figure, a digital condolenoid filter 62
As shown in Fig. 7, the parameter α control signal given as a timbre control signal (especially corresponding to pitch data)
The cutoff frequency is controlled by the parameter β
The filter resonance characteristics are controlled by control signals (corresponding in particular to timbre data). These controls allow the timbre of the generated musical tones to be controlled.

[Modifications] Note that the present invention is not limited to the above-described embodiments, and can be implemented with appropriate modifications. For example, in the above example, the second low-pass filter 5 is connected to the unit filter 1-
Although we have explained the example of inserting between 2 and multiplier 3,
The low-pass filter 5 may be inserted anywhere within the closed loop. For example, as shown in FIG. 8, the same effect can be obtained by inserting it into the main ring-opening circuit of the unit filter 1-1 and the subtracter 4. However, when the coefficient β is made small, oscillation is difficult to occur even if α is brought close to 1, so it is preferable that the filter is not easily influenced by the inserted filter. For this purpose, the inserted filter is preferably located within the feedback system, such as between the unit filters 1-2 and the multiplier 3, or between the multiplier 3 and the subtracter 4.

Further, in the above description, the characteristics of the second low-pass filter 5 were fixed, but as shown in FIG. 8, the coefficient γ (=
The characteristics may be made variable by α′).

Further, the filter to be inserted is not limited to the examples shown in FIGS. 1 and 8, but may be a band-pass filter, for example, as long as the gain decreases near the high frequency f,/2. .

Furthermore, the control of each coefficient (parameter) may be logarithmic control. In this case, multiplication can be replaced with addition, and the process can be simplified.

[Brief explanation of the drawing]

FIG. 1 is a circuit diagram showing the configuration of a digital condromed filter according to an embodiment of the present invention, and FIGS. 2 to 4 are
FIG. 5 is a circuit diagram showing an example of the configuration of the unit filter in FIG. 1, FIG. 5 is a graph showing an example of frequency characteristics of the second low-pass filter in FIG. 1, and FIG. 6 is a diagram showing an example of application of the present invention. A circuit diagram of an electronic musical instrument sound source; FIG. 7 is a detailed explanatory diagram of the digital condrouldo filter in FIG. 6; FIG. 8 is a circuit diagram showing a modification of the digital condrouldo filter in FIG. 1; 10 is a circuit diagram of a conventional analog VCF, FIG.
The frequency characteristic diagram of the digital chondral filter shown in the figure, and FIGS. 12A and 12B are diagrams showing examples of input and output waveforms of the digital chondral filter of FIG. 10. 1-1.1-2: Unit filter (digital first-order low-pass filter) 3, M: Multiplier 4・1+''2 Subtractor 5: Second low-pass filter (insertion filter)

Claims (1)

[Claims] (1) In the characteristic equation of the analog first-order low-pass filter, addition is replaced with an adder, subtraction is replaced with a subtracter, multiplication is replaced with a multiplier, and integral is replaced with an accumulator, so that the same operation is achieved. A unit filter consisting of a digital first-order low-pass filter whose cut-off frequency is set, in which a plurality of unit filters are connected in cascade, a multiplier that multiplies the output of the cascade-connected final stage unit filter by a predetermined coefficient, and an input. an adder/subtracter that subtracts the output of the multiplier from the signal and inputs the result to the cascade-connected first-stage unit filter; A digitally controlled filter comprising: a unit filter; and an insertion filter inserted into a closed loop consisting of a multiplier and an adder/subtractor. (2) The insertion filter is a digital low-pass filter having a cutoff frequency set higher than the cutoff frequency of the unit filter and lower than 1/2 of the sampling frequency that operates the unit filter.
Digitally controlled filter as described. (3) The digitally controlled filter according to claim 1, wherein the insertion filter is inserted into a feedback loop consisting of the multiplier and the adder/subtractor. (4) The unit filter has the symbol H(Z) = output/input = (a)/{1-(1-α)Z^-^, where the symbol representing data one sampling frequency before is Z^-^1. 3. The digitally controlled filter according to claim 2, wherein the characteristic expression is a transfer function represented by 1}.