JPH04176207A - Signal processing system employing primary iir digital filter - Google Patents

Abstract

PURPOSE:To approximate a frequency characteristic of the primary IIR (cyclic) digital filter to a limit of a frequency characteristic of an FIR (acyclic) digital filter whose delay component number is increased by employing the primary IIR digital filter with comparatively simple configuration between a sampler and a hold circuit and setting a prescribed relation to tap coefficients. CONSTITUTION:A tap coefficient c0 between an input of a primary IIR digital filter 3a and a 1st adder and a tap coefficient c1 between the input and a 2nd adder are selected to have a relation of c0=(alpha1+3)/2 and c1=(alpha1-1)/2, where alpha1 is a tap coefficient between an output of the delay element and the 1st adder, and the absolute value of the tap coefficient alpha1 is set as ¦alpha1¦<1.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a signal processing method using a first-order IIR digital filter, and in particular, it digitizes an analog signal, processes the signal with a digital filter on a microcomputer, and converts it back into an analog signal. This invention relates to a signal processing method using a first-order TIR digital filter for reproducing.

[Conventional technology]

The basic form of the digital signal processing method, which converts an analog signal from a controlled object into a digital signal, processes it digitally, and converts it back into an analog signal, is as shown in Figure 8.
A sampler 2 that samples the analog signal Ud(t) from the object 1 and A/D converts it, and a hold circuit 4 that D/A converts the digital conversion signal a and reproduces the analog signal u(t). configured. When signal processing is performed with the configuration shown in FIG. 8, the analog signal Ud(t) output from the object 1-
In order to approximate accurately in the frequency domain, the sampling interval of the sampler 2 needs to be set small.

If the frequency characteristics of the analog signal from the object 1 cannot be accurately approximated with the configuration shown in FIG. 8 due to sampling interval constraints, a digital filter is installed between the sampler 2 and the hold circuit 4 as shown in FIG. It is necessary to design and insert 3.

The digital filter 3 is a circuit that performs filtering on the digital conversion signal a using basic calculation elements such as a digital adder 1 multiplier and a shift register. The filtered digital output signal S is D/A converted by the hold circuit 4 and returned to the analog signal u (L), thereby completing the signal processing.

[Problem to be solved by the invention]

In the digital signal processing method described above, in order to accurately reproduce the analog signal from the object in the frequency domain, the eighth
If the sampling interval is reduced in the configuration shown in the figure, the calculation time will increase, and the sampler and hold circuit must be of high precision, that is, the hold circuit must be of high order, which has the disadvantage of increasing the hardware cost. be. Furthermore, if the bold circuit is made to a higher order, the transfer function of the hold circuit is complicated, so there is a drawback that the stability of the circuit cannot be guaranteed depending on the transfer function of the object or the type of its output signal.

On the other hand, when using a digital filter as shown in Figure 9, it is sufficient to design a digital filter that can completely reproduce the analog signal by canceling the transfer function of the combination of the sampler and the hold circuit. . However, it is impossible to realize such an ideal digital filter, and in reality, the output of the sampler is directly input to the digital filter, and the hold circuit has characteristics similar to the analog signal output from the target object. Until an output of has the disadvantage that the stability of the circuit cannot be guaranteed because the tap coefficient of the filter depends on the sampling interval.

An object of the present invention is to provide a signal processing method using a first-order IIR digital filter that can easily obtain accurate approximation with a small number of man-hours.

[Means to solve the problem]

The signal processing method using the primary 1' I R digital filter of the present invention includes a sampler that samples the analog ET7 signal, converts it to a digital signal, and outputs it, one delay Yasuko and the i-th and a second adder and performs arithmetic processing on a digital human input signal, and a zero-order hold circuit that converts the output into an analog signal. In the signal processing method, the primary I
A tap coefficient C8 between the input of the IR digital filter and the first adder and a tap coefficient CI between the input and the second adder are added to the output of the delay element and the first adder. co-(αt+3)/2, c += (α1=
−1−)/2, and tap coefficient α□ is set to lα11〈1
It is characterized by the following.

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention.

The signal processing method using the first-order IIR digital filter in FIG. 1 is based on the analog signal Ud('t
, ) at a sampling interval T, and a first-order [IR,
It is composed of a digital filter 3a and a zero-order hold circuit 4 which converts the digital output signal from the digital filter 3a into an analog signal and outputs an analog signal u(t). -Next T' I
The R digital filter 3a is 1 as shown in FIG.
A first-order recursive digital filter (Inflnite Recur
sivdigital rilt, er), and each tap coefficient of the -order IIR digital filter 3a of 3° or less, which is selected so that the relationship of equation (1) below holds as shown in the figure, is ( 1) The reason for selecting the formula as in the formula will be explained.

In order for the digital filter to have good characteristics, when the output of the sampler 2 is directly connected to the digital filter, the analog signal IJ,(t,) of the output of the object 1 and the analog signal of the output of the hold circuit 4 must be connected. u (t) and (
2) It suffices to satisfy the relationship of formula.

u (t,) = U d(1-)
---(2) Here, in order to obtain the tap coefficients of the -order FIR digital filter 3a, first, the acyclic digital filter (FINil(・ncc anusiv+・digital filter: hereinafter FIR
A method for analytically determining the limit characteristics of 3C (referred to as a digital filter) will be explained in detail.

The analog signal U reproduced from the hold circuit 4 after performing the signal processing shown in FIG. 3 on the analog signal U d(t). (1) can be expressed as follows, where the number of delay elements is β, the sampling interval is T, and kT≦t<(k+1)T.

Also, the pulse transmission amount of the FIR digital filter 3c is D.
When #(Z), it becomes. However, the document [System and Control JV01.29. NO, 4, PP
259-267 (1958), the tap coefficient α of the FIR digital filter 3c in FIG. 3 is determined by one of the numerical integration methods for the ordinary differential equation shown in FIG. Adams-Bashfo
Corresponding to the coefficients of the rth method, 1♀I r-? , the number of delay elements of the digital filter 3C is Adams-Ba
This corresponds to the number of stages β of the shforth method.

On the other hand, Adams-Bashfor in numerical calculation method
There is a relationship shown in FIG. 5 between the number of stages β of the th method and calculation accuracy. Therefore, if we focus on the fact that the larger β is, the higher the accuracy is, it can be expected that the FIR digital filter of β→■ is as close to an analog signal as possible.

The pulse transfer function of the FIR digital filter with the number of delay elements β is set as Z = ejfdT (, j is a complex number), and D4(ejωT) is rearranged by (1-ejIll) t
7. J) knee, for β-2, = 1+(1/2>(+-e'ωT) for β-3, -(23/12)(12/16)e-jω"t(5/1
2) e-, +2ω1-11 (1/2) (1-e'ωT)
+(5/12)(+ -eJωT)2, (1-e
Adams-Bashf
Coefficients appear when the orth method is expressed in backward difference form.

By analogy with the above example, FTP of β→ω.

The pulse transfer function of the digital filter can be expressed as. However, ε, −(−1>” f2 (Lr) dr
-(6). Here, Adams-Bashfo
Returning to the derivation method of the numerical calculation algorithm of the rth method (5
), l) (eJf, lT) is t4ac
Coefficient ε of laurin expansion. Since it is defined as a generating function that gives
-Σε-(1-eJIJT)m-Σe, , L"m=0 -5"o(1-t)-'dr . . . =-(7) becomes a simple definite integral. Here, (1-t,)-' = exp[-r Ioge(1-
t)], equation (7) becomes. If we put back the replaced t and rearrange it, we get β−÷■
The frequency response of the FTR digital filter in the case of can be analytically determined as. Furthermore, when deformed, D (ejω7) = s i heat 1m>-e L J
It is a ωT/2+ −(10) filter.

On the other hand, if the hold circuit, which is a D/A converter, is zero-order and its transfer function is H(jω), then old jω) - illusion ÷ F -
Good/sword-e topo'2) --(11). As shown in FIG. 3, the FIR digital filter 3c and the hold circuit 4 are always connected in cascade.
e(-JLIIT/2ゝ of formula (11) and e of formula (10)
(jωT/2) is always canceled. Therefore, the only phase shift caused by signal processing is the phase of the sampler 2.

Figures 6 and 7 show the analog signal from the object as U d(
FIG. 4 is a Bode diagram showing the frequency characteristics when the digital processing shown in FIG. 3 is performed when t)=e' and the sampling time is 0.5 ser:. The horizontal axis of the figure is the frequency, the vertical axis is the gain (dB) in Figure 6, and the phase (Figure 7).
deg). The β-1 curve is the frequency characteristic of the analog signal uO(L) reproduced when digital signal processing is performed in the basic form shown in Figure 8, and the β-2 and β-3 curves are shown in Figure 3. The frequency characteristic of the analog signal uo(t) when using the FIR digital filter, β→ω, is the analog signal U for the limit characteristic of the FIR digital filter shown in FIG. This is the frequency characteristic of (1,).

In the gain diagram of FIG. 6, the β-1 curve approximates the original analog signal relatively well and appears to be able to cover a wide frequency band, but the phase characteristics are considerably degraded. On the other hand, when the FTR digital filter is inserted, the gain characteristics are slightly degraded in the high frequency band compared to the digital signal processing formula H with β=1 shown in FIG. However, when the sampling frequency is ω, (=1/T>), it is not actually used in a frequency band other than 0〈ω〈ω3, so in that range, an FTR digital filter with a large β can be inserted. It can be seen that the characteristics are improved.

From the above viewpoint, formula (9) realizes good frequency characteristics.
Let us consider that the limit characteristic of the FrR digital filter of β→■, expressed as , is constructed by a -th order TR digital filter. -order ITr (The pulse transfer function of the digital filter is D (Z)
It is given by 1+α, Z-1. However, Z−ejl″T. Therefore, we can assume that equation (9) and equation (12) are equal.Equation (
13) and expand it into a Tiller series with the product ω1 of the frequency 0) and the sampling interval T, we get -(a++1)+1/2(-u++1>(jωT))
6(σ1+1)(jωT)2[R, [(jωT)3]
・・・・・・(14) CO+CIZ
' -(co+c1)-c+ (jmT)+1/2c+
(ja+T>2+Rh[(jωT)31
(15) However, since j is a complex number, there is a relationship of j2--1. Also, Ra[(jllT)3
], Rb[(jωT) 31 is the term after the third power of jωT.

When α1 is a free parameter and the coefficients up to the first-order term of j6+T are compared, c 1)-1-c 1= (a 1-1 1 )
--・(16)ct-(-α□+1)/2
...(17). Solving the simultaneous equations of equations (16) and (17) yields Co-(α 1-to 3 ) /
2 ... ... (18
〉CI-((2t t) / 2 ・-
-119) is obtained. In order for the filter to be stable, it is a necessary and sufficient condition that the pole in equation (12) exists within the unit circle, so IαI 1<1 ・−・−12
0>3. As a special example that satisfies the range of equation (20), α1
−0, the 78th order (β
It can be seen that the FIR digital filter 3b having the coefficients of the Adams-Bashfor day 1 method of -2) can be easily realized.

〔Effect of the invention〕

As explained in detail above, the signal processing method using the first-order ITR digital filter according to the present invention uses a relatively simple first-order ITR digital filter between the sampler and the hold circuit.
An FI whose tap coefficients are determined by the Adams-Bashforth numerical calculation algorithm by using a digital router and setting a predetermined relationship for the tap coefficients.
The limit of increasing the number of delay elements of the R digital filter (
β→ω) frequency characteristics can be approximated. This-
The following 1■R digital filter has one parameter (α1
), all tap coefficients can be determined using the single-order circuit configuration of the digital filter, eliminating the need to determine combinations of tap coefficients through trial and error, and enabling stable operation that easily adapts to the signal form from the target object. Since it is possible to design a filter that guarantees this, it has the effect of significantly reducing design man-hours. Furthermore, if the parameter α1 that determines the tap coefficient is set to O, it is possible to easily construct an FI R digital filter having a quadratic Adams-Bashforth method tap coefficient. Furthermore, there is an effect that the filter characteristics can be easily changed by changing one parameter.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention, FIG. 2 is a block diagram when the tap coefficient α in FIG. 1 is set to 0, and FIG. A block diagram of the processing method, Figure 4 shows the tap coefficients of the FIR digital filter and the Adams-Bashfo
An explanatory diagram of the relationship between the coefficients of the rth method, Fig. 5 is an explanatory diagram of the relationship between the number of delay elements of an FIR digital filter and calculation accuracy, and Fig. 6 is a characteristic showing the gain versus frequency relationship when using an FIR digital filter. Figure 7 is a characteristic diagram showing the phase versus frequency relationship, Figure 8 is a block diagram showing the basic configuration of the conventional digital signal processing method, and Figure 9 is a general diagram showing the basic configuration of the conventional digital signal processing method. FIG. 2 is a block diagram of a digital signal processing method 1j. 1...Object, 2...Sampler, 3
-...-Digital refill, 3a...--Next T R digital refill filter, 3b...--U next 1" i F?, digital filter, 3C...
・FIR, digital filter, 4...Hold circuit.

Claims (1)

[Claims] A sampler that samples an analog signal, converts it into a digital signal, and outputs it, one delay element, and first and second adders arranged before and after the delay element, and converts the signal into a digital input signal. In a signal processing method using a first-order IIR digital filter that includes a first-order IIR digital filter that performs arithmetic processing and a zero-order hold circuit that converts its output into an analog signal, the input of the first-order IIR digital filter and the first Tap coefficient C_0 between adder
and a tap coefficient C_1 between the input and the second adder
and C_0=(α_1+3)/2, C_1=(α_1-1) for the tap coefficient α_1 between the output of the delay element and the first adder.
/2, and tap coefficient α_1 is |α_1|<1.