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impz

Impulse response of digital filter

Description

example

[h,t] = impz(b,a) returns the impulse response of the digital filter with numerator coefficients b and denominator coefficients a. The function chooses the number of samples and returns the response coefficients in h and the sample times in t.

[h,t] = impz(sos) returns the impulse response of the filter specified by the second-order sections matrix sos.

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[h,t] = impz(d) returns the impulse response of the digital filter d. Use designfilt to generate d based on frequency-response specifications.

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[h,t] = impz(___,n) specifies what impulse-response samples to compute. You can specify the filter using any of the previous syntaxes.

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[h,t] = impz(___,n,fs) returns a vector t with consecutive samples spaced 1/fs units apart.

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impz(___) with no output arguments plots the impulse response of the filter.

Examples

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Design a fourth-order lowpass elliptic filter with normalized passband frequency 0.4 rad/sample. Specify a passband ripple of 0.5 dB and a stopband attenuation of 20 dB. Plot the first 50 samples of the impulse response.

[b,a] = ellip(4,0.5,20,0.4);
impz(b,a,50)

Figure contains an axes object. The axes object with title Impulse Response, xlabel n (samples), ylabel Amplitude contains an object of type stem.

Design the same filter using designfilt. Plot the first 50 samples of its impulse response.

d = designfilt('lowpassiir','DesignMethod','ellip','FilterOrder',4, ...
               'PassbandFrequency',0.4, ...
               'PassbandRipple',0.5,'StopbandAttenuation',20);
impz(d,50)

Figure Figure 1: Impulse Response contains an axes object. The axes object with title Impulse Response, xlabel Samples, ylabel Amplitude contains an object of type stem.

Design an FIR highpass filter of order 18 using a Kaiser window with β=4. Specify a sample rate of 100 Hz and a cutoff frequency of 30 Hz. Display the impulse response of the filter.

b = fir1(18,30/(100/2),'high',kaiser(19,4));
impz(b,1,[],100)

Figure contains an axes object. The axes object with title Impulse Response, xlabel nT (seconds), ylabel Amplitude contains an object of type stem.

Design the same filter using designfilt and plot its impulse response.

d = designfilt('highpassfir','FilterOrder',18,'SampleRate',100, ...
               'CutoffFrequency',30,'Window',{'kaiser',4});
impz(d,[],100)

Figure Figure 1: Impulse Response contains an axes object. The axes object with title Impulse Response, xlabel Time (ms), ylabel Amplitude contains an object of type stem.

Input Arguments

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Transfer function coefficients, specified as vectors. Express the transfer function in terms of b and a as

H(z)=B(z)A(z)=b1+b2z1+bnz(n1)+bn+1zna1+a2z1+amz(m1)+am+1zm

Example: b = [1 3 3 1]/6 and a = [3 0 1 0]/3 specify a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: double | single
Complex Number Support: Yes

Second-order section coefficients, specified as a matrix. sos is a K-by-6 matrix, where the number of sections, K, must be greater than or equal to 2. If the number of sections is less than 2, the function treats the input as a numerator vector. Each row of sos corresponds to the coefficients of a second-order (biquad) filter. The ith row of sos corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

Example: s = [2 4 2 6 0 2;3 3 0 6 0 0] specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: double | single
Complex Number Support: Yes

Digital filter, specified as a digitalFilter object. Use designfilt to generate a digital filter based on frequency-response specifications.

Example: d = designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5) specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Sample numbers, specified as a positive integer, a vector of nonnegative integers, or an empty vector.

  • If n is a positive integer, impz computes the first n samples of the impulse response and returns t as (0:n-1)'.

  • If n is a vector of nonnegative integers, impz computes the impulse response at the locations specified in the vector.

  • If n is an empty vector, impz computes the number of samples automatically. See Algorithms for more information.

Example: impz([2 4 2 6 0 2;3 3 0 6 0 0],5) computes the first five samples of the impulse response of a Butterworth filter.

Example: impz([2 4 2 6 0 2;3 3 0 6 0 0],[0 3 2 1 4 5]) computes the first six samples of the impulse response of a Butterworth filter.

Example: impz([2 4 2 6 0 2;3 3 0 6 0 0],[],5e3) computes the impulse response of a Butterworth filter designed to filter signals sampled at 5 kHz.

Sample rate, specified as a positive scalar. When the unit of time is seconds, fs is expressed in hertz.

Data Types: double

Output Arguments

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Impulse response coefficients, returned as a column vector.

Sample times, returned as a column vector.

Algorithms

impz filters a length-n impulse sequence using

filter(b,a,[1 zeros(1,n-1)])

and plots the result using stem.

Note

If the input to impz is single precision, the function computes the impulse response using single-precision arithmetic and returns single-precision output.

When impz calculates n automatically, the algorithm depends on the properties of the filter:

  • FIR filters — n is the length of b.

  • IIR filters — impz first finds the poles of the transfer function using roots.

    • If the filter is unstable, n is chosen to be the point at which the term from the largest pole reaches 106 times its original value.

    • If the filter is stable, n is chosen as the point at which the term from the largest-amplitude pole is 5 × 10–5 times its original amplitude.

    • If the filter is oscillatory with poles on the unit circle only, impz computes five periods of the slowest oscillation.

    • If the filter has both oscillatory and damped terms, n is the greater of five periods of the slowest oscillation, or the point at which the term due to the largest pole is 5 × 10–5 times its original amplitude.

impz also allows for delays in the numerator polynomial. The number of delays is incorporated into the computation of the number of samples.

Extended Capabilities

Version History

Introduced before R2006a

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See Also

| | (Control System Toolbox) | |