# freqz

Compute frequency response

## Description

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[H,f] = freqz(obj) returns a matrix of complex frequency responses for each filter designed by obj.

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[H,f] = freqz(obj,ind) returns the frequency response of filters with indices corresponding to the elements in vector ind.

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[H,f] = freqz(___,Name,Value) specifies options using one or more Name,Value pair arguments.

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freqz(___) with no output arguments plots the frequency response of the filter bank.

## Examples

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Create a gammatoneFilterBank object. Call freqz to get the complex frequency response, H, of the filter bank and a vector of frequencies, f, at which the response is calculated. Plot the magnitude frequency response of the filter bank.

gammaFiltBank = gammatoneFilterBank;
[H,f] = freqz(gammaFiltBank);

plot(f,abs(H))
xlabel('Frequency (Hz)')

To get the frequency response of a subset of filters in the filter bank, specify the second argument as a row vector of indices between one and the number of filters in the filter bank. Get the frequency response of the 10th filter in the filter bank and plot the magnitude frequency response.

[H,f] = freqz(gammaFiltBank,10);

plot(f,abs(H))
xlabel('Frequency (Hz)')

To specify the number of FFT points used to compute the frequency response, use the NFFT name-value pair. Specify that the frequency response is calculated using a 128-point FFT. Plot the magnitude frequency response.

[H,f] = freqz(gammaFiltBank,'NFFT',128);

plot(f,abs(H))
xlabel('Frequency (Hz)')

To visualize the magnitude frequency response only, call freqz without any output arguments. Plot the magnitude frequency response, in dB, of filters 20, 21, and 22 using a 1024-point DFT.

freqz(gammaFiltBank,[20,21,22],'NFFT',1024)

Create an octaveFilterBank object. Call freqz to get the complex frequency response, H, of the filter bank and a vector of frequencies, f, at which the response is calculated. Plot the magnitude frequency response in dB.

octFiltBank = octaveFilterBank;
[H,f] = freqz(octFiltBank);

plot(f,20*log10(abs(H)))
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')
set(gca,'XScale','log')
axis([10 octFiltBank.SampleRate/2 -100 2])

To get the frequency response of a subset of filters in the filter bank, specify the second argument as a row vector of indices between one and the number of filters in the filter bank. Get the frequency response of the 5th filter in the filter bank and plot the magnitude frequency response in dB.

[H,f] = freqz(octFiltBank,5);

plot(f,20*log10(abs(H)))
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')
set(gca,'XScale','log')
axis([10 octFiltBank.SampleRate/2 -100 2])

To specify the number of FFT points used to compute the frequency response, use the NFFT name-value pair. Specify that the frequency response is calculated using a 8192-point FFT. Plot the magnitude frequency response in dB.

[H,f] = freqz(octFiltBank,'NFFT',8192);

plot(f,20*log10(abs(H)))
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')
set(gca,'XScale','log')
axis([10 octFiltBank.SampleRate/2 -100 2])

To visualize the magnitude frequency response only, call freqz without any output arguments. Plot the magnitude frequency response, in dB, of filters 4, 5, and 6 using a 1024-point DFT.

freqz(octFiltBank,[4,5,6],'NFFT',1024)

## Input Arguments

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Object to get filter frequency responses from, specified as an object of gammatoneFilterBank or octaveFilterBank.

Indices of filters to calculate frequency responses from, specified as a row vector of integers with values in the range [1, N]. N is the total number of filters designed by obj.

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'NFFT',2048

Number of DFT bins, specified as a positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

## Output Arguments

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Complex frequency response of each filter, returned as an M-by-N matrix. M is the number of DFT bins, specified by NFFT. N is the number of filters, which is either length(ind) or, if ind is not specified, the total number of filters in the filter bank.

Data Types: double

Frequencies at which the response is computed in Hz, returned as a column vector.

Data Types: double