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freqz

CWT filter bank frequency responses

Description

[psidft,f] = freqz(fb) returns the frequency responses for the wavelet filters, psidft, and the frequency vector, f, for the continuous wavelet transform (CWT) filter bank, fb. Frequencies are in cycles/sample or Hz. If you specify a sampling period, the frequencies are in cycles/unit time where the time unit is the unit of the duration sampling period.

The frequency responses, psidft, are one-sided frequency responses for the positive frequencies. For the analytic wavelets supported by cwtfilterbank, the frequency responses are real-valued and are equivalent to the magnitude frequency response.

example

[___] = freqz(___,Name=Value) specifies one or more additional name-value arguments. For example, psidft = freqz(fb,FrequencyRange="twosided") returns the full two-sided frequency responses.

example

freqz(___) with no output arguments plots the magnitude frequency responses for the CWT filter bank, fb.

Examples

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Load the Kobe earthquake data. Create a CWT filter bank with period boundary handling that you can apply to the data.

load kobe
fb = cwtfilterbank(SignalLength=numel(kobe),Boundary="periodic");

Obtain the two-sided wavelet and scaling filter responses.

[psidft,f] = freqz(fb,IncludeLowpass=true,FrequencyRange="twosided");

Obtain the CWT of the data. Also obtain the scaling coefficients.

[cfs,~,~,scalcfs] = wt(fb,kobe);

Invert the transform using the filter bank and the scaling coefficients.

xrec = icwt(cfs,ScalingCoefficients=scalcfs,AnalysisFilterBank=psidft);
plot([kobe(:) xrec(:)])
axis tight

Figure contains an axes object. The axes object contains 2 objects of type line.

Obtain the maximum reconstruction error.

norm(kobe(:)-xrec(:),'Inf')
ans = 2.9104e-11

Create a CWT filter bank. Set the voices per octave to 14, the sampling frequency to 1000 Hz, and frequency limits to range from 200 Hz to 300 Hz.

fb = cwtfilterbank(VoicesPerOctave=14,...
    SamplingFrequency=1000,FrequencyLimits=[200 300]);

Plot the frequency responses.

freqz(fb)

Figure contains an axes object. The axes object with title CWT Filter Bank contains 9 objects of type line.

This example shows how boundary handling and signal length affect the range of frequency responses freqz returns.

Reflection / Even Length

Create a CWT filter bank suitable for an even-length signal. Use the default Boundary setting reflection.

sLen = 256;
fb = cwtfilterbank(SignalLength=sLen);

Obtain the one-sided frequency responses of the filter bank. Also obtain the frequency vector.

[psidft,f] = freqz(fb,FrequencyRange="onesided");

Confirm the range of frequencies includes the Nyquist.

f(end)
ans = 0.5000

Plot the frequency response of the filter with the highest center frequency.

plot(f,psidft(1,:))
xlabel("Frequency (samples/cycle)")
ylabel("Magnitude")
title("Reflection / Even / One-sided")

Figure contains an axes object. The axes object with title Reflection / Even / One-sided contains an object of type line.

Obtain and plot the two-sided frequency responses. Confirm the frequency range does not include the Nyquist.

[psidft,f] = freqz(fb,FrequencyRange="twosided");
f(end)
ans = 0.9980
plot(f,psidft(1,:))
xlabel("Frequency (samples/cycle)")
ylabel("Magnitude")
title("Reflection / Even / Two-sided")

Figure contains an axes object. The axes object with title Reflection / Even / Two-sided contains an object of type line.

Reflection / Odd Length

Create a CWT filter bank suitable for an odd-length signal. Use the default Boundary setting reflection.

sLen = 255;
fb = cwtfilterbank(SignalLength=sLen);

Obtain the one-sided frequency responses of the filter bank. Confirm the range of frequencies does not include the Nyquist.

[~,f] = freqz(fb,FrequencyRange="onesided");
f(end)
ans = 0.4990

Periodic / Even Length

Create a CWT filter bank with periodic boundary handling suitable for an even-length signal

sLen = 256;
fb = cwtfilterbank(SignalLength=sLen,Boundary="periodic");

Obtain the one-sided frequency responses of the filter bank. Confirm the range of frequencies does include the Nyquist.

[~,f] = freqz(fb,FrequencyRange="onesided");
f(end)
ans = 0.5000

Periodic / Odd Length

Create a CWT filter bank with periodic boundary handling suitable for an odd-length signal

sLen = 255;
fb = cwtfilterbank(SignalLength=sLen,Boundary="periodic");

Obtain the one-sided frequency responses of the filter bank. Confirm the range of frequencies does not include the Nyquist.

[~,f] = freqz(fb,FrequencyRange="onesided");
f(end)
ans = 0.4980

Input Arguments

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Continuous wavelet transform (CWT) filter bank, specified as a cwtfilterbank object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: psidft = freqz(fb,IncludeLowpass=true) appends the lowpass, or scaling filter, frequency response as the final row of psidft.

Option to append lowpass, or scaling filter, frequency response as the final row of psidft, specified as one of these:

  • 1 (true) — Include the frequency response symmetrically

  • 0 (false) — Do not include the frequency response

For the analytic wavelets supported by cwtfilterbank, the scaling filter frequency response is real-valued and is equivalent to the magnitude frequency response.

Data Types: logical

Frequency range for the wavelet and scaling function frequency responses, specified as one of "onesided", or "twosided". The frequency ranges corresponding to each option are

  • "onesided" — returns the frequency responses from [0,½] when the length of the padded filters is even and [0,½) when the length of the padded filters is odd. Padding is added when the Boundary property of the filter bank is "reflection".

    If a sampling frequency Fs is specified in the filter bank, the intervals become [0,Fs/2] and [0,Fs/2) respectively.

  • "twosided" — returns the full two-sided frequency responses over the range [0,1). If a sampling frequency Fs is specified in the filter bank, the interval becomes [0,Fs).

Note

To use the wavelet and scaling filters in the inverse CWT, set Boundary in the filter bank to "periodic", and use IncludeLowpass=true and FrequencyRange="twosided" in freqz.

Output Arguments

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Frequency responses of a CWT filter bank, returned as a real-valued matrix. Each column of psidft is the response at the frequency in the corresponding element of f.

By default, frequency responses, psidft, are one-sided frequency responses for the positive frequencies. For the analytic wavelets supported by cwtfilterbank, the frequency responses are real-valued and are equivalent to the magnitude frequency response.

Data Types: double

Frequencies, in cycles/sample or hertz, returned as a real-valued vector.

If you specify a sampling period, the frequencies are in cycles/unit time, where the time unit is the unit of the duration SamplingPeriod.

Data Types: double

Extended Capabilities

Version History

Introduced in R2018a