# centfrq

Wavelet center frequency

## Description

example

FREQ = centfrq(wname) returns the center frequency in hertz of the wavelet specified by wname (see wavefun for more information).

FREQ = centfrq(wname,ITER) uses ITER many iterations to generate the wavelet.

[FREQ,XVAL,RECFREQ] = centfrq(wname,ITER,'plot') returns the associated center frequency-based approximation RECFREQ evaluated on the grid XVAL and plots the wavelet function and RECFREQ.

## Examples

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This example shows how to determine the center frequency in hertz for Daubechies' least-asymmetric wavelet with 4 vanishing moments.

cfreq = centfrq('sym4');

Obtain the wavelet and create a sine wave with a frequency equal to the center frequency, cfreq, of the wavelet. Use a starting phase of $-\pi$ for the sine wave to visualize how the oscillation in the sine wave matches the oscillation in the wavelet.

[~,psi,xval] = wavefun('sym4');
y = cos(2*pi*cfreq*xval-pi);
plot(xval,psi,'linewidth',2);
hold on;
plot(xval,y,'r');

This example shows to convert scales to frequencies for the Morlet wavelet. There is an approximate inverse relationship between scale and frequency. Specifically, scale is inversely proportional to frequency with the constant of proportionality being the center frequency of the wavelet.

Construct a vector of scales with 32 voices per octave over 5 octaves for data sampled at 1 kHz.

Fs = 1000;
numvoices = 32;
a0 = 2^(1/numvoices);
numoctaves = 5;
scales = a0.^(0:numvoices*numoctaves-1).*1/Fs;

Convert the scales to approximate frequencies in hertz for the Morlet wavelet.

Frq = centfrq('morl')./scales;

You can also use scal2frq to convert scales to approximate frequencies in hertz.

## Input Arguments

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Wavelet, specified as a character vector or string scalar. See wavefun for more information.

Number of iterations, specified by a positive integer, used to generate the wavelet wname. Internally, centfrq uses wavefun to generate the wavelet.

## Output Arguments

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Wavelet center frequency in hertz, returned as a scalar.

Grid where the center frequency-based approximation to the wavelet is evaluated, returned as a real-valued vector.

Center frequency-based approximation to the wavelet, returned as a vector. Depending on the wavelet, RECFREQ is either a real- or complex-valued vector.

## Version History

Introduced before R2006a