scales

CWT filter bank scales

Syntax

rs = scales(fb)

[rs,cs] = scales(fb)

Description

rs = scales(fb) returns the raw (unitless) scales, or dilation factors, used in creating the wavelet bandpass filters.

[rs,cs] = scales(fb) also returns the wavelet scales expressed as the normalized period of the wavelet corresponding to the scale in samples.

Examples

CWT Filter Bank Scales

Create a CWT filter bank with a sampling period of 0.001 seconds. By default, the filter bank uses the analytic Morse (3,60) wavelet and 10 voices per octave.

fb = cwtfilterbank(SamplingPeriod=seconds(0.001));

Obtain the raw and normalized scales used in creating the wavelet bandpass filters.

[rs,cs] = scales(fb);

Confirm the scales increase by a factor of approximately $$2^{1/|NV|}$$, where $$NV$$ is the number of voices per octave.

nv = 10;
scaleRatios = rs(2:end)./rs(1:end-1);
[2^(1/nv) min(scaleRatios) max(scaleRatios)]

ans = 1×3

    1.0718    1.0718    1.0718

Confirm the normalized scales are equivalent to the wavelet center periods divided by the sampling period. Plot the normalized wavelet center periods as a function of the raw scale.

P = centerPeriods(fb);
Pnormalized = P/seconds(0.001);
plot(rs,[cs(:) Pnormalized(:)])
ylabel("Center Periods (Samples)")
xlabel("Unitless Scale (Dilation Factor)")
title("Normalized Center Period by Dilation Factor")
grid on

Input Arguments

fb — Continuous wavelet transform filter bank

cwtfilterbank object

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

Output Arguments

rs — Raw scales

vector

Raw scales used in creating the wavelet bandpass filters, returned as a real-valued vector of length Ns, where Ns is the number of wavelet bandpass frequencies. Scales are ordered from finest scale to coarsest scale.

Data Types: double

cs — Normalized scales

vector

Normalized scales, returned as a real-valued vector of length Ns, where Ns is the number of wavelet bandpass frequencies. The scales are expressed as the normalized period of the wavelet corresponding to the scale in samples. Equivalently, cs contains the wavelet center periods divided by the sampling period. The elements of cs are ordered from the smallest normalized period to the largest normalized period.

Data Types: double

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018a