Compute a continuous wavelet transform:

Show all the voices for the 8octave:

Use Normal to get all wavelet coefficients explicitly:

Also use All as an argument to get all coefficients:

Use "IndexMap" to find out what wavelet coefficients are available:

Extract specific coefficient arrays:

Extract several wavelet coefficients corresponding to the list of wavelet index specifications:

Extract all coefficients whose wavelet indexes match a pattern:

WaveletScalogram gives a time scale representation of wavelet coefficients:

More voices per octave increases the scale resolution:

Higher number of octaves gives a wider spectrum of scale range:

A single frequency shows up as a horizontal band at the equivalent scale:

Multiple frequencies show up as multiple bands at the equivalent scales:

Sinusoid with linearly increasing frequency:

Wavelet transform gives a good time localization of features:

Higher frequencies are resolved at lower octaves and lower frequencies at higher octaves:

Resolve time and frequency features of a signal:

Use GaborWavelet to perform a continuous wavelet transform:

There is an inverse relationship between scale values and frequency values:

Find pairs of {oct,voc} that resolve frequencies 20 Hz and 70 Hz:

Verify using a WaveletScalogram:

Compute the wavelet transform using different wavelet families:

A narrow wavelet function will have good time and scale resolution:

A broad wavelet function will have poor time and scale resolution:

Use different families of wavelets to capture different features:

MexicanHatWavelet (default):

DGaussianWavelet:

GaborWavelet:

MorletWavelet:

PaulWavelet:

ContinuousWaveletTransform works on Sound as input:

Speech analysis using ContinuousWaveletTransform:

The orange patches correspond to the words "You will return safely to Earth":

Extract octaves 5 and 6:

The settings for Padding are the same as the methods for ArrayPad, including "Periodic":

"Reversed":

"ReversedNegation":

"Reflected":

"ReflectedDifferences":

"ReversedDifferences":

"Extrapolated":

Padding has no effect on the length of wavelet coefficients:

Padding pads the input data to the next higher power of 2 to reduce boundary effects:

Boundary effects at the start:

Boundary effects at the end:

For lists, the Automatic value of SampleRate is set to 1:

Explicitly set the sample rate:

For Sound data, the Automatic value of SampleRate is extracted from the Sound data object:

SampleRate is used for normalizing wavelet transform coefficients:

WaveletScale indicates the smallest resolvable scale used for the transform:

The scales used are given as with wavelet scale, octave, and voice:

By default, WorkingPrecision->MachinePrecision is used:

Use higher-precision computation:

Real wavelet functions can be used to isolate peaks or discontinuities:

Complex wavelets can be used to capture oscillatory behavior:

Amplitude of wavelet coefficients:

Phase of wavelet coefficients:

ContinuousWaveletTransform can be used to filter frequencies:

Filter the cosine with frequency :

Perform InverseContinuousWaveletTransform on a thresholded data object:

The final filtered signal:

Identify musical notes using a scalogram:

Generate a sequence of pitches corresponding to an equal-tempered scale at 300 Hz:

Compute frequencies resolved corresponding to octaves and voices:

Find pairs of {oct,voc} that resolve frequencies 300 Hz: