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tqwtmra

Tunable Q-factor multiresolution analysis

Since R2021b

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    Syntax

    mra = tqwtmra(wt,n)
    mra = tqwtmra(wt,n,QualityFactor=qf)
    tqwtmra(___)

    Description

    mra = tqwtmra(wt,n) returns the tunable Q-factor wavelet multiresolution analysis (MRA) for the TQWT analysis, wt, obtained with the default quality factor of 1.

    mra = tqwtmra(wt,n,QualityFactor=qf) uses the quality factor qf in obtaining the tunable Q-factor MRA. qf must match the value used in obtaining wt from tqwt.

    example

    tqwtmra(___) with no output arguments plots the tunable Q-factor wavelet MRA in a new figure. For complex-valued data, the real part is plotted in the first color in the MATLAB® color order matrix and the imaginary part is plotted in the second color. This syntax does not support multidimensional MRAs.

    Examples

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    Open Live Script

    Load an ECG signal. Obtain the TQWT of the signal down to level 6 with a quality factor of 2.

    load wecg
wt = tqwt(wecg,QualityFactor=2,Level=6);

    Obtain the tunable Q-factor MRA of the signal.

    mra = tqwtmra(wt,length(wecg),QualityFactor=2);

    Plot the original signal and the lowpass subband.

    plot(wecg)
hold on
plot(mra(end,:),linewidth=2)
hold off
axis tight
legend(["Original","Lowpass"])

    Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Original, Lowpass.

    Confirm the sum along the rows of the MRA equals the original signal.

    mraSum = sum(mra,1);
max(abs(mraSum(:)-wecg(:)))
    ans = 
9.4369e-16
    Open Live Script

    Load the Kobe earthquake data. Obtain the tunable Q-factor wavelet transform of the data using a quality factor of 3. 

    load kobe
qf = 3;
wt = tqwt(kobe,QualityFactor=qf);

    Identify the subbands that contain at least 15% of the total energy. Note that the last element of wt contains the lowpass subband coefficients.

    EnergyBySubband = cellfun(@(x)norm(x,2)^2,wt)./norm(kobe,2)^2*100;
idx15 = EnergyBySubband >= 15;
bar(EnergyBySubband)
title("Percent Energy By Subband")
xlabel("Subband")
ylabel("Percent Energy")

    Figure contains an axes object. The axes object with title Percent Energy By Subband, xlabel Subband, ylabel Percent Energy contains an object of type bar.

    Obtain a multiresolution analysis and sum those MRA components corresponding to previously identified subbands.

    mra = tqwtmra(wt,numel(kobe),QualityFactor=qf);
ts = sum(mra(idx15,:));
plot([kobe ts'])
axis tight
legend("Original Data","Large Energy Components",...
        Location="NorthWest")
xlabel("Time (s)")

    Figure contains an axes object. The axes object with xlabel Time (s) contains 2 objects of type line. These objects represent Original Data, Large Energy Components.

    Input Arguments

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    Tunable Q-factor wavelet transform, specified as a cell array. The elements of wt contain the wavelet subband and lowpass coefficients. wt is expected to be the output of tqwt.

    Data Types: single | double
    Complex Number Support: Yes

    Original signal length in samples, specified as a positive integer. If the original signal length n is odd, n is extended to n+1 to obtain the MRA and the final sample is removed before returning the MRA.

    Data Types: single | double

    Quality factor, specified as a real-valued scalar greater than or equal to 1. If unspecified, the quality factor defaults to 1.

    Example: wt = tqwtmra(qt,2024,QualityFactor=1.5) specifies a quality factor of 1.5.

    Data Types: single | double

    Output Arguments

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    Multiresolution analysis, returned as an array. mra is an Ns-by-N-by-C-by-B array where Ns denotes number of subbands in the tunable Q-factor wavelet transform ordered by decreasing center frequency, N is the number of signal samples in time, C is the number of channels, and B is the batch size.

    Data Types: single | double

    References

    [1] Selesnick, Ivan W. “Wavelet Transform With Tunable Q-Factor.” IEEE Transactions on Signal Processing 59, no. 8 (August 2011): 3560–75. https://doi.org/10.1109/TSP.2011.2143711.

    Extended Capabilities

    Version History

    Introduced in R2021b

    See Also

    Apps

    Functions

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