Main Content


Tunable Q-factor multiresolution analysis

Since R2021b


    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.

    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.


    collapse all

    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.

    hold on
    hold off
    axis tight

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

    mraSum = sum(mra,1);
    ans = 9.4369e-16

    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;
    title("Percent Energy By Subband")
    ylabel("Percent Energy")

    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",...
    xlabel("Time (s)")

    Input Arguments

    collapse all

    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

    collapse all

    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


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

    Extended Capabilities

    Version History

    Introduced in R2021b