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itqwt

Inverse tunable Q-factor wavelet transform

    Description

    xrec = itqwt(wt,n) returns the inverse tunable Q-factor transform (TQWT) of the analysis coefficients in wt. wt is a cell array containing the wavelet subband and lowpass coefficients obtained from tqwt using the default quality factor of 1. n is the original signal length specified as a positive scalar.

    example

    xrec = itqwt(wt,n,Name=Value) specifies one or more additional name-value arguments. For example, xec = itqwt(x,1024,QualityFactor=2) specifies a quality factor of 2.

    Examples

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    Load an ECG signal. Obtain the tunable Q-factor wavelet transform to the default maximum decomposition level using a quality factor of 3.

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

    Reconstruct the data from the subband coefficients and confirm perfect reconstruction.

    xrec = itqwt(wt,length(wecg),QualityFactor=qf);
    max(abs(xrec-wecg))
    ans = 5.5511e-16
    

    Return the inverse TQWT at the coarsest scale.

    xrec = itqwt(wt,length(wecg),QualityFactor=qf,Level=length(wt)-2);
    plot(wecg)
    hold on
    plot(xrec,LineWidth=2)
    hold off
    axis tight
    legend("Original Signal","Reconstruction")

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

    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 n is odd, n+1 is used internally to invert the TQWT and the first n samples are returned.

    Data Types: single | double

    Name-Value Arguments

    Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

    Example: xrec = itqwt(wt,2048,Level=3,QualityFactor=2)

    Reconstruction level of analysis coefficients, specified as a nonnegative integer less than or equal to length(wt)-2. If unspecified, itqwt reconstructs the TQWT up to the resolution level of the original signal.

    Example: xrec = itqwt(x,Level=1) returns the inverse TQWT at level 1.

    Data Types: single | double

    Quality factor, specified as a positive scalar greater than or equal to 1. The quality factor must match the value used in the TQWT.

    Example: xrec = itqwt(x,QualityFactor=2) specifies a quality factor of 2.

    Data Types: single | double

    Output Arguments

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    Inverse tunable-Q wavelet transform, returned as a vector, matrix, or 3-D array.

    Data Types: single | double

    Tips

    • To reconstruct only the scaling coefficients, specify a reconstruction level of length(wt)-1.

    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

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

    Introduced in R2021b