itqwt

Inverse tunable Q-factor wavelet transform

Since R2021b

Syntax

xrec = itqwt(wt,n)

xrec = itqwt(wt,n,Name=Value)

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.

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

Examples

Inverse Tunable Q-factor Wavelet Transform

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")

Input Arguments

wt — Tunable Q-factor wavelet transform

cell array

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

n — Original signal length

positive integer

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)

Level — Reconstruction level

0 (default) | nonnegative integer

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

QualityFactor — Quality factor

1 (default) | positive scalar

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

xrec — Inverse tunable-Q wavelet transform

vector | matrix | 3-D array

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™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

• The TQWT array wt is the only supported input argument.

Version History

Introduced in R2021b