Time Frequency Signal Analysis in Mathematica (MMA)

Question

I want to know " Whether there is any Tool Box in Mathematica (MMA) for the Time-Frequency (TF) Signal Analysis".

I am well-versed in MMA Programming, so want to do TF Signal Analysis in MMA. I think if there is toolbox of TF Analysis, then it will be of very much great help in long programming.

Thanks in Advance!!!!

Answer 1

If you are using an older version of Mathematica (pre v.8) and are interested in wavelets - yes, you need an add-on to perform wavelet analysis. More about it here. If you are using v.8 or above then everything wavelet-related is built-in. If you are interested in Fourier analysis - it is built in (since v.1). To showcase the capabilities of the time-frequency analysis functionality:

Suppose we have the signal $2 \exp \left(-\frac{t^2}{10}\right) \cos (5 t)$

We can visualise its Gabor transform

Wigner transform (notice the artifacts)

and the (somewhat) corrected Gabor-Wigner transform

A second test signal

and its spectrogram calculated using partitions of length 256, offset 1 and BlackmanHarrisWindow

its periodogram (with the same options as above)

Now we move onto wavelets Scalogram after a continuous wavelet transform with a Morlet wavelet

and the respective scalogram after performing a discrete wavelet transform

Just because I find it pretty - a scalogram of a simulated noise in 3D