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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!!!!

lennon310
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Sanjay Shri Hari
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1 Answers1

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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 $2 \exp \left(-\frac{t^2}{10}\right) \cos (5 t)$ Mathematica graphics

We can visualise its Gabor transform

Mathematica graphics

Wigner transform (notice the artifacts)

Mathematica graphics

and the (somewhat) corrected Gabor-Wigner transform

Mathematica graphics

A second test signal

Mathematica graphics

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

Mathematica graphics

its periodogram (with the same options as above)

Mathematica graphics

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

Mathematica graphics

and the respective scalogram after performing a discrete wavelet transform

Mathematica graphics

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

Noise

Sektor
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