Time Frequency Signal Analysis in Mathematica (MMA)
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