When I do Time-Frequency analysis using choi William's distribution for a Sine wave (using real data) I should get a single line indicating only one frequency should present over the entire time duration. But I see two lines which is mirror image of the above. Even for FMCW i see the same way.
But if I perform the same for Complex data, I see only one line. Both are having same no of samples (1024) while performing CWD.
The Fourier transform of a real signal is symmetric; hence the mirror image. To ommit this redundancy, we use the analytic version of the signal, which is complex, and results in positive frequency spectra
Generally, the Choi-Williams Distribution (CWD) is a function that is conjugate symmetric with respect to the time and frequency variables and does not always produce a mirror image of a complex-valued signal. However, when the CWD is computed using a uniform window and a Gaussian kernel for real-valued data, the symmetric property of the Fourier transform implies that the resulting CWD will exhibit a mirror image.
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