For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by

Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2).

Then Y(f) is

The Hilbert transform of $$\left[ {\cos \,{\omega _1}t + \,\sin {\omega _2}t\,} \right]$$ is

The power spectral density of a deterministic signal is given by $${\left[ {\sin (f)/f} \right]^2}$$, where 'f' is frequency. The autocorrelation function of this signal in the time domain is