I have a complex signal in the time domain normally distributed. What will be its distribution in the frequency domain?
I assumed since the frequency domain is a linear transformation the distribution will not change.
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Sign up to join this communityI have a complex signal in the time domain normally distributed. What will be its distribution in the frequency domain?
I assumed since the frequency domain is a linear transformation the distribution will not change.
I assume you mean that at each time $t$, the signal is a normally-distributed random variable. This tells you the probability that the signal will take a value in any given range, but it does not tell you whether/how the signal values at different times are related to one another. Typically, for a random signal one defines not only the probability distribution for the signal at each time, but also the autocorrelation function $E \{ x(t) x(u) \}$ or some other measure of how signal values at different times are related or independent. This is required in order to determine how the signal is distributed in the frequency domain.