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The Fourier transform decomposes a signal (a function of time) into frequencies, giving the energy at each frequency.

15 votes
1 answer
9k views

Characteristic function and Fourier transform

I understand the definition of characteristic functions used in probability theory: For a random Variable $X$ with probability density function $f_X$ the characteristic function is defined as: $$\phi_ …
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3 votes
1 answer
697 views

Deconvolution with fourier transform or characteristic function?

Let us consider the following model: $$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$ Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have …
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