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Results tagged with fourier-transform
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user 334706
A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.
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Derivation of Wigner Function of cosine with phase
The Wigner Function of $x(t)$ is
$$ W(t,f) = \frac{1}{2\pi}\int x\Big(t+\frac{\tau}{2}\Big)x^*\Big(t-\frac{\tau}{2}\Big) e^{-j2\pi f\tau}\;d\tau $$
I know how to get the $W(t,f)$ of $$x(t)=\cos(2\pi f …
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