Signal Processing

Convolution & Fourier transformation

Convolution & Fourier transformation
Convolution in time domain can be converted to multiplication in frequency domain by Fourier transformation.

r (t) = s (t) * h (t) \circ - ∙ R (f) = S (f) H (f)

\int | s (t) |^{2} d t \circ - ∙ \int | S (f) |^{2} d f

s (τ) ⋆ g (τ) = s^{*} (- τ) * g (τ)

s^{*} (τ) * g (τ) = s (- τ) ⋆ g (τ)