Fouriertranszformációval
Fourier transform is a mathematical tool that decomposes a function of time into its frequency components. For a function f(t) that is integrable on the real line, the continuous Fourier transform F(ω) is defined by F(ω) = ∫_{-∞}^{∞} f(t) e^{-i ω t} dt. The inverse transform recovers f from F via f(t) = (1/2π) ∫_{-∞}^{∞} F(ω) e^{i ω t} dω, under appropriate conditions.
In digital signal processing, the discrete Fourier transform (DFT) computes F_k = Σ_{n=0}^{N-1} f_n e^{-2π i k
Key properties include linearity and the time- and frequency-shift relations. The Fourier transform converts differentiation into
Applications span signal processing, audio, image and video analysis, physics, and the numerical solution of partial