DefinitionIn mathematics, the convolution theorem states that for suitable integrable functions f and g, the Fourier transform of the convolution of f and g is the pointwise product of the Fourier transform of f and the Fourier transform of g. It means taking the Fourier transform of the derivative of a function in the time domain equal to multiplication of the Fourier transform of the function by the frequency variable as shown in below image. METHODOLOGY: Fourier transform of derivatives AS Signal Processing, Image Processing AND Differential equations are frequently used to investigate the frequency content and dynamics of the analysis signals and systems. For instance if F(ω) is the Fourier transform of f(t), then the Fourier transform of the nth derivative = dtndnf, n∈Z, is (iω)nF(ω), where i is the imaginary unit and ω is the frequency variable.
