Standard Convolution using Circular Convolution
Proof of Validity
Circular convolution of the padded sequence corresponds to the standard
Linear Filtering using the DFT
Frequency domain equivalent:
DFT and then IDFT can be used to compute standard convolution
product and thus to perform linear filtering.
Summary So Far
• Fourier analysis for periodic functions focuses on the
study of Fourier series
• The Fourier Transform (FT) is a way of transforming
a continuous signal into the frequency domain
• The Discrete Time Fourier Transform (DTFT) is a
Fourier Transform of a sampled signal
• The Discrete Fourier Transform (DFT) is a discrete
numerical equivalent using sums instead of integrals
that can be computed on a digital computer
• As one of the applications DFT and then Inverse DFT
(IDFT) can be used to compute standard convolution
product and thus to perform linear filtering 54
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