2023•Unpublished venueOpen access

Discrete Fourier Transform and Computation

S. Palani

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Abstract

After completing this chapter, you should be able to understand about Discrete Fourier Transform (DFT) and establish its relationship with other Transforms. You will also understand the important properties of DFT. As in the continuous time signal, where we study about linear convolution, here study about circular convolution. In circular convolution of two signals one should be periodic and both signals should have same number of samples. You should also be able understand about the Fast Fourier Transform (FFT) in this chapter.

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What this paper is about

After completing this chapter, you should be able to understand about Discrete Fourier Transform (DFT) and establish its relationship with other Transforms. You will also understand the important properties of DFT. As in the continuous time signal, where we study about linear convolution, here study about circular convolution. In circular convolution of two signals one should be periodic and both signals should have same number of samples. You should also be able understand about the Fast Fourier Transform (FFT) in this chapter.

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Available abstract

After completing this chapter, you should be able to understand about Discrete Fourier Transform (DFT) and establish its relationship with other Transforms. You will also understand the important properties of DFT. As in the continuous time signal, where we study about linear convolution, here study about circular convolution. In circular convolution of two signals one should be periodic and both signals should have same number of samples. You should also be able understand about the Fast Fourier Transform (FFT) in this chapter.

Key concepts: Discrete Fourier transform (general), Convolution (computer science), Discrete-time Fourier transform, Overlap–add method, Circular convolution, Fast Fourier transform, Convolution theorem, Cyclotomic fast Fourier transform

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