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Understanding Discrete Fourier Transform through Matrix Equations

Explore how to calculate discrete Fourier transform using matrix equations. Discover the consistent results with Fourier transforms, such as impulses and constant spectrums. Learn about DFT of a specific sequence.

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Understanding Discrete Fourier Transform through Matrix Equations

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  1. The previous example suggests that the discrete Fourier transform can be calculated using a matrix equation:

  2. For the previous examples we have x[n]=d[n]

  3. x[n]=1

  4. In both cases the results are consistent with Fourier transforms: the Fourier transform of an impulse is a constant (white) spectrum, and the Fourier transform of a constant is an impulse in frequency domain (just a D.C. component). Suppose that we found the DFT of x[n] = {1 –1 1 –1}.

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