Discrete Fourier Transforms

(S&K Chapter 10)

We investigate methods of representing an arbitrary sequence as the sum of sinusoids e.g. for spectral analysis.
Recall the bilateral z-transform :

The domain variable z is a complex number.

To study frequency properties we define transforms for which the domain variable is the digital frequency , a real variable.

• The Discrete Time Fourier Transform (DTFT)
• The Discrete Fourier Transform (DFT)
• DFT frequencies in Hertz
  • Absolute amplitude from X(k)
  • Frequency resolution of the DFT
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