Fourier Theorems for the DTFT

This section states and proves selected Fourier theorems for the DTFT.
A more complete list for the DFT case is given in
[263].^{3.4}Since this material was originally part of an appendix, it is
relatively dry reading. Feel free to skip to the next chapter and
refer back as desired when a theorem is invoked.

As introduced in §2.1 above, the Discrete-Time Fourier Transform (DTFT) may be defined as

(3.8) |

We say that is the

- Linearity of the DTFT
- Time Reversal
- Symmetry of the DTFT for Real Signals

- Shift Theorem
- Convolution Theorem
- Correlation Theorem
- Autocorrelation
- Power Theorem
- Stretch Operator
- Repeat (Scaling) Operator
- Stretch/Repeat (Scaling) Theorem
- Downsampling and Aliasing

- Differentiation Theorem Dual

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