Review of DSP Fundamentals

Nyquist Theorem:

In order to allow exact reconstruction back into the continuous-time domain, an analog signal must be sampled at a rate greater then twice its highest frequency;

Discrete-Time Linear Time Invariant Systems (LTI):

Block Diagram:

The difference equation:

Note that:

The spectrum of a sampled signal is periodic, with a period in frequency of fs (sampling frequency).

- If the restrictions indicated by the Nyquist Theorem are followed, then the main "replica" of the periodic spectrum, centered at 0 frequency, can be isolated with a Low-Pass Reconstruction Filter, to retrieve the original analog signal.

- If the restrictions indicated by the Nyquist Theorem are not observed, extraneous frequency components from other replicas will appear in the signal, even after the application of the Low- Pass Reconstruction Filter. This is called "Aliasing".

- Aliasing can be prevented (minimized) by enforcing the Nyquist frequency limit with an "Antialising" Low-Pass Filter applied to the analog signal to be sampled