## Discrete-Time Signals and Systems

###### The following videos work example problems related to Nyquist Sampling of continuous-time signals and the Sampling Theorem which guarantees a sampling rate the captures all information in the original signal.

Nyquist Sampling Problem 01

3/11/13

Running Time: 1:31

Given a real-valued signal x(t) that is uniquely determined by its samples when taken at a given rate, we determine the frequencies \omega such that X(\omega) (the Fourier Transform of x(t)) is equal to zero by using the sampling theorem.

Nyquist Sampling Problem 02

3/11/13

Running Time: 1:33

Given the Fourier Transform X(\omega) of the continuous-time signal x(t), we determine the Nyquist sampling rate of the signal.  The Nyquist sampling rate is just 2X the largest frequency component of the signal.

Nyquist Sampling Problem 03

3/16/13

Running Time: 2:19

A continuous-time signal x(t) is passed through an ideal low-pass filter to yield the signal y(t).  y(t) is then sampled at a given period.  We determine if y(t) can be recovered from its samples by using the Sampling Theorem.

Nyquist Sampling Problem 04

3/16/13

Running Time: 3:11

A continuous-time signal x(t) is analyzed in the frequency domain and it's Nyquist sampling rate is computed.  As x(t) is just a sum of sinusoids, its Fourier Transform X(\omega) is easily looked up in a table or just plotted from memory/inspection.

Nyquist Sampling Problem 05

5/2/13

Running Time: 4:24

A continuous-time sinc function is analyzed in the frequency domain via Fourier Transform table lookup.  The largest frequency is identified which allows the Nyquist Sampling Rate of the signal to be easily computed.

Nyquist Sampling Problem 06

5/2/13

Running TIme: 4:11

This example computes the Nyquist sampling rate of a sinc squared time domain signal.  The signals largest frequency component is found by looking up the corresponding Fourier Transform. The Nyquist rate is just twice this largest frequency.