In this lesson you will learn why aliasing occurs when sampling a signal. Aliasing is when a continuous-time sinusoid appears as a discrete-time sinusoid with multiple frequencies. The sampling theorem establishes conditions that prevent aliasing so that a continuous-time signal can be uniquely reconstructed from its samples. The sampling theorem is very important in signal processing. It tells us how fast we have to sample a signal with a given bandwidth to guarantee a unique correspondence between continuous- and discrete-time signals.

This lesson “simplifies” the sampling theorem because it only uses the non uniqueness of discrete-time sinusoids and the mapping between continuous- and discrete-time frequency. The next two lessons take a more conventional Fourier transform based approach to developing the sampling theorem.

## Prerequisites

## Video

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Chinmay Upadhye says

In general scenario, we use uppercase Omega for DT sugnals & lowercase omega for CT signals. Why this annotation is changed in the video ? (It is used as reverse case)

Barry Van Veen says

The notation that I use throughout the website is for

continuous-timefrequency and fordiscrete-timefrequency. This notation is the same as that used inDiscrete-Time Signal Processingby Oppenheim and Schafer. So this video is consistent with the rest of the site, as best I know.Chinmay Upadhye says

In 6th slide, why shouldn't we consider bandwidth as 20 pi instead of 10 pi ?

Barry Van Veen says

For the purpose of the sampling theorem, bandwidth is defined as the maximum positive frequency present in the signal. It does not include negative frequency. So in this example the maximum positive frequency is 10$$\pi[\latex] rads/sec and we use that for the bandwidth.