In this lesson you will learn how downsampling is implemented to reduce the sampling rate of a signal. You will also learn the effect of downsampling on the discrete-time Fourier transform of the signal.

Downsampling is an important method for balancing cost in practical signal processing systems.

## Prerequisites

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ankith MAnjuanath says

can u please explain how to solve the first question!

Thanks and regards

Ankith Manjunath

Barry Van Veen says

The discrete-time signal occupies the band -pi to pi radians. In order to downsample by 5, you have to reduce the bandwidth to -pi/5 to pi/5. In general, to downsample by P, you have to filter at pi/P radians.

Note that although the sampling frequency of 1000 Hz has nothing to do with the answer in this problem, it does allow an analogy to be made. Downsampling by 5 is "equivalent" to sampling the original continuous-time signal at 200 Hz. Satisfying the sampling theorem would require lowpass filtering at 100 Hz. This maps to a discrete-time frequency of pi/5.