Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 52. Decimation: The Fundamentals

This note introduces the fundamental concepts involved in decimation, which is the name given to the process of decreasing a discrete-time signal’s sampling rate while leaving all other characteristics of the signal unchanged to the maximum extent possible.

Decimation is based on the notion that some discrete-time signal of interest exists in a form that is significantly over sampled. There may be some noise and interference throughout the entire bandwidth of ± F_S/2 that is supported by the sample rate, F_S, but the signal of interest has a spectrum that is confined to a bandwidth much smaller than ± F_S/2.

Consider a discrete-time signal having the periodic spectrum shown in Figure 52.1(a). The spectral images ...