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

Note 21. Using Window Functions: Some Fundamental Concepts

Within DSP, window usage can be divided into two broad categories: (1) windowing of signal segments to reduce leakage in the DFT, and (2) designing FIR filters that are based on using windows to reduce the Gibb’s phenomenon in finite approximations to ideal filters. Additional details concerning the use of windows for FIR filter design are discussed in Notes 23 and 24.

21.1. Elementary Windows

As discussed in Note 14, truncating a DFT input sequence to a length of N samples can be mathematically modeled as multiplying the sequence by a rectangular window sequence that has non-zero values only for sample indices 0 through N – 1

21.1

Rectangular windows are not particularly well suited ...