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

Note 15. Exploring DFT Leakage

This note uses the model of signal truncation developed in Note 14 and applies this model to sinusoidal signals to demonstrate how leakage can corrupt a DFT result—often to the point where the DFT results can be misleading when used to estimate signal frequency. The insights provided by this demonstration are the foundation for the introduction and analysis of windowing techniques in Notes 23 through 27.

The effects of truncation are absent in cases where the input signal is a sinusoid having a frequency that exactly matches one of the DFT bin frequencies. For example:

• Consider a DFT with N = 32 and T = 1.

• The signal of interest is x(t) = cos(2πf_ct), where f_c = 4F.

• Figure 15.1 shows the DFT magnitude spectrum ...