An N-point DFT is often used to analyze a sampled signal that is much longer in duration than N samples. Truncating the DFT input sequence usually introduces spurious frequency content, called leakage, that is not present in the original signal. In order to analyze the effects of truncation, we need to start with a mathematical model of the truncation process. The relationships among the various signals and spectra discussed in this note are summarized in Figure 14.1, below. These relationships are used in Note 15 to explore DFT leakage for sinusoidal input signals.
Figure 14.1. Relationships among the various signals and spectra involved in the analysis of leakage in the DFT