Spectral Leakage

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speech-processing

DFT computes the spectrum at N evenly spaced discrete frequencies and assumes periodicity outside the analysis frame. That is the signal repeats outside of the sampled window.

Spectral leakage refers to [see page 11, discontinuities] which occur due to DFT assuming a signal is periodic. This can happen for:

• periodic signals with a non-whole number of cycles in the analysis frame. Signal gets cut off in the middle of a cycle.
• All aperiodic and stochastic signals.

You can visualise the affect [see page 12, here], notice how the input is a perfect sine wave sampled at a non-integer number of cycles. DFT assumes each input sample is repeated outside of the analysis frame so we get a completely different spectrum for the assumed signal to what the input was.

Leakage Reduction

Applying a Windowing function to the signal reduces the leakage affect from discontinuities... but it also broadens the peaks (peaks are brought closer to other points).