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The short-term Fourier transform

First extract N samples of speech starting at tex2html_wrap_inline2919 and then window:


eqnarray382

Now apply the DFT.

The result is continuous, but it can be sampled at n points without loss of information.
eqnarray389

This equation defines an algorithm that takes an array of N complex numbers (or equivalently an array of N real numbers and N imaginary numbers) and returns an array of N complex numbers.

The inverse short-term DFT can be similarly defined:
eqnarray395


Speech Vision Robotics group/Tony Robinson