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Computation of the STFT consists of the following steps:
1. Read samples of the input signal into a local buffer,
where is called the th frame of the input signal,
and
is the frame length (which we assume is odd
for reasons to be discussed later). The time advance (in
samples) from one frame to the next is called the hop size.
2. Multiply the data frame pointwise by a length spectrum analysis
window
to obtain the th windowed data
frame:
3. Extend
with zeros on both sides to obtain a zeropadded
windowed data frame:
where is the FFT size, chosen to be
a power of two larger than . The number
is called the zeropadding factor.
4. Take a length FFT of
to obtain the STFT at time :
where
, and is the sampling rate in
Hz. The STFT bin number is . Each bin
of
the STFT can be regarded as a sample of the complex signal at the
output of a lowpass filter whose input is
;
this signal is
frequencyshifted so that frequency is
moved to 0 Hz. In this interpretation, the hop size is the downsampling factor applied to each bandpass output, and the
analysis window
is the impulse response of the
antialiasing filter used with the downsampling.
The zeropadding factor is the interpolation factor for the
spectrum, i.e., each FFT bin is replaced by bins, interpolating
the spectrum.
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