Next |
Prev |
Up |
Top
|
JOS Index |
JOS Pubs |
JOS Home |
Search
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 zero-padded
windowed data frame:
where
is the FFT size, chosen to be
a power of two larger than
. The number
is called the zero-padding 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
frequency-shifted 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
anti-aliasing filter used with the downsampling.
The zero-padding factor is the interpolation factor for the
spectrum, i.e., each FFT bin is replaced by
bins, interpolating
the spectrum.
Next |
Prev |
Up |
Top
|
JOS Index |
JOS Pubs |
JOS Home |
Search
Download parshl.pdf