2.3.2 Downsampling:
How Does Downsampling Work?
For a technical explanation of the sampling theorem, please consult our
speech recognition course notes. Downsampling is one application
of multirate signal processing, and is a straightforward extension
of the time-domain interpretation of the sampling theorem.
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The first step in downsampling is filtering.
In digital sound files, the sampling frequency must be at
least twice as high as the highest frequency component in the signal.
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The filter allows the lower frequencies to pass and removes the
higher frequencies. This filter is called a
low pass filter.
Removal of these frequency components is essential in avoiding
distortion when the sample frequency of the signal is decreased.
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If the new sample frequency is half of the original sample
frequency, the resulting file will only be half as large.
The quality of sound is lower because high frequency information
has been removed.
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Once filtered, samples can be simply dropped from the digital file.
For example, if we wanted to downsample a 16 kHz sound file to an
8 kHz sound file, we would drop every other sample.
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In practice, downsampling can be implemented very efficiently by
using
finite impulse response filter
and combinations of integer ratios to achieve the desired change in
frequencies. This allows filtering to be performed at the output
frequency rather than the input frequency. Since the output frequency is
often much lower than the input frequency, this results in significant
computational savings.
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