The Engineer's Guide to Standards Conversion - Snell

a) Input
spectrum
b) Output
spectrum
Halved
sampling rate
Aliasing
Fig 3.1.3 a) Is the spectrum of a sampled system. Reducing the sampling rate
alone causes aliasing b) as the sidebands are unchanged in width.
As the reconstruction filter has the same frequency response, the reconstructed
output waveform must be identical to the original band-limited waveform prior to
sampling. Interpolation may be used to increase or decrease the sampling rate.
Interchange between 525 and 625 line standards will require one or the other
depending on the direction, as will HDTV and SDTV interchange. Fig 3.1.3a) shows
the spectrum of a typical sampled system where the sampling rate is a little more
than twice the analogue bandwidth. Attempts to halve the sampling rate for
downconversion by simply omitting alternate samples, a process known as
decimation, will result in aliasing, as shown in b). It is intuitive that omitting every
other sample is the same as if the original sampling rate was halved. In any sampling
rate conversion system, in order to prevent aliasing, it is necessary to incorporate
low-pass filtering into the system where the cut-off frequency reflects the lower of
the two sampling rates concerned.
An FIR type low-pass filter, as described in section 2, could be installed
immediately prior to the interpolator, but this would be wasteful, as it has been seen
above that interpolation itself requires such a filter. It is much more effective to
combine the anti-aliasing function and the interpolation function in the same filter.
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