Triangle Sprectrum and Aliasing.
Cuthbert Nyack
One way of viewing aliasing is illustrated in the applet below for a
triangular spectrum. When the Highest Frequency/Sampling Frequency is
less than ½ then the green line shows the analog spectrum and
also the spectrum of the recovered signal after filtering by a LPF with
upper cutoff uqual to ½ the sampling frequency. When the
Highest Frequency/Sampling Frequency is greater than ½ then the
spectrum centered at the sampling frequency now extends to frequencies
less than ½ the sampling frequency as shown by the orange curve.
The shaded orange area shows the portion of the spectrum centered at the
sampling frequency which gets added to the part of the spectrum centered
at zero.
If there were no aliasing, then the spectrum of the recovered filtered
signal would be shown by the magenta line i.e. spectrum of the analog
signal cutoff at ½ the sampling frequency. In fact the spectrum of the
recovered signal is shown by the red lines(shifted slightly upwards)
and includes the aliased shaded orange contribution. The shaded green
region shows the portion of the spectrum centered at zero which gets
added to the spectrum centered at the sampling frequency.
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© 1999 Cuthbert A. Nyack.