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The Nyquist-Shannon sampling theorem states that an original continuous signal can be perfectly reconstructed from its discrete time samples. The sampling frequency must be larger than twice the maximum frequency contained in the band-limited signal:
Top: Continuous-time signal. Bottom: Discrete-time signal. The folding frequency is marked by the red line.
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Aliasing Aliasing occurs for undersampled signals containing frequencies higher than the Nyquist frequency. This effect causes unwanted signals, distortions or artifacts in the desired frequency band. Folding Folding can be observed in practice when viewing the spectrum of audio samples, such as in the figure.Aliasing. Wikipedia. https://en.wikipedia.org/wiki/Aliasing Aliasing around the folding frequency A creaful inspection of the spectrum above reveals that the aliased spectrum below
can be obtained by folding the original spectrum like an accordion with pleats at every odd multiple of
.
Consequently, the frequency
is called the folding frequency. Clearly, then, periodic sampling automatically forces a folding of the frequency axis of an analog signal at odd multiples of
,
and this results in the relationship between the frequencies for continuos-time signals and discrete-time signals.
[Extracted from: J.G. Proakis & D.K.Manolakis(2014): Digital Signal Processing(New International Edition).Pearson. p. 402] Audio demo Can you hear a dissonance in the audio signal? The inharmonic combination of tones yields to a sensation of roughness. |