Here - TUM

Representation of Discrete Time Signals and
Spectral Transformation
Spectrum of a sampled signal:
s(t) = X
±(t ¡ nT ) $ S(!) = 2¼
T
n
xs(t) = xc(t) ¢ s(t) $
Sampling means multiplication
of continuous time signal with
pulse train
X
Stephan Henzler Mixed-Signal-Electronics 2012/13
k
±(! ¡ k!s) !s = 2¼
T
Xs(!) = 1
2¼ Xc(!) ¤ S(!)
= 1
T Xc(!) ¤ X
= 1
T
X
k
In frequency domain this translates
into convolution of signal spectrum
with spectrum of pulse train.
This is simply a copy and shift of
the spectrum to multiples of the
sampling frequency
k
Xc(! ¡ k!s)
±(! ¡ k!s)
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