Digital Signal Processing Reference
In-Depth Information
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Sample 1
Pulse response of sample 1
Sample 2
Pulse response of sample 2
Sample 3
Pulse response of sample 3
Sample 4
Pulse response of sample 4
Sequence of the 4 samples
Input
Scale
changed
Filtert signal:
Superposition/addition/
interference of the
4 pulse responses
Output
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Illustration 209:
Digital filtering in the time domain by overlapping the pulse responses
The digital signal or the string of numbers consists of discrete “measurements” which reproduce the
instantaneous curve of the signal. Every measurement is a weighted
-pulse the pulse response of which in
the case of a rectangular-like filter curve has an Si shaped curve. As the overlapping (addition) of the
discrete measurements corresponds to the instantaneous curve of the signal, the addition of their pulse
responses must give the instantaneous curve of the filtered signal.
δ
Illustration 209 shows this in a particularly straightforward way. Here there are four equi-
distant
-pulses of different amplitudes and - below each one - the discrete sinusoidal
pulse responses. The former are intended to represent three “measurements” of the present
signal at the imput of a digital lowpass with their discrete pulse responses at the output.
δ
