Graphics Programs Reference
In-Depth Information
Obviously this fi lter changes the signal dramatically. The output only con-
tains low-frequency components, whereas all higher frequencies are elim-
inated. The comparison of the periodograms of input and output reveals
that all frequencies above
f
=0.1 corresponding to a period of
τ
=10 are sup-
pressed.
[Pxx,F] = periodogram(x5,[],128,1);
[Pyy,F] = periodogram(y5,[],128,1);
plot(F,abs(Pxx),F,abs(Pyy))
Hence, we have now designed a frequency-selective fi lter, i.e., a fi lter that
eliminates certain frequencies whereas other periodicities are more or less
unaffected. The next chapter introduces tools to characterize a fi lter in the
time and frequency domain that help to predict the effect of a frequency-
selective fi lter on arbitrary signals.
6.7 Impulse Response
The impulse response is a very convenient way of describing the fi lter char-
acteristics (Fig. 6.3). A useful property of the impulse response
h
in LTI
systems involves the convolution of the input signal
x
(
t
) with
h
to obtain the
output signal
y
(
t
).
It can be shown that the impulse response
h
is identical to the fi lter weights
in the case of nonrecursive fi lters, but is different for recursive fi lters.
Alternatively, the convolution is often written in a short form:
In many examples, the convolution in the time domain is replaced by a sim-
ple multiplication of the Fourier transforms
H
(
f
) and
X
(
f
) in the frequency
domain.
The output signal
y
(
t
) in the time domain is then obtained by a reverse Fourier
