Graphics Programs Reference
In-Depth Information
6.8 Frequency Response
Next we investigate the frequency response of a fi lter, i.e., the effect of a fi l-
ter on the amplitude and phase of a signal (Fig. 6.4). The frequency response
H ( f ) of a fi lter is the Fourier transform of the impulse response h ( t ). The
absolute of the complex frequency response H ( f ) is the magnitude response
of the fi lter A ( f ).
The argument of the complex frequency response H ( f ) is the phase response
of the fi lter.
Since MATLAB fi lters are all causal it is diffi cult to explore the phase of sig-
nals using the corresponding functions contained in the Signal Processing
Toolbox. The user·s guide for this toolbox simply recommends to delay the
fi lter output in the time domain by a fi xed number of samples, as we have
done it in the previous examples. As an example, a sine wave with a period
of 20 and an amplitude of 2 is used as an input signal.
Magnitude
Unwrapped Phase
1
0
−200
0.8
0.6
−400
0.4
−600
0.2
−800
0
−1000
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
Frequency
Frequency
a
b
Fig. 6.4 a Magnitude and b phase response of a running mean over eleven elements.
Search WWH ::




Custom Search