Geoscience Reference
In-Depth Information
6.8 Frequency Response
We next investigate the frequency response of a i lter, i.e., the ef ect of a i lter
on the amplitude and phase of a signal (Fig. 6.4). h e frequency response
H
(
f
) of a i lter is the Fourier transform of the impulse response
h
(
t
). h e
absolute value of the complex frequency response
H
(
f
) is the magnitude
response of the i lter
A
(
f
).
h e argument of the complex frequency response
H
(
f
) is the phase response
of the i lter.
Since MATLAB i lters are all causal it is dii cult to explore the phase of
signals using the corresponding functions included in the Signal Processing
Toolbox. h e user's guide for this toolbox simply recommends that the i lter
output be delayed in the time domain by a i xed number of samples, as we
have done in the previous examples. As another example a sine wave with a
period of 20 and an amplitude of 2 is used as an input signal.
clear
t = (1:100)';
x8 = 2*sin(2*pi*t/20);
b
a
Fig. 6.4 a
Magnitude and
b
phase response of a running mean over eleven elements.
