Page 147 - MATLAB Recipes for Earth Sciences

6.9 Filter Design 141

Lowpass Filter Highpass Filter

Passband Passband
Transition Transition
Stopband Stopband
1.0 1.0

0.5 Cutoff 0.5 Cutoff
Frequency Frequency
0 0
0 0.25 0.5 0.75 1.0 0 0.25 0.5 0.75 1.0
Frequency Frequency
a b
Bandpass Filter Bandstop Filter
Passband Passband Passband
Transition Transition Transition Transition
Stopband Stopband Stopband
1.0 1.0

0.5 0.5

0 0
0 0.25 0.5 0.75 1.0 0 0.25 0.5 0.75 1.0
Frequency Frequency
c d

Fig. 6.5 Frequency response of the fundamental types of frequency-selective fi lters. a

Lowpass filter to suppress the high-frequency component of a signal. In earth sciences, such
filters are often used to suppress high-frequency noise in a low-frequency signal. b Highpass

filter are employed to remove all low frequencies and trends in natural data. c-d Bandpass

and bandstop filters extract or suppress a certain frequency band. Whereas the solid line in

all graphs depicts the ideal frequency response of a frequency-selective fi lter, the gray band

shows the tolerance for a low-order design of such a filter. In practice, the frequency response

lies within the gray band. Higher-order filters allow to approximate the ideal line better than
low-order fi lters.

differences of causal vs. non-causal versions of the same filter. Filtering and
plotting the results clearly illustrates the effects of the fi lter.
xf12 = filtfilt(b12,a12,xn12);