Page 142 - MATLAB Recipes for Earth Sciences

136 6 Signal Processing

function filter,

b9 = ones(1,11)/11;
m9 = length(b9);
y9 = filter(b9,1,x9);

y9= y9(1+(m9-1)/2:end-(m9-1)/2,1);
y9(end+1:end+m9-1,1)=zeros(m9-1,1);

The output is again in phase with the input, but the amplitude is dramatically
reduced as compared to the input.

plot(t,x9,t,y9)
1-max(y9(40:60))/2

ans =
0.6768

The running mean over eleven elements reduces the amplitude of this sig-

nal by 67%. More generally, the filter response obviously depends on the
frequency of the input. The frequency components of a more complex sig-
nal containing multiple periodicities. Hence, they are affected in a different
way. The frequency response of a fi lter

clear
b10 = ones(1,11)/11;

can be computed using the function freqz.

[h,w] = freqz(b10,1,512);
The function freqz returns the complex frequency response h of the digital
fi lter b10. The frequency axis is normalized to ›. We transform the fre-
quency axis to the true frequency values by
f= w/(2*pi);

Next we calculate the magnitude of the frequency response and plot the
magnitude over the frequency.
magnitude = abs(h);

plot(f,magnitude)
xlabel('Frequency'), ylabel('Magnitude')
title('Magnitude')

This plot can be used to predict the magnitude of the filter for any frequency