Geoscience Reference
In-Depth Information
1-interp1(f,magnitude,1/20)
ans =
0.4260
results in the expected ~43% reduction in the amplitude of a sine wave with
a period of 20. h e sine wave with a period of 15 experiences an amplitude
reduction of
1-interp1(f,magnitude,1/15)
ans =
0.6751
i.e., approximately 68%, which is similar to the value observed previously. It
is very important that such a running mean wipes out certain frequencies,
e.g., those for which
magnitude=0
. As an example, applying the i lter to a
signal with a period of approximately
1/0.09082
completely eliminates
that signal. Furthermore, since the magnitude of the frequency response
is the absolute value of the complex frequency response
h
, the magnitude
response is actually negative between
~0.09082
and
~0.1816
, between
~0.2725
and
~0.3633
, and between
~0.4546
and the Nyquist frequency. All signal
components having frequencies within these intervals are mirrored on the
t
-axis. As an example we try a sine wave with a period of 7 (e.g., a frequency
of approximately
0.1429
), which is within the i rst interval with a negative
magnitude response:
t = (1:100)';
x10 = 2*sin(2*pi*t/7);
b10 = ones(1,11)/11;
m10 = length(b10);
y10 = filter(b10,1,x10);
y10 = y10(1+(m10-1)/2:end-(m10-1)/2,1);
y10(end+1:end+m10-1,1) = zeros(m10-1,1);
plot(t,x10,t,y10)
h e sine wave with a period of 7 experiences an amplitude reduction of
1-interp1(f,magnitude,1/7)
ans =
0.7957
i.e., approximately 80%, but also changes the sign as we can see from the
plot. h e elimination of certain frequencies and l ipping of the signal have