CIC filter gain
gain(hs) returns the gain
of the filter System
hs. The function
hs is a decimator,
the gain for the overall CIC decimator.
hs is an interpolator, the CIC interpolator
inserts zeros into the input data stream, reducing the filter overall
gain by 1/R, where R is the
interpolation factor, to account for the added zero valued samples.
Therefore, the gain of a CIC interpolator is (RM)N/R,
where N is the number of filter sections and M is
the filter differential delay.
this value. The next example presents this case.
gain(hs,j) returns the gain
jth section of a CIC interpolation filter.
When you omit
j is 2*N, where N is the
number of sections, and returns the gain of the last section of the
filter. This syntax does not apply when
hs is a
To compare the performance of two interpolators, one a CIC filter and the other an FIR filter, use gain to adjust the CIC filter output amplitude to match the FIR filter output amplitude. Start by creating an input data set, a sinusoidal signal x.
fs = 1000; % Input sampling frequency. t = 0:1/fs:1.5; % Signal length = 1501 samples. x = sin(2*pi*10*t); % Amplitude = 1 sinusoid. x = x'; l = 4; % Interpolation factor for FIR filter. d = fdesign.interpolator(l); firInterp = design(d,'multistage','SystemObject',true); yfir = firInterp(x);
r = 4; % Interpolation factor for the CIC filter. d = fdesign.interpolator(r,'cic'); cicInterp = design(d,'multisection','SystemObject',true); ycic = cicInterp(x); gaincic = gain(cicInterp); subplot(211); plot([yfir; double(ycic)]); subplot(212) plot([yfir; double(ycic)/gain(cicInterp)]);
After correcting for the gain induced by the CIC interpolator, the second subplot shows that the FIR filter and the CIC filter provide nearly identical interpolation.