CIC filter gain
gain(hm) returns the gain
hm, the CIC decimation or interpolation filter.
hm is a decimator,
the gain for the overall CIC decimator.
hm 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(hm,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
hm is a
gain(hs) returns the gain
of the filter System object™
hs. The function
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
fs = 1000; % Input sampling frequency. t = 0:1/fs:1.5; % Signal length = 1501 samples. x = sin(2*pi*10*t); % Amplitude = 1 sinusoid. l = 4; % Interpolation factor for FIR filter. d = fdesign.interpolator(l); hm = design(d,'multistage'); ym = filter(hm,x); r = 4; % Interpolation factor for the CIC filter. d = fdesign.interpolator(r,'cic'); hcic = design(d,'multisection'); ycic = filter(hcic,x); gaincic = gain(hcic); subplot(211); plot(1:length(ym),[ym; double(ycic)]); subplot(212) plot(1:length(ym),[ym; double(ycic)/gain(hcic)]);
After correcting for the gain induced by the CIC interpolator, the figure shows the filters provide nearly identical interpolation.