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# gain

CIC filter gain

gain(hm)
gain(hm,j)
gain(hs)

## Description

gain(hm) returns the gain of hm, the CIC decimation or interpolation filter.

When hm is a decimator, gain returns the gain for the overall CIC decimator.

When 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. gain(hm) returns this value. The next example presents this case.

gain(hm,j) returns the gain of the jth section of a CIC interpolation filter. When you omit j, gain assumes that 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 decimator.

gain(hs) returns the gain of the filter System object™ hs. The function supports the dsp.CICDecimator and dsp.CICInterpolator filter structures.

## Examples

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.

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.