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# intfilt() - Signal Processing

```b = intfilt(l,p,alpha) designs
a linear phase FIR filter that performs ideal bandlimited interpolation
using the nearest 2*p nonzero
samples, when used on a sequence interleaved with l-1 consecutive
zeros every l samples. It assumes an original bandlimitedness
of alpha times the Nyquist frequency. The returned filter is identical
to that used by interp. b is
length 2*l*p-1.alpha is inversely proportional to the transition bandwidth
of the filter and it also affects the bandwidth of the don't-care
regions in the stopband.  Specifying alpha allows you to specify how
much of the Nyquist interval your input signal occupies. This is beneficial,
particularly for signals to be interpolated, because it allows you
to increase the transition bandwidth without affecting the interpolation
and results in better stopband attenuation for a given l and p.
If you set alpha to 1, your signal is assumed to occupy the entire
Nyquist interval. Setting alpha to less than one allows for don't-care
regions in the stopband. For example, if your input occupies half
the Nyquist interval, you could set alpha to 0.5.b = intfilt(l,n,'Lagrange') designs
an FIR filter that performs nth-order Lagrange
polynomial interpolation on a sequence interleaved with l-1 consecutive
zeros every r samples. b has
length (n+1)*l for n even,
and length (n+1)*l-1 for n odd.
If both n and l are even, the
filter designed is not linear phase.Both types of filters are basically lowpass and have a gain
of l in the passband.```

### Syntax

`b = intfilt(l,p,alpha)b = intfilt(l,n,'Lagrange')`

### Example

```Digital Interpolation FilterOpen This ExampleDesign a digital interpolation filter to upsample a signal by seven, using the bandlimited method. Specify a "bandlimitedness" factor of 0.5 and use
samples in the interpolation.upfac = 7;
alpha = 0.5;
h1 = intfilt(upfac,2,alpha);
The filter works best when the original signal is bandlimited to alpha times the Nyquist frequency. Create a bandlimited noise signal by generating 200 Gaussian random numbers and filtering the sequence with a 40th-order FIR lowpass filter. Reset the random number generator for reproducible results.lowp = fir1(40,alpha);

rng('default')
x = filter(lowp,1,randn(200,1));
Increase the sample rate of the signal by inserting zeros between each pair of samples of x.xr = upsample(x,upfac);
Use the filter function to produce an interpolated signal.y = filter(h1,1,xr);
Compensate for the delay introduced by the filter. Plot the original and interpolated signals.delay = mean(grpdelay(h1));

y(1:delay) = [];

stem(1:upfac:upfac*length(x),x)
hold on
plot(y)

xlim([400 700])

intfilt also performs Lagrange polynomial interpolation.First-order polynomial interpolation is just linear interpolation, which is accomplished with a triangular filter.Zeroth-order interpolation is accomplished with a moving average filter and resembles the output of a sample-and-hold display.Interpolate the original signal and overlay the result.h2 = intfilt(upfac,1,'Lagrange');

y2 = filter(h2,1,xr);
y2(1:floor(mean(grpdelay(h2)))) = [];

plot(y2)
hold off```