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Interpolation — increase sampling rate by integer factor

```
y =
interp(x,r)
```

```
y =
interp(x,r,n,alpha)
```

`[y,b] = interp(x,r,n,alpha)`

Interpolation increases the original sampling rate of a sequence
to a higher rate. It is the opposite of decimation. `interp`

inserts
0s into the original signal and then applies a lowpass
interpolating filter to the expanded sequence.

specifies
two additional values. `y`

=
interp(`x`

,`r`

,`n`

,`alpha`

)`n`

is half the number of
original sample values used to interpolate the expanded signal. Its
default value is 4. It should ideally be less than or equal to 10. `alpha`

is
the normalized cutoff frequency of the input signal, specified as
a fraction of the Nyquist frequency. It defaults to 0.5. The lowpass
interpolation filter has length `2*n*r + 1`

.

`interp`

uses the lowpass interpolation algorithm
8.1 described in [1].

It expands the input vector to the correct length by inserting 0s between the original data values.

It designs a special symmetric FIR filter that allows the original data to pass through unchanged and interpolates to minimize the mean-square error between the interpolated points and their ideal values. The filter used by

`interp`

is the same as the filter returned by`intfilt`

.It applies the filter to the expanded input vector to produce the output.

[1] Digital Signal Processing Committee of
the IEEE Acoustics, Speech, and Signal Processing Society, eds. *Programs
for Digital Signal Processing*. New York: IEEE Press, 1979,
chap. 8.

[2] Oetken, G., Thomas W. Parks, and H. W. Schüssler.
“New results in the design of digital interpolators.” *IEEE ^{®} Transactions
on Acoustics, Speech, and Signal Processing*. Vol. ASSP-23,
1975, pp. 301–309.

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