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.

y =
interp(x,r) increases
the sampling rate of x, the input signal, by
a factor of r. The interpolated vector, y, is r times
as long as the original input, x.

y =
interp(x,r,n,alpha) specifies
two additional values. 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.

[y,b] = interp(x,r,n,alpha) also
returns a vector, b, with the filter coefficients
used for the interpolation.

Normalized cutoff frequency of the input signal, specified as
a positive real scalar not greater than 1. A value of 1 means that
the signal occupies the full Nyquist interval.

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.

References

[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.