Interpolation — increase sample rate by integer factor
Create a sinusoidal signal sampled at 1 kHz. Interpolate it by a factor of four.
t = 0:1/1e3:1; x = sin(2*pi*30*t) + sin(2*pi*60*t); y = interp(x,4);
Plot the original and interpolated signals.
subplot(2,1,1) stem(0:30,x(1:31),'filled','MarkerSize',3) grid on xlabel('Sample Number') ylabel('Original') subplot(2,1,2) stem(0:120,y(1:121),'filled','MarkerSize',3) grid on xlabel('Sample Number') ylabel('Interpolated')
x — Input signal
Input signal, specified as a vector.
r — Interpolation factor
Interpolation factor, specified as a positive integer.
n — Half the number of input samples used for interpolation
4 (default) | positive integer
Half the number of input samples used for interpolation, specified as a
positive integer. For best results, use
n no larger
than 10. The lowpass interpolation filter has length 2 ×
r + 1.
cutoff — Normalized cutoff frequency
0.5 (default) | positive scalar
Normalized cutoff frequency of the input signal, specified as a positive real scalar not greater than 1 that represents a fraction of the Nyquist frequency. A value of 1 means that the signal occupies the full Nyquist interval.
b — Lowpass interpolation filter coefficients
Lowpass interpolation filter coefficients, returned as a column vector.
Interpolation increases the original sample rate of a sequence to a higher rate. It is
the opposite of decimation.
interp inserts zeros into the original
signal and then applies a lowpass interpolating filter to the expanded sequence. The
function uses the lowpass interpolation algorithm 8.1 described in :
Expand the input vector to the correct length by inserting 0s between the original data values.
Design 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
interpis the same as the filter returned by
Apply the filter to the expanded input vector to produce the output.
 Digital Signal Processing Committee of the IEEE Acoustics, Speech, and Signal Processing Society, eds. Programs for Digital Signal Processing. New York: IEEE Press, 1979.
 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, No. 3, June 1975, pp. 301–309.