interp (Signal Processing Toolbox)

Increase sampling rate by an integer factor (interpolation).

Syntax

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

Description

Interpolation increases the original sampling rate for a sequence to a higher rate. interp performs lowpass interpolation by inserting zeros into the original sequence and then applying a special lowpass filter.

y = interp(x,r)

increases the sampling rate of x by a factor of r. The interpolated vector y is r times longer than the original input x.

y = interp(x,r,l,alpha)

specifies l (filter length) and alpha (cut-off frequency). The default value for l is 4 and the default value for alpha is 0.5.

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

returns vector b containing the filter coefficients used for the interpolation.

Example

Interpolate a signal by a factor of four:

t = 0:0.001:1; % time vector
x = sin(2*pi*30*t) + sin(2*pi*60*t);
y = interp(x,4);
stem(x(1:30)); title('Original Signal');
figure
stem(y(1:120)); title('Interpolated Signal');

Algorithm

interp uses the lowpass interpolation Algorithm 8.1 described in [1]:

1.: It expands the input vector to the correct length by inserting zeros between the original data values.

2.: It designs a special symmetric FIR filter that allows the original data to pass through unchanged and interpolates between so that the mean-square errors between the interpolated points and their ideal values are minimized.

3.: It applies the filter to the input vector to produce the interpolated output vector.

The length of the FIR lowpass interpolating filter is 2*l*r+1. The number of original sample values used for interpolation is 2*l. Ordinarily, l should be less than or equal to 10. The original signal is assumed to be band limited with normalized cutoff frequency 0

alpha

1, where 1 is half the original sampling frequency (the Nyquist frequency). The default value for l is 4 and the default value for alpha is 0.5.

Diagnostics

If r is not an integer, interp gives the following error message:

Resampling rate R must be an integer.

`decimate`	Decrease the sampling rate for a sequence (decimation).
`interp1`	One-dimensional data interpolation (table lookup) (see the online MATLAB Function Reference).
`resample`	Change sampling rate by any rational factor.
`spline`	Cubic spline interpolation (see the online MATLAB Function Reference).
`upfirdn`	Upsample, apply an FIR filter, and downsample.