interp

Interpolation — increase sample rate by integer factor

Syntax

y = interp(x,r)

y = interp(x,r,n,cutoff)

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

Description

y = interp(x,r) increases the sample rate of input signal x by a factor of r.

y = interp(x,r,n,cutoff) specifies two additional values:

• n is half the number of original sample values used to interpolate the expanded signal.

• cutoff is the normalized cutoff frequency of the input signal, specified as a fraction of the Nyquist frequency.

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

Examples

Interpolate Signal

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')

Input Arguments

x — Input signal

vector

Input signal, specified as a vector.

Data Types: double | single

r — Interpolation factor

positive integer

Interpolation factor, specified as a positive integer.

Data Types: double | single

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 × n × r + 1.

Data Types: double | single

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.

Data Types: double | single

Output Arguments

y — Interpolated signal

vector

Interpolated signal, returned as a vector. y is r times as long as the original input x.

Data Types: double | single

b — Lowpass interpolation filter coefficients

column vector

Lowpass interpolation filter coefficients, returned as a column vector.

Data Types: double | single

Algorithms

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 [1]:

1. Expand the input vector to the correct length by inserting 0s between the original data values.

2. 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 algorithm that interp uses to design the interpolation filter depends on the data type of the input signal x:

   • Single precision — interp uses the frequency-domain least-squares algorithm on x to design the coefficients of the interpolation filter.

   • Double precision — interp uses the time-domain least-squares algorithm on a band-limited subspace of x to design the coefficients of the interpolation filter. The function partitions the design of interpolation filters of order 2*r*(n+1) into r polyphase subfilters to enhance the computation performance.

3. Apply 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.

[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, No. 3, June 1975, pp. 301–309.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a