MATLAB Code for Interpolation and Up-Sampling

This section presents MATLAB source code for interpolation, also known as up-sampling. We’ll explore the fundamentals of interpolation/up-sampling techniques. Interpolation involves adding new samples between existing values in a vector. This effectively increases the sample rate of the signal or vector, hence the term “up-sampling.”

The most effective approach is to estimate the values between two existing samples to fill in the newly inserted sample values. Several techniques exist, including nearest neighbor, linear, spline, and cubic interpolation.

Up-sampling an Exponential Vector

Here’s an example of how to up-sample an exponential vector in MATLAB:

clc;
clear all;

n = input('Enter length of input sample sequence: ');
l = input('Enter the value of up-sampling factor: ');
m = 0:n-1;
a = input('Enter the value of base of exponent function: ');
x = a.^m;

% Upsampling the exponential vector
y = zeros(1, l*length(x));
y([1:l:length(y)]) = x;

%figure,plot(x);
%figure,plot(y);

figure, stem(m, x);
xlabel({'Time n'; '(a)'});
ylabel('Amplitude');
title('Interpolation input');

figure, stem(m, y(1:length(x)));
xlabel({'Time n'; '(b)'});
ylabel('Amplitude');
title('Upsampled output');

This code first takes user inputs for the length of the input sequence (n), the up-sampling factor (l), and the base of the exponential function (a). It then generates the exponential vector x and creates a new vector y with a length l times that of x. Finally, it inserts the values of x into y with a spacing of l, effectively up-sampling the signal. The stem function is used to visualize the original and upsampled signals.

Up-sampling using resample Function

MATLAB also provides a built-in function called resample for up-sampling. Here’s how to use it:

xi = x;
yi = resample(xi, l, 1);

figure, stem(m, yi(1:length(x)));
xlabel({'Time n'; '(b)'});
ylabel('Amplitude');
title('Upsampled output using matlab function');

This snippet uses the resample function to up-sample the original signal xi by a factor of l. The result is stored in yi and then plotted.

The interp1 Function

Another useful MATLAB function for interpolation/up-sampling is interp1. It offers various interpolation methods like ‘nearest’, ‘linear’, ‘spline’, and ‘cubic’.

Example Images

Here are some example images related to the code:

Interpolation matlab code input image

interpolation input exponential function image

upsampled output image

upsampled output matlab function