Convolution on a nonlinearly spaced data set.

Hi,

I am currently trying to use conv on a data set that is nonlinearly spaced. The convolution works, the issue I'm having is reproducing the amplitude of the convolution signal. For example, if it were a linearly spaced dataset I'd use u = conv(h,f)*dt; where dt is the spacing between points.

In my case I don't have a consistent dt value since it varies. Any suggestions on how to approach this? Thanks, Charles

[Matt J]

In what way does the convolution "work", as you have it so far, if you aren't yet accounting for the varying sample spacing? And is there a reason you don't just apply interp1() and resample the signals so that they are equi-spaced?

[Senaasa]

It works insofar that the profile of the convolution is correct, but the amplitude is incorrect. I had been using a loop to calculate the convolution so I have a comparison. Interpolating is possible, however I wanted to use conv to try to speed up my convolutions. If I have to interpolate and add points (in this case probably several thousand), I'm not sure how much of a benefit I'd gain by using conv. I was hoping there was a cleaner way just through the implementation of conv.

Answer 1

[Image Analyst]

Like Matt J says, the usual solution is to get evenly spaced intervals using interpolation, such as interp1() or spline().

Here's a spline demo if you want to do a cubic fit between the points:

% Demo to show spline interpolation.
% Clean up / initialize
clc; 
close all; 
clear all; 
workspace; % Display workspace panel.

% Create the original knot points.
lengthX = 10;
x = 1:lengthX;
y = rand (lengthX,1);
% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.

% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;
newXSamplePoints = linspace(1, lengthX, lengthX * samplingRateIncrease);
smoothedY = spline(x, y, newXSamplePoints);

% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(newXSamplePoints, smoothedY, '-ob');
title('Spline Interpolation Demo', 'FontSize', 20);

legend('Original Points', 'Spline Points');

% Mathworks Demo code from their Help
% x = 0:10;
% y = sin(x);
% xx = 0:.25:10;
% yy = spline(x,y,xx);
% plot(x,y,'o',xx,yy)

The input points don't need to be uniformly spaced like I did in the demo.