How to numerically integrate two vectors in 2012a
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Bold = edit I've been trying to integrate two vectors t & a each with approx 100 values. I need to integrate c(T) = int a(t) dt between T and 0.
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I have two vectors a, and t. I need a vector answer c. each vector has aprox 100 values, and i need c to have this amount of answers too
c(T) = integral of a(b) with respect to t (dt), between T and 0. (T>0)
And i need c(T) to be in vector form. I've tried trapz, but this only gives me a single value. And i cant use the 'quad', or 'intergral' function, as i do not have an imput function. (Or cannot figure out how to create a function for this that works).
I am getting my a, and t, values from another function. Each t value corresponds to each a value.
3 Comments
Image Analyst
on 16 Dec 2012
Should we assume T is less than 0, T is greater than 0, or must it be able to handle both?
Accepted Answer
Image Analyst
on 16 Dec 2012
Joe, is this what you mean?
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
imtool close all; % Close all imtool figures.
clear; % Erase all existing variables.
workspace; % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
t = linspace(0, 15, 350);
% Create some crazy function.
period = 5;
a = t .* abs(sin(2*pi*t/period) + 1);
% Plot it
subplot(3,1,1);
plot(t, a, 'b-', 'LineWidth', 3);
grid on;
title('Original Signal', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Get the cdf
cdf = cumsum(a);
subplot(3,1,2);
plot(t, cdf, 'b-', 'LineWidth', 3);
grid on;
title('CDF of Original Signal', 'FontSize', fontSize);
% Let's say T = 5.
% Find out what element has t = 5
startingElement = find(t >= 5, 1, 'first')
% Get the integral from that point on.
subplot(3,1,3);
cdf5 = max(0, cdf - cdf(startingElement));
plot(t, cdf5, 'b-', 'LineWidth', 3);
grid on;
title('Integral of signal from 5 on', 'FontSize', fontSize);
More Answers (2)
per isakson
on 16 Dec 2012
See
quad
Numerically evaluate integral, adaptive Simpson quadrature
1 Comment
John D'Errico
on 16 Dec 2012
No! Quad is not the tool to do numerical integration of data vectors. Use trapz instead.
Image Analyst
on 16 Dec 2012
Here's what my help for int says:
int
--- help for filtstates.int ---
int Convert a FILTSTATES.CIC object to an integer matrix.
int(Hs) returns an signed integer matrix for the FILTSTATES.CIC
object.
EXAMPLE:
Hm = mfilt.cicdecim;
hs = Hm.states; % Returns a FILTSTATES.CIC object
states = int(hs); % Convert object to a signed integer matrix.
See also
FILTSTATES/CIC.
Obviously not what you want. Depending on how you define integrate, you can use sum() or trapz().
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