How to numerically integrate two vectors in 2012a

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Chris 2012-12-15

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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.

----edit----

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.

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Image Analyst 2012-12-16

Should we assume T is less than 0, T is greater than 0, or must it be able to handle both?

Chris 2012-12-16

T>0, T= largest value of t

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Answer 1

Image Analyst 2012-12-16

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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);

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Chris 2012-12-16

编辑：Chris 2012-12-16

No, but thankyou for your time. I'm sorry my question doesnt put forward what i wish. Though, finding the solution now, your answer has a part of it in it, and infact lead me to the solution.

For anyone looking for this answer, it was a combination of cumsum, and cumtrapz.

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Answer 2

per isakson 2012-12-16

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See

    quad 
    Numerically evaluate integral, adaptive Simpson quadrature

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John D'Errico 2012-12-16

No! Quad is not the tool to do numerical integration of data vectors. Use trapz instead.

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Answer 3

Image Analyst 2012-12-16

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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.