How to integrate functions dependant on heaviside functions.

Question

Marco Ramirez 2018-4-1

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https://ww2.mathworks.cn/matlabcentral/answers/391906-how-to-integrate-functions-dependant-on-heaviside-functions

回答： Walter Roberson 2018-4-1

I'm trying to integrate the functions powerSquared and innerProduct but nothing seems o work. the following is my code:

           clc
           clear all
           close all
            t = linspace(0,4);
            y = @(t) heaviside(t)-2*heaviside(t-2)+heaviside(t-4);
            x = @(t) (t).*heaviside(t)-2*(t-1).*heaviside(t-1)+2*(t-3).*heaviside(t-3)-(t-4).*heaviside(t-4);
 powerSquared = @(x) x.^2;
 innerProduct = @(x,y) y.*x;
        inner = integral(powerSquared,0,1)
       energy = integral(innerProduct,0,1)
            c = inner./energy

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Answer 1

Walter Roberson 2018-4-1

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https://ww2.mathworks.cn/matlabcentral/answers/391906-how-to-integrate-functions-dependant-on-heaviside-functions#answer_312941

在 MATLAB Online 中打开

innerProduct = @(x,y) y.*x is a function of two variables, but you are using integral() with it, which is the integral of a function of 1 variable.

It is confusing that you are using functions named x and y but you are using parameter names x and y.

My guess at what you want:

            t = linspace(0,4);
            y = @(t) heaviside(t)-2*heaviside(t-2)+heaviside(t-4);
            x = @(t) (t).*heaviside(t)-2*(t-1).*heaviside(t-1)+2*(t-3).*heaviside(t-3)-(t-4).*heaviside(t-4);
 powerSquared = @(t) x(t).^2;
 innerProduct = @(t) y(t).*x(t);
        inner = integral(powerSquared,0,1)
       energy = integral(innerProduct,0,1)
            c = inner./energy