Convolution integral in matlab without conv function

In summary, the conversation discusses the calculation of a convolution integral and the use of discreet points to compute it. The speaker mentions using a convolution function in Matlab and comparing the results to the integral calculation, noting that they are different. They express confusion and request an explanation for the discrepancies.
  • #1
schulzy
8
0

Homework Statement



I have a convolution integral:[tex]H(\omega)=\int E_{L}(\omega -\omega_{T})E_{T}(\omega_{T})d\omega_{T}[/tex]

I would like calculate this integral at every [tex]\omega[/tex], but I have just discreet points, also first I calculated this with H=conv([tex]E_{L},E_{T}[/tex]), but I think so this is not equal with convolution integral, because we do not give the step size [tex]d\omega[/tex]

I wrote a convolution function in matlab, and I compared the two result
k=1:..
for j = 1 : length(y)
if (k-j+1>0 && k-j+1<= length(y))
S(j)=x(j)*y(k-j+1);
end
end
S;
trapz(S)*dw
sum(S)

The sum(S) is equal H(k), but if I compute the integral result, I get some different result.
I think, I misunderstand something.
Please, can somebody explain me, what is different and why do not get we the step size in the convolution function.
 
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  • #2
Homework EquationsThe Attempt at a SolutionI think, I misunderstand something. Please, can somebody explain me, what is different and why do not get we the step size in the convolution function.
 

What is a convolution integral?

A convolution integral is a mathematical operation that combines two functions to produce a third function. It is commonly used in signal processing and image processing to model the output of a linear system.

What is the purpose of using convolution in MATLAB?

The purpose of using convolution in MATLAB is to simulate the output of a linear system with the given input. It is a useful tool for analyzing and manipulating signals and images.

How do you perform a convolution integral in MATLAB without using the conv function?

To perform a convolution integral in MATLAB without using the conv function, you can use the built-in function conv2 for 2D convolution or conv for 1D convolution. Alternatively, you can also use a for loop to manually calculate the convolution.

What are the limitations of using convolution in MATLAB without the conv function?

The main limitation of using convolution in MATLAB without the conv function is that it may be computationally intensive and time-consuming, especially for large data sets. Additionally, manually calculating the convolution may be prone to human error.

Are there any alternative methods for performing a convolution in MATLAB?

Yes, besides using the conv function, there are other methods for performing a convolution in MATLAB, such as using the filter function or the convmtx function. These methods may offer different advantages or disadvantages depending on the specific application.

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