How I implement this matrix?

If s(t) is a guassian signal, then the jth column of Ψi corresponds to πj that πj is a 3D vector [xj; yj; zj] is:

How can I implement this formula in MATLAB?

Answer 1

[Shlok]

Hi Navid,

I understand that you’re trying to implement the matrix , where each column is a time-shifted and normalized version of a Gaussian signal. To approach this in MATLAB, follow the following steps:

• Start by creating a time vector using "linspace", something like "t = linspace(-1, 1, 1000)" depending on your signal duration and resolution.
• Next, define your Gaussian signal as an anonymous function. For example:

s = @(t) exp(-t.^2 / (2 * sigma^2));

• Choose a suitable "sigma" based on how narrow or wide you want the pulse.
• Now, define a reference point (here, "receiver"). Then compute the delay for each ""​, use the Euclidean distance formula and divide by the propagation speed "c", like this:

delay = norm(pi_j(:, j) - receiver) / c;

• Once you have the delay, shift your signal in time by using:

shifted = s(t - delay);

• To normalize it, use the L2 norm function "norm(shifted, 2)" and divide:

normalized = shifted / norm(shifted, 2);

• Repeat this for each "j", and store the result into the matrix .

This method ensures that each column of the matrix is correctly calculated and normalized as per the above mentioned formula.

Refer to the following documentation links to know more about various functions useful in the above approach:

• linspace: https://www.mathworks.com/help/matlab/ref/double.linspace.html
• norm: https://www.mathworks.com/help/matlab/ref/norm.html

Also, the above question appears to be a homework question. To understand how to ask a homework question, you can go through the following MATLAB Answer:

https://www.mathworks.com/matlabcentral/answers/8626-how-do-i-get-help-on-homework-questions-on-matlab-answers