Generation of n_th anonymouse Walsh function

I need Walsh functions for fourier approximation of some test function (let it be sinx on interval from -pi to pi). So I need to find n_th Walsh function as a function of x to use in integral for coefficients. Here is my try (I tried to use haddamar matrices)

function y = wal(x,n)
    N = 2^n;
    H = hadamard(N); 
    id = fix(x*N -1e-9) + 1;
    y = H(N,id);
end

But here is my problem, first of all these functions are not correct. Secondly, they are defined only on (0,1) interval, and I don't know how to generalise in on [-pi,pi]. Thirdly input x is an array, and I need to make anonymous func @(x), but then my id is undefined and function is not working at all

Answer 1

[Suraj Kumar]

Hi Andrei,

To generate the nth Walsh function in MATLAB, you can refer to the following steps and the attached code snippets:

1. To use Walsh functions over the interval [-π, π], you can map this interval to the interval [0,1].

% Map x from [-pi, pi] to [0, 1] 
x_mapped = (x + pi) / (2 * pi); 

2. Ensure the Hadamard matrix is of appropriate size to compute the Walsh function correctly by using ‘nextpow2’ function.You can refer the following documentations for more information:

https://www.mathworks.com/help/matlab/ref/double.nextpow2.html

N = 2^nextpow2(n); 
H = hadamard(N); 

3. Use ‘arrayfun’ function to compute the Walsh function for each element in the array and calculate the index in the Hadamard matrix ensuring it is within the bounds.

walshFunc = @(x) arrayfun(@(xi) computeWalsh(xi, n, H, N), x); 
id = fix(x_mapped * N - 1e-9) + 1; 
if id > N 
    id = N; 
elseif id < 1 
    id = 1; 
end 

For more information on ‘hadamard’ or ‘arrayfun’ function in MATLAB, kindly go through the following links:

• https://www.mathworks.com/help/matlab/ref/hadamard.html
• https://www.mathworks.com/help/matlab/ref/arrayfun.html

Hope this helps!