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I'm offering services of research and development (R&D) and consulting.

I'll help everyone that asks me using this blog, the services of R&D and consulting are for "bigger helps" necessities.

This is the advertising about what I'm offering. If you're interested, you may tell me.

Any questions, everyone can use this blog too.

Discrete Fourier Transform - DFT

I made some posts about Discrete Fourier Transform (DFT), they're here.

But, I received a comment asking me how to do a function that implements DFT.


Let's only write a script, not optimized, that calculates DFT:

function X = DFT(x)
n = length(x); //number of elements in 'x'

omega = exp(-2*%pi*%i/n);
j=0:(n - 1);
F=omega.^(j'*j); //Fourier matrix

X = F*x(:); //X = DFT(x)
endfunction;


If anyone wants to try the showed function, you could do like this:

N = 10;
x = rand(N, 1);

X1 = DFT(x)
X2 = dft(x, -1) // dft(.) function uses flag = -1 for direct transform and flag = 1 for inverse transform
X3 = fft(x)


Now, look the values of X1, X2 and X3.


Did I help?

Fractions with numerator and denominator

I received a comment here.

The commentator asked me how to show a fraction as same as it was inserted.

For example:

x = 1/2;

disp(x)
1
-
2


So, I made a simple form for it.

-->function [x] = frac(n, d)
--> x = (n*%s)/(d*%s);
-->endfunction;

-->x1 = frac(1, 2);

-->disp(x1);

1
-
2

-->x2 = frac(2, 3);

-->disp(x2);

2
-
3

-->disp(x1 + x2);

7
-
6

-->disp(x1*x2);

2
-
6

-->x1 + 1
ans =

3
-
2

-->x1 + x2 - 2
ans =

- 5
-
6



PS.: The element %s is used in polynomial definitions.

Is it all right now?