Creating a DFT without built in function

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Robin
Robin 2022-10-18
评论： Robin 2022-10-18
Hello, I'm trying to create a discrete fourier transform and plot amplitude without the built in matlab function. I also need to make a shift so my axis shows half positive half negative. My code dosent work, it plots the square wave which it should but it dosent plot amplitude spectrum and generate dft. Does anybode know where my code is wrong? Here's the error message:
>> question3
Array indices must be positive integers or logical values.
Error in question3>dft (line 32)
p = p+xn(n)*exp(-2*pi*1j*k*n/N);
Error in question3 (line 17)
Y = dft(x);
Here's the code:
figure(1)
Fs = 100;
Ts = 1/Fs;
T = 5;
N = T/Ts;
t = (0:Ts:(N-1)*Ts);
x = square(2*pi*t);
plot(t,x);
xlim([0,5])
ylim([-1.5, 1.5]);
legend('Square Wave');
xlabel('t(s)');
ylabel('x(t)');
grid on;
figure(2)
Y = dft(x);
omega=2*pi*(-N(2:1:N/2-1))/T;
f_hz=omega/(2*pi);
P = abs(Y/N);
stem(f_hz,P);
title('Amplitude spectrum');
xlabel('f(hz)');
ylabel('pf');
function Xk = dft(xn)
N = length(xn);
Xk = zeros(1,N);
for n=0:1:N-1
p = 0;
for k=0:1:N-1
p = xn*exp(2*pi*-1i*n*k/N);
end
Xk(k+1) = p;
end
end

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回答（1 个）

Jan
Jan 2022-10-18
编辑：Jan 2022-10-18
p = 0;
for k = 0:1:N-1
p = xn * exp(2*pi*-1i*n*k/N);
end
This overwrites p N times. Should this be a sum?
If xn is a vector, p is also. Xk(k+1) = p tries to assign a vector to the scalar element of Xk.
"My code dosent work" - Then it is useful to post a copy of the complete error message, which tells you exactly, what I have written above.
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Steven Lord
Steven Lord 2022-10-18
Thank you for adding that information. That does help determine the cause of the error. Let's look at your dft function
function Xk = dft(xn)
N = length(xn);
Xk = zeros(1,N);
for n=0:1:N-1
p = 0;
for k=0:1:N-1
p = p+xn(n)*exp(-2*pi*1j*k*n/N);
end
At the first iteration through the outer loop, n is 0. That means inside the loop you're trying to get element 0 of the array xn. Arrays in MATLAB don't have an element 0; the first element is element 1. That why MATLAB complains that the array index is neither a "positive integers or logical values" (emphasis added.)
Later in your dft function you accounted for this when you assigned to element k+1 (which in the case where k is 0 assigns to element 1, the first element) of Xk:
end
Xk(k+1) = p;
end
end
You need to do the same thing on the line where the error occurs.
Also FYI, you can simplify your expression inside the exp call a little bit. You can write complex numbers as a number followed by either i or j. So instead of computing -2*pi*1j you could use -pi*2j or -2j*pi.
Robin
Robin 2022-10-18
I changed the first element to 1, now the errors are gone. Thanks so much! (Unfortunately I'm used to program in C)
You said that I needed to do that on the lines where it said error, Y = dft(x) also said error before. Not now tho, but I guess I don't need to change that?
Also thanks for the advice on writing complex number!

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