How to create fft Magnitude and Phase using stem Matlab?

With the function

cos(w0t)

, first create your own time domain data and second, conduct

the FT (Fourier transform). When you solve the problem, use the MATLAB codes with

two “for ~ end” loops without using already built-in functions except for the fundamental

ones such as “linspace” and “cos”. Then draw the result of the FT in frequency domain in

terms of “Magnitude vs. freq.” and “Phase vs. freq.” by using “stem” instead of “plot”.

Here, let’s set w0=2pi/T and T = 1(sec).

Answer 1

[EE_student]

This is the amplitude spectrum for cos(2*pi*1*t) for a 2 second long signal length. I will leave the phase spectrum up to you.

clear
clc
clearAllMemoizedCaches
clear
sampleR= 1000; % sample rate in Hz
t= 0:1/sampleR:2; % time vector
N= length(t);  % number of samples

signal= cos(2*pi*1*t);  % defining signal
% random dc offset,amplitude and frequency 

t_hat= (0:N-1)/N ;  % normalised time vector
harmonics= zeros(size(signal)); % empty vector that stores the computed Harmonics

plot(t,signal)
grid on
title('Signal(t)')
xlabel('Time')
ylabel('Amplitude')
for delta_f=1:N
    e= exp(-1j*2*pi*(delta_f-1)*t_hat);
    harmonics(delta_f)= (sum(signal.*e))/N;
end

freq= linspace(0,sampleR/2,floor(N/2)+1); % scaling frequency 
amp= abs(harmonics);    % extracting amplitudes and scaling them 
amp(2:length(freq)) = 2*amp(2:length(freq)); % double only the ac harmonics 
stem(freq,amp(1:length(freq)))           % making the vectos same in length 
xlim([0 10])              % limits must be included 
title('DFT of Signal(t)')
xlabel('Freq/Hz')
ylabel('Amplitude')
grid on