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
