amplitude and phase spectrum

i have this signal.

x=8*cos(30*pi*t+pi/3)+6*sin(50*pi*t-pi/3)+8*cos(70*pi*t-pi/4)

i want to make

1. single-sided amplitude spectrum
2. single-sided phase spectrum
3. double-sided amplitude spectrum
4. double-sidedphase spectrum

i want the final graphs to look like this. how do i do this ? This above image is just an example not the correct values. Im confused because all the answers suggest fft

Answer 1

[Star Strider]

No idea what the sampling frequency is, so I created one.

Try this:

Fs = 600;
t = linspace(0, Fs*10, Fs*10)/Fs;
x=8*cos(30*pi*t+pi/3)+6*sin(50*pi*t-pi/3)+8*cos(70*pi*t-pi/4);
L = numel(t);
Fc = fft(x)/L;
Ts = mean(diff(t));
Fn = Fs/2;
Fv2 = linspace(-Fn, Fn, numel(t));
figure
subplot(2,1,1)
plot(Fv2, fftshift(abs(Fc)))
title('Amplitude')
grid
subplot(2,1,2)
plot(Fv2, angle(fftshift(Fc)))
title('Phase')
grid
sgtitle('Double-Sided Fourier Transform')

Fv = linspace(0, 1, fix(L/2)+1)*Fn;
Iv = 1:numel(Fv);
figure
subplot(2,1,1)
plot(Fv, abs(Fc(Iv))*2)
title('Amplitude')
grid
subplot(2,1,2)
plot(Fv, angle(Fc(Iv)))
title('Phase')
grid
sgtitle('Single-Sided Fourier Transform')

.