How to plot these equations ?

Hello

I'm trying to plot these polynomials shown in the image, but I keep receiving errors and I'm not if my code is correct of not. Could you please help ?

regards

clear all
close all
clc
%%

Fs = 1000;                    % Sampling frequency
T = 1/Fs;                     % Sampling period
L = 1024;                     % Length of signal
t = 2*(0:L-1)*T;               % Time vector
x = 0;
c = 1+i;

P(1) = 1;
Q(1) = 1;
P(2) = P(1) + exp(i*(2^(0))*t)*Q(1);
Q(2) = P(1) - exp(i*(2^(0))*t)*Q(1);
P(3) = P(2) + exp(i*(2^(1))*t)*Q(2);
Q(3) = P(2) - exp(i*(2^(1))*t)*Q(2);
P(4) = P(3) + exp(i*(2^(2))*t)*Q(3);
Q(4) = P(3) - exp(i*(2^(2))*t)*Q(3);

for m=1:16
    x = x +c*exp(i*2*pi*m*t).*P(m);
end

figure
subplot(2,2,1)
plot(t,x)
title('signal')

[Image Analyst]

What is this "x" that you're overwriting on each iteration of the for loop? I thought you wanted to compute p and q, not x.

And MATLAB thinks i is a variable. So if you want to use it as a variable you need to use

i = sqrt(-1);

or else use a 1 in front of it: 1i

[Matt J]

They don't look like polynomials to me. Also, they are complex-valued, so what does it mean to "plot" them? If you want to plot their absolute value, do plot(t,abs(x)).

[Mohamed Ahmed]

I did try plot them but I keep getting this error "Unable to perform assignment because the left and right sides have a different number of elements"

[Mohamed Ahmed]

x is waveform I want to plot which will contait the frequency components.

I tried using i = sqrt(-1);

but it wasn't the problem, I keep getting this error "Unable to perform assignment because the left and right sides have a different number of elements" for this line ==> "P(2) = P(1) + exp(i*(2^(0))*t)*Q(1);"

[Matt J]

That is correct. P(2) is a scalar location. It cannot hold a vector

[Mohamed Ahmed]

Answer 1

[Matt J]

Change P(m) to P{m} and Q(m) to Q{m} everwhere.

Fs = 1000;                    % Sampling frequency
T = 1/Fs;                     % Sampling period
L = 1024;                     % Length of signal
t = 2*(0:L-1)*T;               % Time vector
x = 0;
c = 1+i;


P{1} = 1;
Q{1} = 1;

for m=2:16
    
P{m} = P{m-1} + exp(1i*(2^(m-2))*t).*Q{m-1};
Q{m} = P{m-1} - exp(1i*(2^(m-2))*t).*Q{m-1};
    
end

for m=1:16
    x = x +c*exp(1i*2*pi*m*t).*P{m};
end

whos x

  Name      Size              Bytes  Class     Attributes

  x         1x1024            16384  double    complex   

[Mohamed Ahmed]

I received this error "Index exceeds the number of array elements (2)"

[Matt J]

Make sure you're using my latest iteration of the code.

[Mohamed Ahmed]

Yes, It worked, I also plotted the magnitude and phase spectrum of the signal.

Is this plot considered a flat spectrum ?

Thank you :)

[Matt J]

I'm glad it worked, but please Accept click the answet to indicat so.

Whether it's to be considered flat is probably subjective...