why do we get different values by angle command

When i run this code i am getting the result as shown below

clc;clear all; close all;

N=input('Enter the fundamental period of the signal (N)');

M=input('Enter how many points of Fourier series to compute(m>N and m=multiples of N) ')

n=0:N-1;

x=[sin(2*pi*n/6)];

for k=0:M-1;

Sum=0;

for n=0:N-1;

Ck(k+1)=x(n+1)*exp(-j*2*pi*k*n/N);

Sum=Sum+Ck(k+1);

end

Ck(k+1)=Sum/N;

end

Mag=abs(Ck);Phase_ang=angle(Ck);

disp(Ck);disp(Mag);disp(Phase_ang);

Output

Enter the fundamental period of the signal (N)6

Enter how many points of Fourier series to compute(M=N or M=multiples of N) 6

M =

6

0.0000 + 0.0000i 0.0000 - 0.5000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.5000i

0.0000 0.5000 0.0000 0.0000 0.0000 0.5000

0 -1.5708 2.9229 1.5075 0.0588 1.5708

The values of phase angle are supposed to be

0 -1.5708 0 0 0 1.5708

But for the same array if i use command window i get the proper result

>>angle([0.0000 + 0.0000i 0.0000 - 0.5000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.5000i])

ans =

0 -1.5708 0 0 0 1.5708

[Stephen23]

"But for the same array..."

No, that is a different array, with different values. The values displayed (by default with four decimal places) are not the same as those stored in memory. So if you simply copy the displayed data, then you will have different values.

N=6;
M=6;
n=0:N-1;
x=sin(2*pi*n/6); % got rid of the superfluous square brackets
for k=0:M-1;
    Sum=0;
    for n=0:N-1;
        Ck(k+1)=x(n+1)*exp(-j*2*pi*k*n/N); 
        Sum=Sum+Ck(k+1);
    end 
    Ck(k+1)=Sum/N;
end
format long G
Ck

Ck = 
  Columns 1 through 3

       5.55111512312578e-17 +                     0i       5.55111512312578e-17 -                   0.5i      -1.66533453693773e-16 +  3.70074341541719e-17i

  Columns 4 through 6

       1.85037170770859e-17 +  2.91747532808639e-16i       3.14563190310461e-16 +  1.85037170770859e-17i       2.22044604925031e-16 +                   0.5i

[Kavita Guddad]

Thank you very much stephen for the answer.Got my problem solved.

Answer 1

[Sandeep Mishra]

Hello Kavita,

I understand that you are trying to create a Fourier series with M points, fundamental frequency N and you are also trying to find the phase angle and magnitude of the series.

In MATLAB, "angle" provides you with the functionality to find the phase angle of the complex array in [-π,π] interval.

In MATLAB, the default data type of numerical value is "double-precision floating-point" which requires 64 bits, So the value stored in your Sum variable and Ck series has more than 4 decimal points and it is different from your command line's input array.

You can round off the Ck array to 4 decimal places to get your desired results and compare the generated series by their difference as below.

clc;clear all; close all; 
N= 6;
M= 6;

n=0:N-1;
x=[sin(2*pi*n/6)];

for k=0:M-1
    Sum=0;
    for n=0:N-1
        Sum=Sum+x(n+1)*exp(-1j*2*pi*k*n/N); 
    end 
    Ck(k+1)=Sum/N;
end

Mag=abs(Ck);Phase_ang=angle(Ck);

% Input array
inputArray = [0.0000 + 0.0000i   0.0000 - 0.5000i  -0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.5000i];

% Difference between input array and generated result
difference = Ck - inputArray;
disp(difference);

   1.0e-15 *

   0.0555 + 0.0000i   0.0555 + 0.0555i  -0.1665 + 0.0370i   0.0185 + 0.2917i   0.3146 + 0.0185i   0.2220 + 0.0000i

% Rounding off the value
Ck = round(Ck, 4);
disp(Ck);

   0.0000 + 0.0000i   0.0000 - 0.5000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.5000i

% Angle calculated from input array
angleInput = angle(inputArray);
disp(angleInput)

         0   -1.5708         0         0         0    1.5708

% Angle calculated from generated series
angleGiven = angle(Ck);
disp(angleGiven)

         0   -1.5708         0         0         0    1.5708

You can refer to the documentation below to learn more about "angle", "double-precision floating-point", and "data-types" in MATLAB.

angle - MATLAB - MathWorks India

Double-Precision Floating Point - MATLAB - MathWorks India

Data Types - MATLAB - MathWorks India

[Kavita Guddad]

Thank you Sandeep for the answer. Got my problem solved.