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PROBLEM IN PLOTTING THE FOURIER SEIRES

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Saqib Zafar
Saqib Zafar on 28 Nov 2019
hy Mr Star, I am trying to implement the code but later part of the code is not generating the required output. the Graph provided is general and we can suppose required thing to replicate it. Code is shown below:
clc
clear all;
close all;
syms t
N=18;
T1=2;
T2=4;
T3=6;
syms t w
xw1=int((t^2).*exp(-j*w*t),t,0,T1);
xw2=int((T1^2).*exp(-j*w*t),t,T1,T2);
xw3=int(((-T1*t)+(3*T1^2)).*exp(-j*w*t),t,T2,T3);
xw=xw1+xw2+xw3;
w=-N:.1:N;
z=eval(xw);
plot(w,z)
%% this part isn't giving required output
syms w
x11=(1/(2*pi))*int(xw.*exp(j*w*t),w,-N,N);
t=0:.1:3*T1;
zt=eval(x11);
plot(t,zt)
Expected Result
The Output I get

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Answers (1)

Constantino Carlos Reyes-Aldasoro
Edited: Constantino Carlos Reyes-Aldasoro on 29 Nov 2019
The problem you are facing is that your calculations are generating NaNs:
>> zt
zt =
Columns 1 through 3
NaN + NaNi 0.0118 + 0.0000i 0.0412 + 0.0000i
Columns 4 through 6
0.0877 + 0.0000i 0.1595 + 0.0000i 0.2528 + 0.0000i
Columns 7 through 9
0.3593 + 0.0000i 0.4871 + 0.0000i 0.6422 + 0.0000i
Columns 10 through 12
0.8124 + 0.0000i 0.9962 + 0.0000i 1.2089 + 0.0000i
Columns 13 through 15
1.4452 + 0.0000i 1.6887 + 0.0000i 1.9540 + 0.0000i
Columns 16 through 18
2.2552 + 0.0000i 2.5655 + 0.0000i 2.8782 + 0.0000i
Columns 19 through 21
3.2399 + 0.0000i 3.6352 + 0.0000i 3.9282 + NaNi
Columns 22 through 24
4.0240 + 0.0000i 4.0011 + 0.0000i 3.9882 + 0.0000i
Columns 25 through 27
4.0045 + 0.0000i 4.0058 + 0.0000i 3.9947 + 0.0000i
Columns 28 through 30
3.9976 + 0.0000i 4.0051 + 0.0000i 4.0003 + 0.0000i
Columns 31 through 33
3.9955 + 0.0000i 4.0012 + 0.0000i 4.0039 + 0.0000i
Columns 34 through 36
3.9975 + 0.0000i 3.9967 + 0.0000i 4.0042 + 0.0000i
Columns 37 through 39
4.0024 + 0.0000i 3.9930 + 0.0000i 4.0006 + 0.0000i
Columns 40 through 42
4.0130 + 0.0000i NaN + NaNi 3.8118 + 0.0000i
Columns 43 through 45
3.6006 + 0.0000i 3.3945 + 0.0000i 3.2021 + 0.0000i
Columns 46 through 48
3.0022 + 0.0000i 2.7976 + 0.0000i 2.5997 + 0.0000i
Columns 49 through 51
2.4017 + 0.0000i 2.1992 + 0.0000i 1.9993 + 0.0000i
Columns 52 through 54
1.8012 + 0.0000i 1.5994 + 0.0000i 1.3993 + 0.0000i
Columns 55 through 57
1.2018 + 0.0000i 0.9992 + 0.0000i 0.7977 + 0.0000i
Columns 58 through 60
0.6041 + 0.0000i 0.4004 + 0.0000i 0.1891 + 0.0000i
Column 61
NaN + NaNi
>>
and that is why your lines look broken. You can do several things:
1) check the equations so that no NaNs are generated
or
2) deal with the NaNs a-posteriori, that is you can detect the nans and remove them or get the average between the neighbours (assuming that they are isolated)
>> ztn = isnan(zt)
ans =
1×61 logical array
Columns 1 through 16
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Columns 17 through 32
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Columns 33 through 48
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
Columns 49 through 61
0 0 0 0 0 0 0 0 0 0 0 0 1
>>
Once you know that you have nans, you can replace them, but be aware that this code ONLY works if the NaN has neighbour values that are valid:
zt2 = [0 zt 0]; % duplicate the function and add zeros to the sides
zt2n = isnan(zt2); % find the nans
zt2(zt2n) = 0.5*zt2(find(zt2n)-1)+0.5*zt2(find(zt2n)+1); % replace the nans with the average of neighbours
plot(t,zt2(2:end-1)) % display again
solidLines.jpg
Problem solved.
Hope that helps.

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