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Inverse Fourier analysis problem - matlab

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0

$begingroup$

Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.

The pulse looks like this

syms t
x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;

With the code below, I acquire 16 first coefficients of the series:

NT = 15;
X=[];
ind = -NT : NT;
for p = ind
 Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
 X(p + NT + 1) = Xn;
end

However, while doing the inverse operation, the supposed graph of three periods is:

• of frequency 2 times greater


• of amplitude 2 times smaller


• "lifted" 0.5 units up

... and looks like this

The code:

BND = [t1,t2] + offset; 
step = (BND(2) - BND(1))/1000;
tt = [BND(1)-T0 : step: BND(2) + T0];
xx1 = zeros(1,length(tt));
figure
plot(tt,xx1,'m');
hold on;
for n = ind+NT+1
 xx1_n = X(n)*exp(1i*w0*n*tt);
 xx1 = xx1 + xx1_n;
 plot(tt,abs(xx1_n),'r');
 plot(tt,abs(xx1),'m');
 title(sprintf('n = %d',n-NT));
 pause(0.5)
end
plot(tt,abs(xx1),'k','LineWidth',2);

What am I doing wrong?

fourier-analysis fourier-series matlab

share|cite|improve this question

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

$endgroup$

add a comment | 

0

$begingroup$

Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.

The pulse looks like this

syms t
x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;

With the code below, I acquire 16 first coefficients of the series:

NT = 15;
X=[];
ind = -NT : NT;
for p = ind
 Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
 X(p + NT + 1) = Xn;
end

However, while doing the inverse operation, the supposed graph of three periods is:

• of frequency 2 times greater


• of amplitude 2 times smaller


• "lifted" 0.5 units up

... and looks like this

The code:

BND = [t1,t2] + offset; 
step = (BND(2) - BND(1))/1000;
tt = [BND(1)-T0 : step: BND(2) + T0];
xx1 = zeros(1,length(tt));
figure
plot(tt,xx1,'m');
hold on;
for n = ind+NT+1
 xx1_n = X(n)*exp(1i*w0*n*tt);
 xx1 = xx1 + xx1_n;
 plot(tt,abs(xx1_n),'r');
 plot(tt,abs(xx1),'m');
 title(sprintf('n = %d',n-NT));
 pause(0.5)
end
plot(tt,abs(xx1),'k','LineWidth',2);

What am I doing wrong?

fourier-analysis fourier-series matlab

share|cite|improve this question

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

$endgroup$

add a comment | 

$begingroup$

Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.

The pulse looks like this

syms t
x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;

With the code below, I acquire 16 first coefficients of the series:

NT = 15;
X=[];
ind = -NT : NT;
for p = ind
 Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
 X(p + NT + 1) = Xn;
end

However, while doing the inverse operation, the supposed graph of three periods is:

• of frequency 2 times greater


• of amplitude 2 times smaller


• "lifted" 0.5 units up

... and looks like this

The code:

BND = [t1,t2] + offset; 
step = (BND(2) - BND(1))/1000;
tt = [BND(1)-T0 : step: BND(2) + T0];
xx1 = zeros(1,length(tt));
figure
plot(tt,xx1,'m');
hold on;
for n = ind+NT+1
 xx1_n = X(n)*exp(1i*w0*n*tt);
 xx1 = xx1 + xx1_n;
 plot(tt,abs(xx1_n),'r');
 plot(tt,abs(xx1),'m');
 title(sprintf('n = %d',n-NT));
 pause(0.5)
end
plot(tt,abs(xx1),'k','LineWidth',2);

What am I doing wrong?

fourier-analysis fourier-series matlab

share|cite|improve this question

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

$endgroup$

syms t
x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;

NT = 15;
X=[];
ind = -NT : NT;
for p = ind
 Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
 X(p + NT + 1) = Xn;
end

BND = [t1,t2] + offset; 
step = (BND(2) - BND(1))/1000;
tt = [BND(1)-T0 : step: BND(2) + T0];
xx1 = zeros(1,length(tt));
figure
plot(tt,xx1,'m');
hold on;
for n = ind+NT+1
 xx1_n = X(n)*exp(1i*w0*n*tt);
 xx1 = xx1 + xx1_n;
 plot(tt,abs(xx1_n),'r');
 plot(tt,abs(xx1),'m');
 title(sprintf('n = %d',n-NT));
 pause(0.5)
end
plot(tt,abs(xx1),'k','LineWidth',2);

share|cite|improve this question

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

share|cite|improve this question

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

asked Mar 14 at 16:06

Filip FreyFilip Frey

13

asked Mar 14 at 16:06

Filip FreyFilip Frey

13