Can anyone help me with fourier series of a signal?

I got a signal as attached. My doubt is can I break the signal in a triangle and a straight line, then calculating fourier series for each. Will this break may affect my answer (magnitude * frequency)

[Image Analyst]

Can you show us the signal without us having to save the figure, then open it up in MATLAB? Like copy it to the clipboard and paste it into http://snag.gy and then insert it here with the frame icon?

[Ajay Goyal]

https://i.snag.gy/EYDexk.jpg Sir, please check the attached image

[Image Analyst]

I meant post it here with the green and brown frame icon. Here, I will do it for you:

Please read this: http://www.mathworks.com/matlabcentral/answers/13205#answer_18099

Answer 1

[Star Strider]

If you’re doing a numeric fft, do the Fourier Transform of the entire signal.

To do it symbolically, separate it into two segments for each part of the triangle, and add:

syms w t f1(t) f2(t)
f1(t) = 40*t;
f2(t) = 40-40*t;
F(w) = int(f1(t)*exp(1i*w*t), t, 0, 0.5) + int(f2(t)*exp(1i*w*t), t, 0.5, 1);
F(w) = simplify(F(w), 'steps',20)

F(w) =

-(40*(exp((w*1i)/2) - 1)^2)/w^2

It is zero elsewhere, so you can ignore that section.

[Ajay Goyal]

Thank you very much Sir. My use of FS is restricted to collection of all peak magnitudes and respective frequencies of each sine and cosine wave generated from FS for the given signal. As I have understood from your last statement that I can ignore the straight line of zero magniture. Can I continue my research work by calculating FS of triangle waveform (as I am not using FFT)? I have prepared attached code.

[Star Strider]

My pleasure.

Your code is very difficult to follow. Instead of using separate sine and cosine terms, I would use the complex exponential to calculate the Fourier transform.

For a single pulse, you can ignore the zero segment. If your pulse repeats at regular intervals, you must include at least two pulses, with the pulses defined just as the first one was, as segments of straight lines (in this example), each with appropriate slopes and intercepts and integrated over the appropriate time intervals. The zero-value interval is implicit in those integrations, but does not have to be specifically included.