Fourier series question (Interested Beginner)

[Bernie bolt]

Hi there,
I am a music student and have no math background whatsoever but was wondering if you guys could help me with something that I read in a book on signal processing. I want to create a periodic waveform that is described by the following Fourier series http://dsp-bg.info/files/example_119.jpg . I would like to know how to figure out different values of f with f1 being the fundamental frequency, for example I want to be able to calculate the values for f1+ f2+ f3...+n ect. I have been given the amplitude values (An) of N=8 already but need the frequency components (f1 ect) in order to generate the waveform. I am pretty ignorant in this area so If I have not been clear in my question I apologise in advance. Hope someone can help. Thanks,B.

 

[Swapnil]

I am not really sure what you want. Your frequencies f1, f2, ..., fN would just be integral multiple of your fundamental frequency i.e. f1, 2f1, ... Nf1, respectively.

 

[Bernie bolt]

Thank you for your prompt reply Swapnil, that was what I assumed but as this area is completely new to me I was not so sure. Would anyone be so kind as to explain the equation to me? I understand the principle of the summation but don't know how to use the equation to find out the specific values of n. The first 8 values of An (N=8) have been given as N1-0.2846 N2-0.1062 N3- 0.0589 N4- 0.0386 N5- 0.0278 N6- 0.0212 N7- 0.0169 N8- 0.0139 but I can't work out how these values are calculated, so If anyone can provide a step by step way of calculating them from the equation or point me in the right direction I would be most grateful. As I said before I am clueless when it comes to this stuff so any input will be most appreciated as days of searching the internet has got me nowhere. Thanks in advance, B

 

[Swapnil]

So you want to know the fundamental frequency given all the 8 different values of the amplitude? I don't think that is possible unless you have more information. Perhaps you are given the graph of the function you have to generate?

 

[Bernie bolt]

A graph is given that shows one cycle of the waveform with time values on its x-axis and from this I was able to work out the frequency value of the fundamental frequency and recreate the the waveform using additive synthesis. What I would like to know is how the amplitude values given were figured out? Does the equation given supply this information? Thanks again,B.

 

[Swapnil]

No, that equation does not give you enough information to calculate the amplitude at different values of n. Usually, when doing Fourier series, you are given an arbitrary periodic graph which you then have to put in the following form:

$$C_0 + \sum_{n=1}^{\infty} A_n \cos(2\pi nft) + B_n\sin(2\pi nft)$$

You do this by evaluating the Fourier coefficients $$C_0, A_n,$$ and $$B_n$$ by the means of a formula. Here's one of the many sites that lists those formulas:
http://en.wikipedia.org/wiki/Fourier_series

In short, you use the parameters given in the graph of you signal and plug them into the formula for $$A_n$$ to get the value of $$A_n$$ as a function of n. Judging from the given equation, the coefficients $$C_0, B_n$$ would turn out to be zero once you evaluate them.

 

[Bernie bolt]

Brilliant! Thanks for all your help swapnil. Much appreciated,Mike.