Finding the spectral component of a wave - Page 1
Forum section: electronics / beginners

author: BRetonDP
author_rank: Contributor
timestamp: September 11, 2015, 01:01:14 pm
content: Hello, EEVBlog Community!I am just beginning my Power Electronics course and the problem posted in the attachment is part of my first homework.I do not understand what is the "spectral component" of the wave, and what steps I should follow to find it. I've tried googling what the spectral component of a wave is, but haven't really found instructions to solve a problem as this one. Can anyone give me a hand and help me answer the problem, lead me in the right direction or show me the reading material to figure this problem out?I am currently a study abroad student and am not taking all of the courses I should be taking back in my home university. Had I stayed, I would be taking my Signals class in hand with the Power Electronics course, so maybe I am stuck because of the lack of such information.Thanks in advance!

author: matseng
author_rank: Frequent Contributor
timestamp: September 11, 2015, 01:09:24 pm
content: All waveforms (except pure sines) are basically constructed by a number of sinewaves at many different frequencies and amplitudes. When they are added together they become a squarewave, a triangular wave (as in your example) or any other arbitrary shape.Your example is a triangular wave at 10Hz. One of the sines that this is constructed of have a frequency of 50Hz. Your task is to find out at what amplitude this particular frequency have.https://en.wikipedia.org/wiki/Fourier_transformis a good place to start reading.

author: rfeecs
author_rank: Frequent Contributor
timestamp: September 11, 2015, 04:52:36 pm
content: Quote from: matseng on September 11, 2015, 01:09:24 pmFor a periodic waveform like this, Fourier Series is basically the same thing but a little easier:https://en.wikipedia.org/wiki/Fourier_series

author: TimFox
author_rank: Super Contributor
timestamp: September 11, 2015, 07:06:44 pm
content: Everyperiodicwaveform has a corresponding Fourier series: a sum of sine and cosine waves (or sine waves with different phase angles), where the lowest frequency in the series has a frequency equal to the repetition frequency of the periodic waveform, and all higher frequencies are integer multiples (harmonics) of that fundamental frequency. The Fourier transform is more general.

author: qno
author_rank: Frequent Contributor
timestamp: September 15, 2015, 07:42:30 pm
content: When you look at the wikipedia page you can see that a triangle is a sinus wave with its 3th and 5 harmonic and 7th as the first harmonics.With a 10 Hz ground wave 50Hz is the 5th and a 1/25 of the amplitude of the ground wave.In this case about 4V.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 16, 2015, 05:46:06 am
content: You're being asked to find the inner product with a sin/cos of the given frequency. In other words, the integral:V5 = Integral(t = 0 to T) exp(j*5*2*pi*t/T) f(t) dt(Sadly the forum does not support equations, so you will have to use your imagination.)Which will be a complex number, giving the cos/sin components as Re/Im parts. Or you can perform two integrals, one with cos(10*pi*t/T) instead of the exp(j*...) stuff, and the other with sin. In either case, f(t) is the function given; you'll have to construct the piecewise linear function that describes it.When you perform this calculation for general N, rather than N = 5, you obtain the complete Fourier series.Or, recognizing what the waveform is, you can look it up in a table, because it's an easy one that somebody, somewhere, has already solved for you.To check your answer, it should be around 100 * (4/pi) / 5^2 V peak amplitude, sine.Tim

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 16, 2015, 08:33:41 am
content: Sorry, 4/pi is for squaresServes me for not doing the integral eitherTim