This wikipedia page follows your convention without comment. In this useful 28 page PDF Introduction to the Fourier series ewuation (3) on page 4 uses a0 and not a0/2, thus differing from your example, and violating the consistent convention as mentioned above. We are trying to fit a single side signal in one case only into an otherwise bipolar system. The above arguably arises because an AC value is measured about its mean value = about 0 and so implies that an equal and opposite peak value exists. To maintain a consistent convention we set If we apply the same convention for DC, for DC to have Vdc = a0 implies a DC peak to peak value of 2a0 (as is the case with ai sine terms). RMS magnitude of any single sine term is sqrt(2).ai Peak to peak magnitude of any sine term = 2ai. Change the function generator output to produce a 1 kHz, 2.00 Vpp (bipolar) square wave (this is 1 Vrms). Assuming you have just completed Procedure A (measuring a sine wave using FFT), leave the oscilloscope set as it was (10.0 ms/div sweep speed), and FFT turned on. Same argument applies to bi and cos terms.įor any ith term with i > 0 if ai = 1 you get a sinusoid that extends from -1 to +1. Procedure B Measuring a Square Wave Using FFT: 1. This is not formal and may be just wrong but it seems to work and make sense:ĭeal with ai and sine terms. \$ g(x) = a_0 + \displaystyle \sum_\$ term was added to the expression of the Fourier series. This stumped me for a while as well but it is actually quite simple.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |