1. Engineering
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  3. 2 determine a sine waves fourier coefficients let ftf sin...

Question: 2 determine a sine waves fourier coefficients let ftf sin...

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2. Determine a sine waves Fourier coefficients. Let f(t)F sin wt in the integrals found in Table B.1. Note: These integrals define the period as 2T. Many of the coefficients are zero, but you must evaluate the integrals to prove that they vanish. Use of symbolic math software such as MathCADT*, MathematicaT, or Wolfram.comM is encouraged as long as you document what you have done 3. Use the math handbook page located in Appendix B to determine the first five harmonic frequencies of the series and their amplitude coefficients for a triangle wave and a square wave. Modify the equations to show w (which requires that you relate period to frequency) so you can clearly identify the la, 2a, 3a, 4w and 5w terms. Also modify the equations to yield a waveform with an amplitude of A 0.5.For a periodic function f(t) we can obtain a Fourier series of constants An and Bn such that rnt n Cos and 2T f (t) cos (B.2) 嚇 (B.3) where 2T is the period of the periodic waveform.f(x) = Sin- 2L f(x) SinCOS_ 2L f(x) 2L f(x) 1 11 nTr f(x) = 2-21 n sin T 2L f(x) 2L f(x) (-1)(n-1)/2, nTr sin_ 2L Table B.1: Table of common waveforms with their Fourier transforms

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