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Evaluate Fourier series coefficients and power of a signal
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[QUOTE="John Park, post: 5715995, member: 616032"] A few minor points first: in the equation defining the Fourier series, [I]x[/I]([I]t[/I]) should be [I]s[/I]([I]t[/I]); and [I]θ[/I] = [I]ω[/I][SUB]o[/SUB][I]t[/I] , so you should have sin([I]kθ[/I]/2) etc. What happens when [I]k [/I]= 0? And in your equation defining [I]a[/I][SUB][I]k[/I][/SUB], why do you restrict [I]k[/I] to be positive? I don't have full answers to your questions, but you may be expected to derive a power series whose sum is [I]A[/I][SUP]2[/SUP][I]θ[/I]/[I]T. [/I] It should be obvious from symmetry that your Fourier series will be a sum of cosines; you could show this by combining the +[I]k[/I] and -[I]k[/I] terms. When you square it, you'll get terms proportional to cos([I]kω[/I][SUB]o[/SUB][I]t[/I]).cos([I]lω[/I][SUB]o[/SUB][I]t[/I]), where [I]k [/I]and [I]l[/I] are integers. Most of these terms will vanish when you integrate over one period, [I]T[/I]. Which ones will remain, and what will they look like after integration? Without working it out, I think from that point everything might reduce to a sensible answer. [/QUOTE]
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Evaluate Fourier series coefficients and power of a signal
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