Problem 2.1. Thinking about differentiating Taylor series, compute the sum n=0 for any z < 4.
7. Derive the time domsin representation of the Sollowing Lapince transiorm espressicnbasi on e sivee Roc ROC:0< Rels) < X(s) = s(s-1),
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1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
1. Let x[n] be a periodic sequence with period N with Fourier series representation x[n] = akek(34)n k=<N> Assume that N is even. Derive the expressions for the following signals (a) x[n] – x[n – (b) x[n] + x[n + 1 (Note that this signal is periodic with period ) (c) (-1)" x[n]
1 1 Find the Taylor series for f(x) about <= 5. 3.2 4 The general term is an = The first five terms of the Taylor series are Show or upload your work below.
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develop f(z)=(z(z-3)) into a laurent serkes valid for the following
domains
develop g(z)= 1/((z-1)(z-2)) into a laurent series valid for
the following domains
develop h(z)= z/((z+1)(z-2)) into a laurent series valid for
the following domains
7) 0 < 1 2 -3/ <3 6) 1८11-4/<4 9) 0시레시 10) 0<l2-2시 ) ۵ < ( 2 + ( ( 3 (2) 02 ( 2 -2) 3.
+ for (a)0</zl</ (6) 12/> 1. -6) Find the two Laurent series in powers of z that represent sin --
1. Find the complex Fourier series of the following f(x) = x, -π < x < π
Exercise 3. Suppose that |2 < 2. Prove that the series converges absolutely.
- Express the Fourier series of that particular function - when - 1 < x < 0 4 f(x) = { when 0<x<T