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102_1_disc5

# 102_1_disc5 - Er“ A EMU Signais 8 bystems Discussion#5...

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Unformatted text preview: Er“. A- EMU Signais 8: bystems Discussion #5 October 29 2010 Zhongnan Fang 1. Discrete Time Fourier Series FE. , n 19 U 3 ‘J 21M: 17M 2 Z (”.er kr<1V> 1 __j‘27ri<"n, We (11,: N Z while J N {ﬁg ‘ n:<N> m, {ii W 2. Calculate Discrete Time Fourier Series (a) )[7?]~—1T3LTPLZ n] (b) :‘I:[77,) : { 1 W S 2 O otfmimjis a T26 3. Review. Things you need to know. (a) Operations on the signal :1(t:i:T), 27% t), r(2—t) .‘L‘[”I'L i N 1,; [2n], .42 —~ 71] (b) Linearity. Input (i: 33(1‘ ), output amt); lnput:1:1(t)+.1,g(t ), output: y1(t)+y2(t ), Where g1(2‘)and y2(t )is the output wheninput .7710?) and \$205) seperately. (c) Time Invariance. Input a delayed signal( 2: (f ~— T), will the system output be a T delayed output of Mt), where gm is the output when input is 2(2‘)? (d) Causality. Is the system output only after there is input? w FLU) is zero when t < 0? (e) Some special signals. (Ht), ma), MU), reoﬁt). (1‘) Even and odd Signals. Even part of signa}: I? (1:) Odd part of Sigma}: ;.:.,(t} .» . 57-49‘3/ zit/t) 2 :17,..{t) +11:0(2i) (g) Convolution. +159 yﬁf) : / ;I;i{7')fz,(f ~- 7):??? v00 1 “l—CK; r 1 ylng :: E aﬂklhpr, M A?) I; : re no (h) How to do Convolution graphicaiiy? 1. Reverse h(t) / h[n]. 2. Shift the h by tor n. (Shift to right for positive t / n) 3. Multiply and find the sum. Continous Fourier Series. Synthesis Equation +00 V )7 :1;(t) 2 Z (1L4(,*7k<%)1 k2v—oe Analysis Equation 1 I ,~ t, 27‘“ at: r: 7; /:I:(t)e’~’l“('I—"tdt ‘ 51‘ Continous Fourier Series Properties. Discrete Fourier Series. Synthesis Equation 1 ,"27rim'l mm x Z arkev’ N k2<N> Analysis Equation 1 . _,-21rlmw ak, 2: ’V Z :1; We J N A NI<N> Discrete Fourier Series Properties. iii 35 if a!“ “HE ; v V‘ "L E é; E; 6m ...
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102_1_disc5 - Er“ A EMU Signais 8 bystems Discussion#5...

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