Question

No.1 (2 points) List the basic properties of Z-Transform. What are differences between Fourier Series and Fourier Transform.

Answer 1

fourier senes Tourier bonetom is periodic cignal is it non periodic signals represented as sum of ore repreended by conti complex exponentials -nuou sum superposition se integral of complex exponentials i signals are sines and it at breaks signale into cosines, and harmonic constituent frequencies of each other I frequency domain view). iliy valid only for perio iiiy for non periodes, -dic signals and finite signals: in Uses orthogonal iuy fourier series actually relationship of sine and provides motivation for tourier transform. u) Used in signal processing, uy Used in image com Image processing, pression, estimation of nave simplification signal spectrum cosine

Basic properties of a tranctorn y Linearity un X(2) gen) - Y(A) an(n) +byen) - ax (x) +6 412) 26 time shifting an) - X(2) min-m) Z-mx(z) 3) multiplication by exponential sequence (n) x() ; an aim - XlHa) H7 time reversal aln) (); (n) = x(x1) 5) Convolution min) —> X(*)', yin) —> YCF) min) *yin) -> *()YCZ) 64 Correlation ain) —— X(X) ; yon) — 4() ten) Ⓡyen) > X(7)4(%) A Differentiation an) →X() 3 nkain) –> (gezt dax(7), dZk
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