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Eq1) The utility of this frequency domain function is rooted in the Poisson summation formula Let X (f) be the Fourier transform of any function, x (t) , whose samples at some interval T (seconds) are equal (or proportional) to the x n sequence, ie T ⋅ x (nT) = x n Then the periodic function represented by the Fourier series is a periodic summation of X (f) in terms of frequency f.

B nunx. 24 c JFessler,May27,04,1310(studentversion) 212 Classication of discretetime signals The energy of a discretetime signal is dened as Ex 4= X1 n=1 jxnj2 The average power of a signal is dened as Px 4= lim N!1 1 2N 1 XN n= N jxnj2 If E is nite (E < 1) then xn is called an energy signal and P = 0 If E is innite, then P can be either nite or innite. ROCz>aa n u(n1) ↔ \(\frac{1}{1az^{1}} = \frac{z}{za}\);. (b) x(n)=(n3)05(n1) (c) x(n)=2n ·(n4) (d) x(n)=2n ·u(n2) (e) x(n)=(1)n u(n4) (f) x(n)=2(n4)(n2)u(n3) (g) x(n)= X1 k=0 4(n3k 1) (h) x(n)= X1 k=1 (1)k (n3k) 112 Make a sketch of each of the following signals (a) x(n)= X1 k=1 (09)k (nk) (b) x(n) = cos(⇡n)u(n) (c) x(n)=u(n)2u(n4)u(n8) 113 Sketch x(n), x1(n), x2(n), and x3(n)where x(n)=u(n4)u(n),x1(n)=x(n3),.

In mathematics, the special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1 The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case The group operation is matrix multiplicationThe special unitary group is a subgroup of the unitary group U(n), consisting. (b) Again let x(n) = u(n) Find yb(n) by convolving x(n) with the result of the convolution of h1 (n) and h2 (n) ie yb(n) = x(n) * h1(n) * h2(n) Your results for parts (a) and (b) should be identical, illustrating the associative property of convolution Problem 26* If the output of a system is the input multiplied by a complex constant. H n u n x n u n n n = = b) 6S For each of the following pairs of waveforms, use the convolution integral to find response y(t) of the LTI system with impulse response h(t) and x(t) Sketch your results a) ( ) ( ) ( ) ( ) h t e u t x t e u t t t.

There are a variety of methods of solving such problems, depending on the properties of A and b MATLAB offers us two solutions, x = A\b and x = pinv(A)*b We've seen the "backslash" A\b solution before;. B 2 3 1 n u n x n c otherwize n n n x 3 3 Problem No5 The following are the from IT 341 at Cairo University. 6003 Homework #3 Solutions / Fall 11 2 2 YinYang Determinethesystemfunctional Y X forthefollowingsystem A B C X Y whereA,B.

Block Diagram System Functional Di erence Equation System Function UnitSample Response Delay Delay X Y Y X = H (R ) = 1 1 RR 2 y n = x n y n 1 y n 2 H (z) =. (b) Write the difference equation relating the output yn to input xn Solution (a) xn=(e)(n1)un=e(enun),Xz=e z z e Yz=HzXz= ez2 (z02)(z 08)(z e) Therefore Yz z = ez (z02)(z 08)(z e) = 132 z e 0186 z02 113 z 08 Yz=132 z z e 0186 z z02 113 z z 08 yn=132(e)n 0186( 02)n 113(08)nun (b) From Hz= Yz Xz = z (z02)(z 08) we have. Answer b Explanation a n u(n) ↔ \(\frac{1}{1az^{1}} = \frac{z}{za}\);.

#title #points 687 #rows 1097 #sense 1 #xorigin 739 #yorigin #rotation 0 #ptseparation 005 #rwseparation 005 #transform #unit_length km,1000 #map_projection "nad27 / *lcc90" nad27,,,0. A You are given a signal xn = a ^(n)un b^(n)un c^(n)u−n − 1 i Determine the ztransform and its ROC ii Without explicitly evaluating X(z), determine the ROC of the ztransforms for each of the following sequences and determine if its DTFT exists.

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