# Practice Problems - 1. The response of a linear system with...

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1.The response of a linear system with input x nis  23nkny nx k Find and sketch h n2.Find   y nx nh nif   1knx nnkNh na U naDoes the output have an analytic z-transform? (Analytic means it has no poles or othersingularities in some region where the z-transform converges)3.To simulate a continuous time differentiatoraHjthe following discrete systems aresometimes used with af nfnT,   aatnTddg ngnTftftdtdt:    1221211fnfngnTgngnfnfnTFind the corre4sponding discrete system functions 1Hzand 2Hzand sketch theirfrequency responses.4.Find all inverse transforms of the functiona  212zFzzz5.Show that, if  f nF zThen  dnfnzFzdz 6.Use Problem 5 to find the transform of  nf nna U n7.Let1aand nfn a. Find F z
8.Suppose we are given M+1 real numbers0..nnMaLet21NMand0022cosMmnnAaanmNthen0022cosMnmmAaAnmNNN9.Let3nmNaAbe a DFT pairDefine auxiliary sequences
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DFT, 2m, 0 m, Discrete system

Unformatted text preview: 3 nn mN b a B 3 1 n nm N c a C 3 2 n n m N d a D Show that the 3N-point DFT can be written as a sum of 3 N-point DFTs as follows: 2 2 2 3 3jm j m N N m m m m A B eC eD 10. Find the DFT m n A a of the sequence 5 4cos 2sin na nT nT using the relation between aliased samples of a time function and aliased samples of its Fourier transform. 11. Find the frequency response of a causal system governed by the following recursive equation: 1 1 1 1 2 3 3 1 34 2 y nTyn T y n T y n Tx nTx n T Where 1 2 T 12. Determine the analog system a H s for which the above is a discrete time digital simulator....
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