Lecture 6 problems - Lecture 6 problems 1 for the given system DN N sample delay Suppose N=2 the system is causal(1 Find impulse response h(n give a

Lecture 6 problems - Lecture 6 problems 1 for the given...

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Lecture 6 problems 1. for the given system D N : N sample delay Suppose N=2, the system is causal. (1). Find impulse response h(n) , give a well labeled plot of h(n) . (2). Find frequency response |H(ω)|, plot |H(ω)|. 2. for the given digital filter 1 ( ) 1 0 1 j H e ϖ ϖ α α - = - < < - , Find |H(ω)| and ( ) H ϖ R . 3. The frequency response function : G R C of a discrete time filter is characterized as follows: , ( ) 1 1 ( ) 1 j j e G where note e ϖ ϖ α ϖ ϖ α α α - - + 2200 = - < < + R R Determine a simple expression for the magnitude response |G(ω)|, π ϖ π - . 4. Evaluate the convolution integral * i i y h x = , where x is the continuous-time step function and the impulse response h i is as given below, i=1,2,3 . 1 2 3 0, 0 , 0 , 0 ( ) ( ) ( ) ( ) ( ) ( ) 0 , 0 , 0 , 0 t t t t t e t e t a h t b h t c h t t e t e t - - = = = < < < 5. consider a discrete time LTI system :[ ] [ ] F Z C Z C having input signal
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