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Unformatted text preview: 1. Oppenheims book: 4.46, 4.53 2. Consider the following discrete-time system with L=3 and M=4. Suppose ) ( z H is a linear phase FIR filter with length 60. Assume that ) ( n x has a sampling rate of 100 KHz. L M ) ( z H ) ( n x ) ( n y . (a) If ) ( z H is implemented directly (i.e., no polyphase forms), what is the time available for each multiplier to perform one multiplications? (b) Suppose the structure is implemented in the best possible way (i.e., using polyphase form similar to the architecture shown in the classnote). Then what is the time available for each multiplier to perform one multiplication? (c) Find the number of multiplications and additions per second in part (b). 3. A generalization of the polyphase decomposition is considered in this problem. Let ) ( z H be a causal FIR transfer function of degree 1- N with N even: - =- = 1 ] [ ) ( N n n z n h z H (a) Show that ) ( z H can be expressed in the form ( 29 ( 29 ( 29 ( 29 2 1 1 2 1 1 1 ) ( z H z z H z z H-...
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- Fall '05