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quiz 5

# quiz 5 - M = 3 2 Compute the four-point DFT X k of the...

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ECEN 487 QUIZ 5 NAME:_________________ 1. Let h [ n ] be the finite length impulse response for a lowpass filter used in the anti- aliasing stage of a decimator. The decimation rate is M = 3. a) Specify the values of the impulse response for e 1 [ n ] in a polyphase filter implementation, given: h [0] = 6, h [1] = 5, h [2] = 4, h [3] = 3, h [4] = 2, h [5] = 1, otherwise h [ n ] = 0, e 1 [ n ] = h [ Mn + 1] e 1 [0] = 5; e 1 [1] = 2; 0 otherwise b) By what rate will the computational burden of this filter be lowered by using a polyphase implementation as compared to the straightforward filter then decimate approach?
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Unformatted text preview: M = 3. 2. Compute the four-point DFT, X [ k ], of the sequence: x [0] = 1, x [1] = − j , x [2] = − 1, x [3] = j . X [ k ] = x [ n ] W 4 kn n = 3 ∑ = x [ n ] e − jkn π /2 n = 3 ∑ = x [ n ]( n = 3 ∑ − j ) nk X [0] = (1)(1) + ( − j )(1) + ( − 1)(1) + ( j )(1) = X [1] = (1)(1) + ( − j )( − j ) + ( − 1)( − 1) + ( j )( j ) = X [2] = (1)(1) + ( − j )( − 1) + ( − 1)(1) + ( j )( − 1) = X [3] = (1)(1) + ( − j )( j ) + ( − 1)( − 1) + ( j )( − j ) = 4 X [ k ] = 4 δ [ n − 3]...
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