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090116Lecture06

090116Lecture06 - ECE 700 Digital Signal Processing Lecture...

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ECE 700 WI 2009 ECE 700 Digital Signal Processing Lecture 6 01/16/09 1
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ECE 700 WI 2009 Interpolator using Type 2 polyphase decomposition x [ n ] L H(z) y [ n ] 0 () L Rz 1 L 1 L L z -1 z -1 z -1 + + x [ n ] y [ n ] L 0 1 1 L z -1 z -1 z -1 + + y [ n ] L L L x [ n ] 1. Do a type 2 decomposition of H ( z ) 2. After using Noble identity
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ECE 700 WI 2009 Rational sampling rate converter x [ n ] y [ n ] H(z) L M 0 () Rz 1 1 L z -1 z -1 z -1 + + y [ n ] L L L x [ n ] M 0 1 1 L z -(L-1) + + y [ n ] L L L x [ n ] M z -(L-2) M M
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ECE 700 WI 2009 Development of (k) th branch () k Rz L z -(L-k-1) M If L and M are relatively prime, there exist positive integers μ and λ such that M - L =1. (1 ) ( 1 ) ) ( ) ) ) ) ) Lk L k M L L kM kL LkM zz z z μλ λμ −−− − −+ −− + + + +− + = = = = k R z L M ) L z + ) z −+
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ECE 700 WI 2009 More on the k th branch () k R z L M (1 ) kL L z λ + ) kM z μ −+ k R z L M )1 k z + ) k z k Rz L M k z + ) k z Do a M -component polyphase on this.
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ECE 700 WI 2009 M -component polyphase on k th branch ,0 () k E z z 1 + + M z 1 ,1 k E z M kM E z M
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090116Lecture06 - ECE 700 Digital Signal Processing Lecture...

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