090107Lecture02

# 090107Lecture02 - Lecture 2 Wi 09 ECE 700 Digital Signal...

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1 Lecture 2 Wi 09 ECE 700 Digital Signal Processing Lecture 2 01/07/09

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2 Lecture 2 Wi 09 Upsampling Upsampling a signal x [ m ] by an integer factor L > 0 is an operation that inserts L -1 zeros between successive samples of x [ m ]. [] , . 0, otherwise nn x yn LL = Z L x [ m ] y [ n ] 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 x [ m ] y [ n ] n m L = 2 6 7 8 9 10
3 Lecture 2 Wi 09 Transform analysis of upsampling : () [] n n n n n L kL k L Yz y nz n xz L xkz Xz =−∞ = = = = Z Then, ( ) jj L Ye Xe ωω =

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4 Lecture 2 Wi 09 Pictorial view of upsampling in frequency domain L = 2 2 () ( ) jj Ye Xe ω =
5 Lecture 2 Wi 09 Downsampling 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 x [ m ] y [ n ] n m M = 2 Downsampling a signal x [ m ] by an integer factor M > 0 is an operation that keeps every M th sample and discards the rest. [] [ ] . yn xnM = M x [ m ] y [ n ]

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6 Lecture 2 Wi 09 Transform analysis of downsampling / () [] 1, 0, , 2 , where [ ] . 0, otherwise n n n n mM M m M Yz ynz xnM z xmc mz M cm =−∞ = = = ± = " 1 2/ 0 1 .
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090107Lecture02 - Lecture 2 Wi 09 ECE 700 Digital Signal...

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