Upsampling

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The operation of upsampling by factor L∈ℕ

describes the insertion of L-1

L 1

zeros between every sample of the input signal. This is denoted by " ↑L

↑ L

" in block diagrams, as in Figure 1.

Figure 1

Formally, upsampling can be expressed in the time domain as yn=xnLifnL∈ℤ0otherwise

y n x n L n L 0

In the z

-domain, Yz=∑nynz-n=∑nnL∈ℤxnLz-n=∑kxkz-kL=XzL

Y z n y n z n n nL x n L z n k x k z k L X z L

and substituting z=ⅇⅈω

z ω

for the DTFT,

Yⅇⅈω=XⅇⅈωL

Y ω X ω L

(1)

As shown in Figure 2, upsampling compresses the DTFT by a factor of L

along with the ω

axis.

Figure 2

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Last edited by Charlet Reedstrom on Oct 18, 2005 4:23 pm GMT-5.

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