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Upsampling

Module by: Phil Schniter

Summary: (Blank Abstract)

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Upsampling

The operation of upsampling by factor L∈ℕ L 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
Figure 1 (m10403fig1.png)

Formally, upsampling can be expressed in the time domain as yn=xnLifnL∈ℤ0otherwise y n x n L n L 0 In the zz-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 LL along with the ωω axis.

Figure 2
Figure 2 (m10403fig2.png)

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