Downsampling (Decimation) Operator

Figure 11.3 shows the symbol for downsampling by the factor . The downsampler selects every th sample and discards the rest:

In the frequency domain, we have

Thus, the frequency axis is *expanded* by the factor
, wrapping
times around the unit circle, adding to itself
times. For
, two partial spectra are summed, as indicated in Fig.11.4.

Using the common *twiddle factor* notation

(12.1) |

the aliasing expression can be written as

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University