Decimation by a factor D

Is decimation LTI operation?

Decimation by a factor D

Decimation by a factor D

Decimation by a factor D

Evaluate the Z-transform on unit circle with frequency variable

Thus, gets stretched to by down-sampling

If is correctly designed, then aliasing is eliminated and

Decimation by a factor D

Interpolation by a factor I

DTFT:

Interpolation by a factor I

As the frequency component of

are unique in the range

Images beyond that in

should be rejected by low pass

filtering

C = ?

Interpolation by a factor I

is the desired normalization factor

Sampling rate conversion by a rational factor I/D

Sampling rate conversion by a rational factor I/D

Sampling rate conversion by a rational factor I/D

Frequency response of the combined filter

Sampling rate conversion by a rational factor I/D

Change of variable

We know

Time-varying filter

Sampling rate conversion by a rational factor I/D