Z-transform of a downsampler

1. How do you find the z-transform of a sequence?
2. How do you find z-transform in DSP?
3. How do you calculate the z-transform for a function?
4. What is the downsampling factor?

How do you find the z-transform of a sequence?

To find the Z Transform of this shifted function, start with the definition of the transform: Since the first three elements (k=0, 1, 2) of the transform are zero, we can start the summation at k=3. In general, a time delay of n samples, results in multiplication by z-n in the z domain.

How do you find z-transform in DSP?

The replacement z=ejw is used for Z-transform to DTFT conversion only for absolutely summable signal. The above equation represents a two-sided Z-transform equation. If it is a continuous time signal, then Z-transforms are not needed because Laplace transformations are used.

How do you calculate the z-transform for a function?

Concept of Z-Transform and Inverse Z-Transform

X(Z)|z=ejω=F. T[x(n)].

What is the downsampling factor?

This factor multiplies the sampling interval or, equivalently, divides the sampling rate. For example, if compact disc audio at 44,100 samples/second is decimated by a factor of 5/4, the resulting sample rate is 35,280. A system component that performs decimation is called a decimator.