# Signal Processing

Signal Processing.

The Z- Transform. See attachment

Signal Processing.

Inverse Z-transform and poles and zeros

When finding the inverse Z-transform of functions with z^(-1) terms in the numerator, that fact that z^(-1) can be thought of as a delay operator can be used to simplify the computation. Consider.

X(z)=(1-z^(-10))/(1-z^(-1) )

Use the Z-transform of u[n] and the properties of the Z-transformation to find x[n].

If we consider X(z) a polynomial in negative powers of z, what would be its degree and the values of its coefficients?

Find the poles and the zeros of X(z) and plot them on the z-plane. Is there a pole or zero at z=1? Explain.

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#### Solution Preview

Please find attached, thanks

9.14

(a)

We are given the domain transfer function below

First we will work out the right hand side of the above by algebraic manipulation as below

But and so we get

We define our domain transfer function

Where is the output and is the input

Thus

Multiplying out we get

In terms of a difference equation in time domain we get from the definition of the transform from time domain

So we get a series of time advance functions

We can reduce each of these time indices by 10 to get (as long as each of the indices are reduced by the same ...

#### Solution Summary

The expert examines signal processing for the Z-transform.