How to show that y[n] = x[n] * h[n] turns into the Y(z) = X(z).H(z)?

1. How do you find the Z-transform of a sequence?
2. How do you calculate the Z-transform for a function?
3. How do you find impulse response using Z-transform?
4. What is the Z-transform of the signal x N Anu N )? *?

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 calculate the Z-transform for a function?

Concept of Z-Transform and Inverse Z-Transform

X(Z)|z=ejω=F. T[x(n)].

How do you find impulse response using Z-transform?

Remember: x[n]∗h[n]Z⟶X(z)H(z). In case the impulse response is given to define the LTI system we can simply calculate the Z-transform to obtain :math:`H(z). In case the system is defined with a difference equation we could first calculate the impulse response and then calculating the Z-transform.

What is the Z-transform of the signal x N Anu N )? *?

What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)? =>Zu(n)-u(n-N)=\frac1-z^-N1-z^-1.