1 Crore+ students have signed up on EduRev. Have you? 
The ztransform of a signal x(n) whose definition is given byis known as:
Explanation: The ztransform of the x(n) whose definition exists in the range n=∞ to +∞ is known as bilateral or two sided ztransform. But in the given question the value of n=0 to +∞. So, such a ztransform is known as Unilateral or one sided ztransform.
For what kind of signals one sided ztransform is unique?
Explanation: One sided ztransform is unique only for causal signals, because only these signals are zero for n<0.
What is the one sided ztransform X^{+}(z) of the signal x(n)={1,2,5,7,0,1}?
Explanation: Since the one sided ztransform is valid only for n>=0, the ztransform of the given signal will be X^{+}(z)= 5+7z^{1}+z^{3}.
Explanation: Since the signal x(n)= δ(nk) is a causal signal i.e., it is defined for n>0 and x(n)=1 at z=k
So, from the definition of one sided ztransform X^{+}(z)=z^{k}.
Explanation: Since the signal x(n)= δ(n+k) is an anti causal signal i.e., it is defined for n<0 and x(n)=1 at z= k. Since the one sided ztransform is defined only for causal signal, in this case X^{+}(z)=0.
If X+(z) is the one sided ztransform of x(n), then what is the one sided ztransform of x(nk)?
Explanation: From the definition of one sided ztransform we have,
If x(n)=a^{n}, then what is one sided ztransform of x(n2)?
Explanation:
If x(n)=a^{n}, then what is one sided ztransform of x(n+2)?
Explanation: We will apply the time advance theorem with the value of k=2.We obtain,
If X+(z) is the one sided ztransform of the signal x(n), then lim┬(n→∞)x(n)=lim┬(z→1)(z1) X^{+} (z) is called Final value theorem.
Explanation: In the above theorem, we are calculating the value of x(n) at infinity, so it is called as final value theorem.
The impulse response of a relaxed LTI system is h(n)=a^{n}u(n),a<1. What is the value of the step response of the system as n→∞?
Explanation: The step response of the system is y(n)=x(n)*h(n) where x(n)=u(n)
On applying ztransform on both sides, we get
3 videos50 docs54 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
3 videos50 docs54 tests








