UNIT5-Z TRANSFORMS

The z-transform of a signal X(n) whose definition is given by X(z)=

 $\sum_{n=0}^{\infty}x\left(n\right)z^{-n}$  is known as

• Unilateral Z-transform

• Bilateral Z-transform

• Rational Z-transform

• None of the above

For what kind of signals one sided Z-transfrom is unique

• All signals

• Anti-causal signal

• Causal signal

• None of the above

Z-transform is linear

• True

• False

The Z-transform of

 $\delta\left(n+k\right)>0$  is

•  $z^{-k,\ }z\ne0$  

•  $z^k,z\ne0$  

•  $z^{-k},\ all\ z$  

•  $z^k,all\ z$  

Z-transform of the sequence $\left\{2^k\right\},k\ge0\ is\ \frac{z}{z-2}$  

• True

• False

 $Z-transform\ of\ the\ sequence\ \left\{\frac{a^k}{k!}\right\},k\ge0=e^{\frac{a}{z}}$  

• True

• False

 $Z-transform\ of\ the\ sequence\ \left\{nc_r\right\},\left(0\le r\le n\right)\ is\ \left(1+z\right)^n$  

• True

• False

 $The\ value\ of\ the\ Radius\ of\ convergence\ of\ f\left(n\right)=2^n,n<0\ is$  

• 0< $\left|z\right|$ <1

• -2< $\left|z\right|$  

•  $\left|z\right|$  <2

• z-plane

 $The\ ROC\ of\ u\left(n\right)=4^n,for\ n<0;2^n,for\ n\ge0\ is$  

• 0<z<1

• z<4

• 2<z

• 2<z<4

 $The\ Inverse\ Z-transform\ of\frac{z}{\left(z+1\right)^2}is$  

•  $\left(-1\right)^{n+1}$  

•  $n\left(-1\right)^{n-1}$  

•  $\left(-1\right)^{n-1}$  

•  $n\left(-1\right)^{n+1}$