Let u|n| be the unit-step signal and $x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right] + {\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]$. The region of convergence of z-transform of x[n] is

$\left| z \right| < \frac{1}{2}$

$\left| z \right| > \frac{1}{3}$

$\frac{1}{3} < \left| z \right| < \frac{1}{2}$

$\left| z \right| > \frac{1}{2}$

$\left| z \right| < \frac{1}{2}$

Find the Z-transform of a periodic sequence x(n) = {1, 0, -3, 1}?

X(z) = 1 – 3z-2 + z-3; |z| ≠ 0

X(z) = 1 – 3z-2 + z-3; |z| ≠ ∞

X(z) = 1 – 3z-2 + z-3; |z| ≠ 0 and |z| ≠ ∞

X(z) = (1 – 3z-2 + z-3)/(1 – z-4)

Let 3 + 4j be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is

$\frac{3}{{25}} + \frac{4}{{25}}j$

$\frac{3}{{25}} - \frac{4}{{25}}j$

If x[n] ↔ X(z), the z-transform of x[-n] will be:

$X\left( { - \frac{1}{z}} \right)$

$X\left( {\frac{1}{z}} \right)$

A realization of a stable discrete-time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is

$5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]$

$4{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right]$

$5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right] - 3{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]$

$5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right]$

$5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]$

Consider the following system function of a discrete-time LTI system:$H\left( z \right) = \frac{{{z^{ - 1}}{a^*}}}{{1 - a{z^{ - 1}}}}$Where a* is the complex conjugate of a. The frequency response of such a system is

periodic; does not depend on frequency ω

aperiodic; depends on frequency ω

aperiodic; does not depend on frequency ω

periodic; depends on frequency ω

periodic; does not depend on frequency ω

If $X(z)=\frac{4z}{{(z+0.5)}^2} ;|z|>0.5$ and impulse response h(n) = x(n). Find Y(z).

$ Y(z)=\frac{16z^3}{{(z+0.5)}^2} $

$ Y(z)=\frac{4z^2}{{(z+0.5)}^2} $

$ Y(z)=\frac{4z^3}{{(z+0.5)}^4} $

$ Y(z)=\frac{16z^2}{{(z+0.5)}^4} $

Find the inverse z-transform of $X\left( z \right) = \frac{1}{{\left( {1 - 0.25{z^{ - 1}}} \right)}}$

${\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]$

${\left( {\frac{1}{4}} \right)^n}u\left[ { - n + 1} \right]$

${\left( {\frac{1}{2}} \right)^n}$

${\left( {\frac{1}{4}} \right)^n}u\left[ n \right]$

${\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]$

If input x[n] = [1, 4, 7] and output is y[n] = [-1, -4], then system difference equation is ______

y[n] – 4y[n - 1] – 7y[n - 2] = x[n] + 4x[n - 1]

y[n] + 4y[n - 1] + 7y[n - 2] = x[n] + 4x[n - 1]

y[n] + 4y[n - 1] + 7y[n - 2] = -x[n] – 4x[n - 1]

y[n] – 4y[n - 1] – 7y[n - 2] = x[n] + 4x[n - 1]

-y[n] – 4y[n - 1] + 7y[n - 2] = x[n] + 4x [n - 1]

Modified z-transform is used

for systems having a large time constant

for systems having zero dead-time

for systems having dead-time which is an integer multiple of sampling time

for systems having dead-time which is not an integer multiple of sampling time

for systems having a large time constant

Consider a discrete time signal given by$x\left[ n \right] = {\rm{\;}}{\left( { - 0.25} \right)^n}{\rm{\;}}u\left[ n \right]{\rm{\;}} + {\rm{\;}}{\left( {0.5} \right)^n}{\rm{\;}}u\left[ { - n - 1} \right]$The region of convergence of its Z – transform would be

The region inside the circle of radius 0.5 and cantered at origin

the region outside the circle of radius 0.25 and centred at origin

the angular region between the two circles, both centred at origin and having radii 0.25 and 0.5

Let $x\left[ n \right]={\left( { - \frac{1}{9}} \right)^n}u\left[ n \right] - {\left( { - \frac{1}{3}} \right)^n}u\left[ { - n - 1} \right]$. The Region of convergence (ROC) of the z-transform

is $\left| z \right| > \frac{1}{9}$

is $\left| z \right| < \frac{1}{3}$

is $\frac{1}{3} > \left| z \right| > \frac{1}{9}$

Consider an LTI system with a system function$H\left( z \right) = \frac{1}{{1 - \frac{1}{4}{z^{ - 1}}}}$Its difference equation will be:

$y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$

$y\left( n \right) - \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$

$y\left( n \right) - \frac{1}{4}y\left( {n - 1} \right) = x\left( n \right)$

$y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$

$y\left( n \right) - \frac{1}{4}y\left( {n + 1} \right) = x\left( n \right)$

Find the z-transform of an u(n)

$\frac{{\left( {z + a} \right)}}{z}$

$\frac{z}{{\left( {z - a} \right)}}$

$\frac{{\left( {z + a} \right)}}{z}$

$\frac{z}{{\left( {z + a} \right)}}$

$\frac{{\left( {z - a} \right)}}{z}$

Consider the difference equation $y\left[ n \right] - \frac{1}{3}y\left[ {n - 1} \right] = x\left[ n \right]$ and suppose that $x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right]$. Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is

$\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}$

$3{\left( {\frac{1}{3}} \right)^n} - 2{\left( {\frac{1}{2}} \right)^n}$

$- 2{\left( {\frac{1}{3}} \right)^n} + 3{\left( {\frac{1}{2}} \right)^n}$

$\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}$

$\frac{1}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{2}{3}{\left( {\frac{1}{2}} \right)^n}$

Find the z transform of (n + 1)2

$\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$

$\frac{{{z^2}\left( {z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$

$\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$

$\frac{{\left( {2 + z} \right)}}{{{{\left( {z - 1} \right)}^2}}}$

$\frac{{\left( {3z + 2} \right)}}{{z - 1}}$

Directions:The following question consist of two statements, one labelled as ‘Statement (I)’ and the other as ‘Statement (II)’. You are to examine these two statements carefully and select the answers to these items using the code given below:Statement (I): Z-transform approach is used to analyze the discrete time systems and is also called as pulse transfer function approach.Statement (II): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.Code

Both Statement (I and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)

Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)

Both Statement (I and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)

Statement (I) is true but Statement (II) is false

Statement (I) is false but Statement (II) is true

Find the z – transform of cosh(nθ)

$\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}$

$\frac{{z\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2z\;cosh\theta + 1} \right)}}$

$\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}$

$\frac{{\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2x\;cosh\theta + 1} \right)}}$

$\frac{{z\left( {z - coth\theta } \right)}}{{\left( {{z^2} - 2zcoth\theta + 1} \right)}}$

Determine the inverse z-transform of: $X\left( z \right) = \frac{1}{{1 - 1.5{z^{ - 1}} + 0.5{z^{ - 2}}}}$ Where ROC: |Z| > 1

$x\left[ n \right] = \left\{ {1,\frac{2}{3},\frac{7}{4}, \ldots } \right\}$

$x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}},\frac{7}{4}, \ldots } \right\}$

$x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}}, - \frac{7}{4}, \ldots } \right\}$

$x\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} 1\\ \uparrow \end{array},\frac{3}{2},\frac{7}{4}, \ldots } \right\}$

56 + Mcqs in Hilbert Transform in Analog Communications Page 1 McqOptions

1.	The advantage of using mechanical filter in filter system of sideband suppression is good attenuation characteristics.
A.	True
B.	False
Answer» B. False

Discussion

2.	In India, the subcarrier frequency for transmission of color difference signals in television is approximately ________
A.	10.47 MHZ
B.	5.4 MHZ
C.	7.67 MHZ
D.	1.3 MHZ
Answer» E.

Discussion

3.	The output of a battery eliminator is closed to ________
A.	70V DC
B.	70V AC
C.	6V AC
D.	6V DC
Answer» E.

Discussion

4.	In frequency modulation, there is a large increase in noise and hence decrease in the signal to noise ratio.
A.	True
B.	False
Answer» C.

Discussion

5.	Consider the sequence $\rm x[n] = a^nu[n] +b^nu [n]$, where $\rm u[n]$ denotes the unit-step sequence and $\rm 0 < \|a\| < \|b\| < 1$. The region of convergence (ROC) of the z-transform of $\rm u[n]$ is
A.	$\rm \|z\| > \|a\|$
B.	$\rm \|z\| > \|b\|$
C.	$\rm \|z\| < \|a\|$
D.	$\rm \|a\| < \|z\| < \|b\|$
Answer» C. $\rm \|z\| < \|a\|$

Discussion

6.	Consider the following statements regarding z-transform:a) The z-transform replaces the Laplace transform for sampled-data systemb) The z-transform replaces the Laplace transform for continuous-data systemc) The z-transform provides direct parallels to the s-plane analysis of transients, steady-state errors, stability, etc.d) We cannot map points on s-plane to points on z-planeWhich of the above statements are correct?
A.	(a) and (c) only
B.	(a) and (d) only
C.	(b), (c) and (d) only
D.	(a), (b) and (d) only
Answer» B. (a) and (d) only

Discussion

7.	Let u\|n\| be the unit-step signal and $x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right] + {\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]$. The region of convergence of z-transform of x[n] is
A.	$\left\| z \right\| > \frac{1}{3}$
B.	$\frac{1}{3} < \left\| z \right\| < \frac{1}{2}$
C.	$\left\| z \right\| > \frac{1}{2}$
D.	$\left\| z \right\| < \frac{1}{2}$
Answer» D. $\left\| z \right\| < \frac{1}{2}$

Discussion

8.	Frequency scaling [relationship between discrete time frequency (Ω) and continuous time frequency (ω)] is defined as
A.	ω = 2Ω
B.	ω = 2 TS/Ω
C.	Ω = 2 ω/TS
D.	Ω = ωTS
Answer» E.

Discussion

9.	Convolution of two sequences X1[n] and X2[n] is represented as
A.	X1(z) ∗ X2(z)
B.	X1(z) X2(z)
C.	X1(z) + X2(z)
D.	X1(z) / X2(z)
Answer» C. X1(z) + X2(z)

Discussion

10.	Find the Z-transform of a periodic sequence x(n) = {1, 0, -3, 1}?
A.	X(z) = 1 – 3z-2 + z-3; \|z\| ≠ 0
B.	X(z) = 1 – 3z-2 + z-3; \|z\| ≠ ∞
C.	X(z) = 1 – 3z-2 + z-3; \|z\| ≠ 0 and \|z\| ≠ ∞
D.	X(z) = (1 – 3z-2 + z-3)/(1 – z-4)
Answer» E.

Discussion

11.	Let 3 + 4j be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is
A.	3 – 4j
B.	$\frac{3}{{25}} + \frac{4}{{25}}j$
C.	$\frac{3}{{25}} - \frac{4}{{25}}j$
D.	$\frac{1}{3} - \frac{1}{4}j$
Answer» E.

Discussion

12.	Consider a two-sided discrete-time signal (neither left sided, nor right sided). The region of convergence (ROC) of the z-transform of the sequence is:1) All region of z-plane outside a unit circle (in z-plane)2) All region of z-plane inside a unit circle (in z-plane)3) Ring in z-planeWhich of the above is/are correct?
A.	1 only
B.	2 only
C.	3 only
D.	1 and 3
Answer» D. 1 and 3

Discussion

13.	For an all pass system $H\left( z \right) = \;\frac{{{z^{ - 1}} - b}}{{1 - a{z^{ - 1}}}}$ If Re(a)≠0, Im(a)≠0, then b equals.
A.	a
B.	a*
C.	1/a*
D.	1/a
Answer» C. 1/a*

Discussion

14.	If the region of convergence of Z-transform of x[n] + y[n] is 0.3 < \|z\| < 0.6 then, the region of convergence of Z-transform of x[n] – y[n] is
A.	0.6 < \|z\| < 3
B.	0.3 < \|z\| < 0.6
C.	0.3 < \|z\|
D.	\|z\| < 0.6
Answer» C. 0.3 < \|z\|

Discussion

15.	Let x[n] = x[-n] Let X(z) be the Z-transform of x[n]. if 1 + j2 is a zero of X(z). Which one of the following must also be a zero of X(z)
A.	0.2 + j 0.4
B.	0.2 – j 0.4
C.	1 + j 2
D.	1 – j 0.5
Answer» C. 1 + j 2

Discussion

16.	Consider two discrete-time signals:x1(n) = {1, 1} and x2(n) = {1, 2}, for n = 0, 1.The Z-transform of the convoluted sequence x(n) = x1(n) * x2(n) is
A.	1 + 2z-1 + 3z-2
B.	z2 + 3z + 2
C.	1 + 3z-1 + 2z-2
D.	z-2 + 3z-3 + 2z-4
Answer» D. z-2 + 3z-3 + 2z-4

Discussion

17.	If ${\rm{x}}\left[ {\rm{n}} \right] = {\left( {\frac{1}{3}} \right)^{\left\| {\rm{n}} \right\|}}-{(\frac{1}{2})}^n \ u(n) $ then, the region of convergence of its z transform in the z-plane will be
A.	$ \frac{1}{3}<\left\| z \right\| < 3$
B.	$ \frac{1}{2}<\left\| z \right\| < 3$
C.	$ \frac{1}{3}<\left\| z \right\| < \frac{1}{2}$
D.	$ \frac{1}{3}<\left\| z \right\| $
Answer» C. $ \frac{1}{3}<\left\| z \right\| < \frac{1}{2}$

Discussion

18.	If the z-transform of a system is given by $H\left( z \right) = \frac{{\alpha + {z^{ - 1}}}}{{1 + \alpha {z^{ - 1}}}}$ where α is real-valued, \|α\| < 1, ROC : \|z\| > \|α\|, then the system is
A.	a low-pass filter
B.	a band-pass filter
C.	an all-pass filter
D.	a high-pass filter
Answer» D. a high-pass filter

Discussion

19.	If x[n] ↔ X(z), the z-transform of x[-n] will be:
A.	$X\left( { - \frac{1}{z}} \right)$
B.	$X(z)$
C.	X(-Z)
D.	$X\left( {\frac{1}{z}} \right)$
Answer» E.

Discussion

20.	If the discrete-time sequence x(n), n ≥ 0 is defined to be u(n), then the Z transform X(z) is (for \|z\|>1):
A.	$\frac{1}{{z - 1}}$
B.	$\frac{Z}{{z + 1}}$
C.	$\frac{1}{{z + 1}}$
D.	$\frac{Z}{{z - 1}}$
Answer» E.

Discussion

21.	If Z transform of x(n) is X(z) then the Z transform of x(n - k) is _______
A.	X(z-k z)
B.	X(zk z)
C.	z-k X(z)
D.	zk X(z)
Answer» D. zk X(z)

Discussion

22.	Let $X\left( z \right) = \frac{1}{{1 - {z^{ - 3}}}}$ be the z-transform of a causal signal x[n].Then, the values of x[2] and x[3] are
A.	0 and 0
B.	0 and 1
C.	1 and 0
D.	1 and 1
Answer» C. 1 and 0

Discussion

23.	Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z-1 + z-2, the z-transform of p[n] = x[n] ∗ h[n − 2] is
A.	2 + 3z + z−2
B.	3z + z−2
C.	2z2 + 3z + 1
D.	2z−2 + 3z−3 + z−4
Answer» E.

Discussion

24.	A realization of a stable discrete-time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is
A.	$4{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right]$
B.	$5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right] - 3{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]$
C.	$5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right]$
D.	$5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]$
Answer» D. $5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]$

Discussion

25.	Consider the following system function of a discrete-time LTI system:$H\left( z \right) = \frac{{{z^{ - 1}}{a^}}}{{1 - a{z^{ - 1}}}}$Where a is the complex conjugate of a. The frequency response of such a system is
A.	aperiodic; depends on frequency ω
B.	aperiodic; does not depend on frequency ω
C.	periodic; depends on frequency ω
D.	periodic; does not depend on frequency ω
Answer» D. periodic; does not depend on frequency ω

Discussion

26.	If $X(z)=\frac{4z}{{(z+0.5)}^2} ;\|z\|>0.5$ and impulse response h(n) = x(n). Find Y(z).
A.	$ Y(z)=\frac{16z^3}{{(z+0.5)}^2} $
B.	$ Y(z)=\frac{4z^2}{{(z+0.5)}^2} $
C.	$ Y(z)=\frac{4z^3}{{(z+0.5)}^4} $
D.	$ Y(z)=\frac{16z^2}{{(z+0.5)}^4} $
Answer» E.

Discussion

27.	Find the inverse z-transform of $X\left( z \right) = \frac{1}{{\left( {1 - 0.25{z^{ - 1}}} \right)}}$
A.	${\left( {\frac{1}{4}} \right)^n}u\left[ { - n + 1} \right]$
B.	${\left( {\frac{1}{2}} \right)^n}$
C.	${\left( {\frac{1}{4}} \right)^n}u\left[ n \right]$
D.	${\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]$
Answer» D. ${\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]$

Discussion

28.	An inverse z-transform x(kT) of $X\left( z \right) = \frac{{z\left( {1 - {e^{ - aT}}} \right)}}{{\left( {z - 1} \right)\left( {z - {e^{ - aT}}} \right)}}$ is
A.	1 – e-akT
B.	1 + e-akT
C.	1 – eakT
D.	1 + eakT
Answer» B. 1 + e-akT

Discussion

29.	If input x[n] = [1, 4, 7] and output is y[n] = [-1, -4], then system difference equation is ______
A.	y[n] + 4y[n - 1] + 7y[n - 2] = x[n] + 4x[n - 1]
B.	y[n] + 4y[n - 1] + 7y[n - 2] = -x[n] – 4x[n - 1]
C.	y[n] – 4y[n - 1] – 7y[n - 2] = x[n] + 4x[n - 1]
D.	-y[n] – 4y[n - 1] + 7y[n - 2] = x[n] + 4x [n - 1]
Answer» C. y[n] – 4y[n - 1] – 7y[n - 2] = x[n] + 4x[n - 1]

Discussion

30.	Modified z-transform is used
A.	for systems having zero dead-time
B.	for systems having dead-time which is an integer multiple of sampling time
C.	for systems having dead-time which is not an integer multiple of sampling time
D.	for systems having a large time constant
Answer» D. for systems having a large time constant

Discussion

31.	Consider a four-point moving average filter defined by the equation $y\left[ n \right]=\mathop{\sum }_{i=0}^{3}{{\alpha }_{i}}x\left[ n-i \right].$The condition on the filter coefficients that results in a null at zero frequency is:
A.	α1 = α2 = 0; α0 = -α3
B.	α1 = α2 = 1; α0 = -α3
C.	α0 = α3 = 0; α1 = α2
D.	α1 = α2 = 0; α0 = α3
Answer» B. α1 = α2 = 1; α0 = -α3

Discussion

32.	If the z-transform of a discrete time signal x[n] is denoted as X(z), then the z-transform of x[n - 2] and x[n/2] will be, respectively,
A.	z-2 X(z), 2X (2z)
B.	z2 X(z), X(2z)
C.	X (z - 2), X(z/2)
D.	z-2 X(z), X(z2)
Answer» B. z2 X(z), X(2z)

Discussion

33.	Consider a discrete time signal given by$x\left[ n \right] = {\rm{\;}}{\left( { - 0.25} \right)^n}{\rm{\;}}u\left[ n \right]{\rm{\;}} + {\rm{\;}}{\left( {0.5} \right)^n}{\rm{\;}}u\left[ { - n - 1} \right]$The region of convergence of its Z – transform would be
A.	The region inside the circle of radius 0.5 and cantered at origin
B.	the region outside the circle of radius 0.25 and centred at origin
C.	the angular region between the two circles, both centred at origin and having radii 0.25 and 0.5
D.	The entire Z plane
Answer» D. The entire Z plane

Discussion

34.	Consider a signal $x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}1\left[ n \right]$, where 1[n] = 0 if n < 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n - k], k > 0 is $\frac{{{z^{ - k}}}}{{1 - \frac{1}{2}\;{z^{ - 1}}}}$ with region of convergence being
A.	\|z\| < 2
B.	\|z\| > 2
C.	\|z\| < 1/2
D.	\|z\| > 1/2
Answer» E.

Discussion

35.	Let $x\left[ n \right]={\left( { - \frac{1}{9}} \right)^n}u\left[ n \right] - {\left( { - \frac{1}{3}} \right)^n}u\left[ { - n - 1} \right]$. The Region of convergence (ROC) of the z-transform
A.	is $\left\| z \right\| > \frac{1}{9}$
B.	is $\left\| z \right\| < \frac{1}{3}$
C.	is $\frac{1}{3} > \left\| z \right\| > \frac{1}{9}$
D.	does not exist
Answer» D. does not exist

Discussion

36.	For the discrete-time system$H\left( z \right) = \frac{{ - 3{z^2} + 1}}{{4{z^2} + 2z - 1}}$ the system is:
A.	Stable
B.	Marginally stable
C.	Unstable
D.	Undeterminable
Answer» B. Marginally stable

Discussion

37.	Consider $H\left( z \right) = \frac{{4z - 1}}{{{z^2} + 3z - 1}}$; Determine the steady-state output of the system if it is excited by input x(n) = 8u(n)
A.	8
B.	4
C.	0
D.	1
Answer» B. 4

Discussion

38.	A discrete-time signal x[n] = δ [n - 3] + 2δ [n - 5] has a z-transform X(z). If Y(z) = X(-z) is the z-transform of another signal y[n], then
A.	y[n] = x[n]
B.	y[n] = x[-n]
C.	y[n] = - x[n]
D.	y[n] = - x[-n]
Answer» D. y[n] = - x[-n]

Discussion

39.	If the z-transform of a sequence x[n] = {1, 1, -1, -1} is X[z], then the value of $X\left( {\frac{1}{2}} \right)$ is
A.	- 9
B.	1.875
C.	-1.125
D.	15
Answer» B. 1.875

Discussion

40.	Consider an LTI system with a system function$H\left( z \right) = \frac{1}{{1 - \frac{1}{4}{z^{ - 1}}}}$Its difference equation will be:
A.	$y\left( n \right) - \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$
B.	$y\left( n \right) - \frac{1}{4}y\left( {n - 1} \right) = x\left( n \right)$
C.	$y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$
D.	$y\left( n \right) - \frac{1}{4}y\left( {n + 1} \right) = x\left( n \right)$
Answer» C. $y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)$

Discussion

41.	Find the z-transform of an u(n)
A.	$\frac{z}{{\left( {z - a} \right)}}$
B.	$\frac{{\left( {z + a} \right)}}{z}$
C.	$\frac{z}{{\left( {z + a} \right)}}$
D.	$\frac{{\left( {z - a} \right)}}{z}$
Answer» B. $\frac{{\left( {z + a} \right)}}{z}$

Discussion

42.	Consider the difference equation $y\left[ n \right] - \frac{1}{3}y\left[ {n - 1} \right] = x\left[ n \right]$ and suppose that $x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right]$. Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is
A.	$3{\left( {\frac{1}{3}} \right)^n} - 2{\left( {\frac{1}{2}} \right)^n}$
B.	$- 2{\left( {\frac{1}{3}} \right)^n} + 3{\left( {\frac{1}{2}} \right)^n}$
C.	$\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}$
D.	$\frac{1}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{2}{3}{\left( {\frac{1}{2}} \right)^n}$
Answer» C. $\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}$

Discussion

43.	Find the z transform of (n + 1)2
A.	$\frac{{{z^2}\left( {z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$
B.	$\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$
C.	$\frac{{\left( {2 + z} \right)}}{{{{\left( {z - 1} \right)}^2}}}$
D.	$\frac{{\left( {3z + 2} \right)}}{{z - 1}}$
Answer» B. $\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}$

Discussion

44.	Directions:The following question consist of two statements, one labelled as ‘Statement (I)’ and the other as ‘Statement (II)’. You are to examine these two statements carefully and select the answers to these items using the code given below:Statement (I): Z-transform approach is used to analyze the discrete time systems and is also called as pulse transfer function approach.Statement (II): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.Code
A.	Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
B.	Both Statement (I and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
C.	Statement (I) is true but Statement (II) is false
D.	Statement (I) is false but Statement (II) is true
Answer» B. Both Statement (I and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)

Discussion

45.	Find the z – transform of cosh(nθ)
A.	$\frac{{z\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2z\;cosh\theta + 1} \right)}}$
B.	$\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}$
C.	$\frac{{\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2x\;cosh\theta + 1} \right)}}$
D.	$\frac{{z\left( {z - coth\theta } \right)}}{{\left( {{z^2} - 2zcoth\theta + 1} \right)}}$
Answer» B. $\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}$

Discussion

46.	Determine the inverse z-transform of: $X\left( z \right) = \frac{1}{{1 - 1.5{z^{ - 1}} + 0.5{z^{ - 2}}}}$ Where ROC: \|Z\| > 1
A.	$x\left[ n \right] = \left\{ {1,\frac{2}{3},\frac{7}{4}, \ldots } \right\}$
B.	$x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}},\frac{7}{4}, \ldots } \right\}$
C.	$x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}}, - \frac{7}{4}, \ldots } \right\}$
D.	$x\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} 1\\ \uparrow \end{array},\frac{3}{2},\frac{7}{4}, \ldots } \right\}$
Answer» E.

Discussion

47.	If the lower limit of Region of Convergence (ROC) is greater than the upper limit of ROC, the series $X\left( Z \right) = \mathop \sum \nolimits_{n = - \infty }^\infty x\left( n \right){Z^{ - n}}$
A.	Converges
B.	Zero
C.	Does not converge
D.	None of the above
Answer» D. None of the above

Discussion

48.	THE_ADVANTAGE_OF_USING_MECHANICAL_FILTER_IN_FILTER_SYSTEM_OF_SIDEBAND_SUPPRESSION_IS_GOOD_ATTENUATION_CHARACTERISTICS.?$
A.	True
B.	False
Answer» B. False

Discussion

49.	In India, the subcarrier frequency for transmission of color difference signals in television is approximately _______?
A.	10.47 MHZ
B.	5.4 MHZ
C.	7.67 MHZ
D.	1.3 MHZ
Answer» E.

Discussion

50.	The output of a battery eliminator is closed to _______?
A.	70V DC
B.	70V AC
C.	6V AC
D.	6V DC
Answer» E.

Discussion

5.	Consider the sequence \(\rm x[n] = a^nu[n] +b^nu [n]\), where \(\rm u[n]\) denotes the unit-step sequence and \(\rm 0 < \|a\| < \|b\| < 1\). The region of convergence (ROC) of the z-transform of \(\rm u[n]\) is
A.	\(\rm \|z\| > \|a\|\)
B.	\(\rm \|z\| > \|b\|\)
C.	\(\rm \|z\| < \|a\|\)
D.	\(\rm \|a\| < \|z\| < \|b\|\)
Answer» C. \(\rm \|z\| < \|a\|\)

7.	Let u\|n\| be the unit-step signal and \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right] + {\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]\). The region of convergence of z-transform of x[n] is
A.	\(\left\| z \right\| > \frac{1}{3}\)
B.	\(\frac{1}{3} < \left\| z \right\| < \frac{1}{2}\)
C.	\(\left\| z \right\| > \frac{1}{2}\)
D.	\(\left\| z \right\| < \frac{1}{2}\)
Answer» D. \(\left\| z \right\| < \frac{1}{2}\)

14.	If the region of convergence of Z-transform of x[n] + y[n] is 0.3 < \|z\| < 0.6 then, the region of convergence of Z-transform of x[n] – y[n] is
A.	0.6 < \|z\| < 3
B.	0.3 < \|z\| < 0.6
C.	0.3 < \|z\|
D.	\|z\| < 0.6
Answer» C. 0.3 < \|z\|

17.	If \({\rm{x}}\left[ {\rm{n}} \right] = {\left( {\frac{1}{3}} \right)^{\left\| {\rm{n}} \right\|}}-{(\frac{1}{2})}^n \ u(n) \) then, the region of convergence of its z transform in the z-plane will be
A.	\( \frac{1}{3}<\left\| z \right\| < 3\)
B.	\( \frac{1}{2}<\left\| z \right\| < 3\)
C.	\( \frac{1}{3}<\left\| z \right\| < \frac{1}{2}\)
D.	\( \frac{1}{3}<\left\| z \right\| \)
Answer» C. \( \frac{1}{3}<\left\| z \right\| < \frac{1}{2}\)

27.	Find the inverse z-transform of \(X\left( z \right) = \frac{1}{{\left( {1 - 0.25{z^{ - 1}}} \right)}}\)
A.	\({\left( {\frac{1}{4}} \right)^n}u\left[ { - n + 1} \right]\)
B.	\({\left( {\frac{1}{2}} \right)^n}\)
C.	\({\left( {\frac{1}{4}} \right)^n}u\left[ n \right]\)
D.	\({\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]\)
Answer» D. \({\left( {\frac{1}{2}} \right)^{ - n}}u\left[ { - n} \right]\)

11.	Let 3 + 4j be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is
A.	3 – 4j
B.	\(\frac{3}{{25}} + \frac{4}{{25}}j\)
C.	\(\frac{3}{{25}} - \frac{4}{{25}}j\)
D.	\(\frac{1}{3} - \frac{1}{4}j\)
Answer» E.

13.	For an all pass system \(H\left( z \right) = \;\frac{{{z^{ - 1}} - b}}{{1 - a{z^{ - 1}}}}\) If Re(a)≠0, Im(a)≠0, then b equals.
A.	a
B.	a*
C.	1/a*
D.	1/a
Answer» C. 1/a*

19.	If x[n] ↔ X(z), the z-transform of x[-n] will be:
A.	\(X\left( { - \frac{1}{z}} \right)\)
B.	\(X(z)\)
C.	X(-Z)
D.	\(X\left( {\frac{1}{z}} \right)\)
Answer» E.

20.	If the discrete-time sequence x(n), n ≥ 0 is defined to be u(n), then the Z transform X(z) is (for \|z\|>1):
A.	\(\frac{1}{{z - 1}}\)
B.	\(\frac{Z}{{z + 1}}\)
C.	\(\frac{1}{{z + 1}}\)
D.	\(\frac{Z}{{z - 1}}\)
Answer» E.

22.	Let \(X\left( z \right) = \frac{1}{{1 - {z^{ - 3}}}}\) be the z-transform of a causal signal x[n].Then, the values of x[2] and x[3] are
A.	0 and 0
B.	0 and 1
C.	1 and 0
D.	1 and 1
Answer» C. 1 and 0

24.	A realization of a stable discrete-time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is
A.	\(4{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right]\)
B.	\(5{\left( { - \frac{2}{3}} \right)^n}u\left[ n \right] - 3{\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]\)
C.	\(5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right]\)
D.	\(5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]\)
Answer» D. \(5{\left( {\frac{2}{3}} \right)^n}u\left[ n \right] - 5{\left( {\frac{1}{3}} \right)^n}u\left[ n \right]\)

26.	If \(X(z)=\frac{4z}{{(z+0.5)}^2} ;\|z\|>0.5\) and impulse response h(n) = x(n). Find Y(z).
A.	\( Y(z)=\frac{16z^3}{{(z+0.5)}^2} \)
B.	\( Y(z)=\frac{4z^2}{{(z+0.5)}^2} \)
C.	\( Y(z)=\frac{4z^3}{{(z+0.5)}^4} \)
D.	\( Y(z)=\frac{16z^2}{{(z+0.5)}^4} \)
Answer» E.

28.	An inverse z-transform x(kT) of \(X\left( z \right) = \frac{{z\left( {1 - {e^{ - aT}}} \right)}}{{\left( {z - 1} \right)\left( {z - {e^{ - aT}}} \right)}}\) is
A.	1 – e-akT
B.	1 + e-akT
C.	1 – eakT
D.	1 + eakT
Answer» B. 1 + e-akT

34.	Consider a signal \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}1\left[ n \right]\), where 1[n] = 0 if n < 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n - k], k > 0 is \(\frac{{{z^{ - k}}}}{{1 - \frac{1}{2}\;{z^{ - 1}}}}\) with region of convergence being
A.	\|z\| < 2
B.	\|z\| > 2
C.	\|z\| < 1/2
D.	\|z\| > 1/2
Answer» E.

35.	Let \(x\left[ n \right]={\left( { - \frac{1}{9}} \right)^n}u\left[ n \right] - {\left( { - \frac{1}{3}} \right)^n}u\left[ { - n - 1} \right]\). The Region of convergence (ROC) of the z-transform
A.	is \(\left\| z \right\| > \frac{1}{9}\)
B.	is \(\left\| z \right\| < \frac{1}{3}\)
C.	is \(\frac{1}{3} > \left\| z \right\| > \frac{1}{9}\)
D.	does not exist
Answer» D. does not exist

36.	For the discrete-time system\(H\left( z \right) = \frac{{ - 3{z^2} + 1}}{{4{z^2} + 2z - 1}}\) the system is:
A.	Stable
B.	Marginally stable
C.	Unstable
D.	Undeterminable
Answer» B. Marginally stable

37.	Consider \(H\left( z \right) = \frac{{4z - 1}}{{{z^2} + 3z - 1}}\); Determine the steady-state output of the system if it is excited by input x(n) = 8u(n)
A.	8
B.	4
C.	0
D.	1
Answer» B. 4

40.	Consider an LTI system with a system function\(H\left( z \right) = \frac{1}{{1 - \frac{1}{4}{z^{ - 1}}}}\)Its difference equation will be:
A.	\(y\left( n \right) - \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)\)
B.	\(y\left( n \right) - \frac{1}{4}y\left( {n - 1} \right) = x\left( n \right)\)
C.	\(y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)\)
D.	\(y\left( n \right) - \frac{1}{4}y\left( {n + 1} \right) = x\left( n \right)\)
Answer» C. \(y\left( n \right) + \frac{1}{2}y\left( {n - 1} \right) = x\left( n \right)\)

41.	Find the z-transform of an u(n)
A.	\(\frac{z}{{\left( {z - a} \right)}}\)
B.	\(\frac{{\left( {z + a} \right)}}{z}\)
C.	\(\frac{z}{{\left( {z + a} \right)}}\)
D.	\(\frac{{\left( {z - a} \right)}}{z}\)
Answer» B. \(\frac{{\left( {z + a} \right)}}{z}\)

42.	Consider the difference equation \(y\left[ n \right] - \frac{1}{3}y\left[ {n - 1} \right] = x\left[ n \right]\) and suppose that \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right]\). Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is
A.	\(3{\left( {\frac{1}{3}} \right)^n} - 2{\left( {\frac{1}{2}} \right)^n}\)
B.	\(- 2{\left( {\frac{1}{3}} \right)^n} + 3{\left( {\frac{1}{2}} \right)^n}\)
C.	\(\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}\)
D.	\(\frac{1}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{2}{3}{\left( {\frac{1}{2}} \right)^n}\)
Answer» C. \(\frac{2}{3}{\left( {\frac{1}{3}} \right)^n} + \frac{1}{3}{\left( {\frac{1}{2}} \right)^n}\)

43.	Find the z transform of (n + 1)2
A.	\(\frac{{{z^2}\left( {z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}\)
B.	\(\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}\)
C.	\(\frac{{\left( {2 + z} \right)}}{{{{\left( {z - 1} \right)}^2}}}\)
D.	\(\frac{{\left( {3z + 2} \right)}}{{z - 1}}\)
Answer» B. \(\frac{{\left( {2z + 1} \right)}}{{{{\left( {z - 1} \right)}^3}}}\)

45.	Find the z – transform of cosh(nθ)
A.	\(\frac{{z\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2z\;cosh\theta + 1} \right)}}\)
B.	\(\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}\)
C.	\(\frac{{\left( {z - cosh\theta } \right)}}{{\left( {{z^2} - 2x\;cosh\theta + 1} \right)}}\)
D.	\(\frac{{z\left( {z - coth\theta } \right)}}{{\left( {{z^2} - 2zcoth\theta + 1} \right)}}\)
Answer» B. \(\frac{{z\left( {z - \cos h\theta } \right)}}{{\left( {{z^2}02z\cos h\theta } \right)}}\)

46.	Determine the inverse z-transform of: \(X\left( z \right) = \frac{1}{{1 - 1.5{z^{ - 1}} + 0.5{z^{ - 2}}}}\) Where ROC: \|Z\| > 1
A.	\(x\left[ n \right] = \left\{ {1,\frac{2}{3},\frac{7}{4}, \ldots } \right\}\)
B.	\(x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}},\frac{7}{4}, \ldots } \right\}\)
C.	\(x\left[ n \right] = \left\{ {1,\frac{2}{{\begin{array}{*{20}{c}} 3\\ \uparrow \end{array}}}, - \frac{7}{4}, \ldots } \right\}\)
D.	\(x\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} 1\\ \uparrow \end{array},\frac{3}{2},\frac{7}{4}, \ldots } \right\}\)
Answer» E.

Explore topic-wise MCQs in Analog Communications.

The advantage of using mechanical filter in filter system of sideband suppression is good attenuation characteristics.

In India, the subcarrier frequency for transmission of color difference signals in television is approximately ________

The output of a battery eliminator is closed to ________

In frequency modulation, there is a large increase in noise and hence decrease in the signal to noise ratio.

Consider the sequence \(\rm x[n] = a^nu[n] +b^nu [n]\), where \(\rm u[n]\) denotes the unit-step sequence and \(\rm 0 < |a| < |b| < 1\). The region of convergence (ROC) of the z-transform of \(\rm u[n]\) is

Let u|n| be the unit-step signal and \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right] + {\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]\). The region of convergence of z-transform of x[n] is

Frequency scaling [relationship between discrete time frequency (Ω) and continuous time frequency (ω)] is defined as

Convolution of two sequences X1[n] and X2[n] is represented as

Find the Z-transform of a periodic sequence x(n) = {1, 0, -3, 1}?

Let 3 + 4j be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is

For an all pass system \(H\left( z \right) = \;\frac{{{z^{ - 1}} - b}}{{1 - a{z^{ - 1}}}}\) If Re(a)≠0, Im(a)≠0, then b equals.

If the region of convergence of Z-transform of x[n] + y[n] is 0.3 < |z| < 0.6 then, the region of convergence of Z-transform of x[n] – y[n] is

Let x[n] = x[-n] Let X(z) be the Z-transform of x[n]. if 1 + j2 is a zero of X(z). Which one of the following must also be a zero of X(z)

Consider two discrete-time signals:x1(n) = {1, 1} and x2(n) = {1, 2}, for n = 0, 1.The Z-transform of the convoluted sequence x(n) = x1(n) * x2(n) is

If \({\rm{x}}\left[ {\rm{n}} \right] = {\left( {\frac{1}{3}} \right)^{\left| {\rm{n}} \right|}}-{(\frac{1}{2})}^n \ u(n) \) then, the region of convergence of its z transform in the z-plane will be

If the z-transform of a system is given by \(H\left( z \right) = \frac{{\alpha + {z^{ - 1}}}}{{1 + \alpha {z^{ - 1}}}}\) where α is real-valued, |α| < 1, ROC : |z| > |α|, then the system is

If x[n] ↔ X(z), the z-transform of x[-n] will be:

If the discrete-time sequence x(n), n ≥ 0 is defined to be u(n), then the Z transform X(z) is (for |z|>1):

If Z transform of x(n) is X(z) then the Z transform of x(n - k) is _______

Let \(X\left( z \right) = \frac{1}{{1 - {z^{ - 3}}}}\) be the z-transform of a causal signal x[n].Then, the values of x[2] and x[3] are

Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z-1 + z-2, the z-transform of p[n] = x[n] ∗ h[n − 2] is

A realization of a stable discrete-time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is

Consider the following system function of a discrete-time LTI system:\(H\left( z \right) = \frac{{{z^{ - 1}}{a^*}}}{{1 - a{z^{ - 1}}}}\)Where a* is the complex conjugate of a. The frequency response of such a system is

If \(X(z)=\frac{4z}{{(z+0.5)}^2} ;|z|>0.5\) and impulse response h(n) = x(n). Find Y(z).

Find the inverse z-transform of \(X\left( z \right) = \frac{1}{{\left( {1 - 0.25{z^{ - 1}}} \right)}}\)

An inverse z-transform x(kT) of \(X\left( z \right) = \frac{{z\left( {1 - {e^{ - aT}}} \right)}}{{\left( {z - 1} \right)\left( {z - {e^{ - aT}}} \right)}}\) is

If input x[n] = [1, 4, 7] and output is y[n] = [-1, -4], then system difference equation is ______

Modified z-transform is used

Consider a four-point moving average filter defined by the equation \(y\left[ n \right]=\mathop{\sum }_{i=0}^{3}{{\alpha }_{i}}x\left[ n-i \right].\)The condition on the filter coefficients that results in a null at zero frequency is:

If the z-transform of a discrete time signal x[n] is denoted as X(z), then the z-transform of x[n - 2] and x[n/2] will be, respectively,

Consider a discrete time signal given by\(x\left[ n \right] = {\rm{\;}}{\left( { - 0.25} \right)^n}{\rm{\;}}u\left[ n \right]{\rm{\;}} + {\rm{\;}}{\left( {0.5} \right)^n}{\rm{\;}}u\left[ { - n - 1} \right]\)The region of convergence of its Z – transform would be

Consider a signal \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}1\left[ n \right]\), where 1[n] = 0 if n < 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n - k], k > 0 is \(\frac{{{z^{ - k}}}}{{1 - \frac{1}{2}\;{z^{ - 1}}}}\) with region of convergence being

Let \(x\left[ n \right]={\left( { - \frac{1}{9}} \right)^n}u\left[ n \right] - {\left( { - \frac{1}{3}} \right)^n}u\left[ { - n - 1} \right]\). The Region of convergence (ROC) of the z-transform

For the discrete-time system\(H\left( z \right) = \frac{{ - 3{z^2} + 1}}{{4{z^2} + 2z - 1}}\) the system is:

Consider \(H\left( z \right) = \frac{{4z - 1}}{{{z^2} + 3z - 1}}\); Determine the steady-state output of the system if it is excited by input x(n) = 8u(n)

A discrete-time signal x[n] = δ [n - 3] + 2δ [n - 5] has a z-transform X(z). If Y(z) = X(-z) is the z-transform of another signal y[n], then

If the z-transform of a sequence x[n] = {1, 1, -1, -1} is X[z], then the value of \(X\left( {\frac{1}{2}} \right)\) is

Consider an LTI system with a system function\(H\left( z \right) = \frac{1}{{1 - \frac{1}{4}{z^{ - 1}}}}\)Its difference equation will be:

Find the z-transform of an u(n)

Consider the difference equation \(y\left[ n \right] - \frac{1}{3}y\left[ {n - 1} \right] = x\left[ n \right]\) and suppose that \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right]\). Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is

Find the z transform of (n + 1)2

Find the z – transform of cosh(nθ)

Determine the inverse z-transform of: \(X\left( z \right) = \frac{1}{{1 - 1.5{z^{ - 1}} + 0.5{z^{ - 2}}}}\) Where ROC: |Z| > 1

If the lower limit of Region of Convergence (ROC) is greater than the upper limit of ROC, the series \(X\left( Z \right) = \mathop \sum \nolimits_{n = - \infty }^\infty x\left( n \right){Z^{ - n}}\)

THE_ADVANTAGE_OF_USING_MECHANICAL_FILTER_IN_FILTER_SYSTEM_OF_SIDEBAND_SUPPRESSION_IS_GOOD_ATTENUATION_CHARACTERISTICS.?$

In India, the subcarrier frequency for transmission of color difference signals in television is approximately _______?

The output of a battery eliminator is closed to _______?

Consider the following system function of a discrete-time LTI system:\(H\left( z \right) = \frac{{{z^{ - 1}}{a^}}}{{1 - a{z^{ - 1}}}}\)Where a is the complex conjugate of a. The frequency response of such a system is