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QUESTION: 1

If relation between input x[n] and output y[n] of a system is given by *y[n] - ^{1/2} y[n -*1] =

then the system is

Solution:

Simply lake Z transform from both sides:

Then H(z)

it is right of the right - most pole

QUESTION: 2

lf x[n] = - u[-n -1] + (1 /2)^{n} u[-n -1] then ROC of signal is:

Solution:

*Overall ROC is IZI < 1 /*2

QUESTION: 3

Consider, discrete time signal x[n] = (1 /3)^{n} u[n] If signal y[n] is defined as y[n] = x[—n], —∞< n < ∞ then value of equals to

Solution:

Now

Put

QUESTION: 4

If signal x(t) and h(t) shown in figure are convolved to yield y(t).

Solution:

Simply use difference and sum between points.

QUESTION: 5

Given that g (t) g (t) = t exp (—t) u(t) then value of g(t) is

Solution:

QUESTION: 6

If u(t) r(t) denotes unit step and unit ramp respectively then u(t) r(t) denotes their convolution, then function u(t + 1) r(t — 2) is given by.

Solution:

y(t) = u(t) r(t)

Y(s) = 1/s^{3}

QUESTION: 7

If wave form is given only for I period then

**Q. Waveform x (t) is**

Solution:

QUESTION: 8

If wave form is given only for I period then

**Q. **Fourier series representation on of x (t) will be.

Solution:

it is an odd function with half symmetry.

QUESTION: 9

If complex Fourier- series coefficient C_{k} is given as C_{k} = (— 1/2)^{|k|} then value of x(t) is:

Solution:

QUESTION: 10

Which statements are true about Fourier transform?

- If x(t) is real then X(jω) is complex conjugate symmetric.
- If x(t) is imaginary then X(jω) is complex conjugate anti-symmetric
- If x(t) is even then X(jω) is also even.

Solution:

QUESTION: 11

Check status of linearity of given functions.

I . x_{1}(t) = x(t) .cost

2. x_{2}(t) = cos(x(t)).t

Solution:

x_{2}(t) = t cos (x (t)

if x(t) = 0 ⇒ x_{2}(t) = t

So x_{2}(t) is non - linear

QUESTION: 12

If Fourier transform of x(t) is X(ω) then Fourier transform of

Solution:

QUESTION: 13

0*.*5 If Z-Transform X(z) of a sequence x[n] is given by .It is given that R.O.C. of X (z) includes unit circle then

**Q. **Value of x[0] is

Solution:

QUESTION: 14

0*.*5 If Z-Transform X(z) of a sequence x[n] is given by .It is given that R.O.C. of X (z)includes unit circle then

**Q. **In above system if x[n] is causal then value of x[0] is

Solution:

if it includes, unit - circle then, Iz| < 2

x[n] = - (0.5) 2^{n} u(-n-1)

x[0] = 0

if it is causal then

QUESTION: 15

If frequency response of a causal & stable linear Time Invariant system is *, *then value of phase delay and group delay are.

Solution:

QUESTION: 16

**Which among the following are the stable discrete time systems?**

1. y(n) = x(4n)

2. y(n) = x(-n)

3. y(n) = ax (n) + 8

4. y(n) = cos x(n)

Solution:

*Answer can only contain numeric values

QUESTION: 17

For given Fourier — series coefficients for real signals Co = 1, C_{1} = — 2, C_{2} = — 1 then power of this signal is _______

Solution:

QUESTION: 18

What is inverse Fourier transform of

Solution:

QUESTION: 19

Which statement is true about y[n] = x[n] . cos (ω_{o} n)

Solution:

*Answer can only contain numeric values

QUESTION: 20

For given signal s(t), shown below what is slope of matched filter output during interval 1 ≤ t ≤ 2 is

Solution:

*h(t) = **= s(2*

*y(t) = NW** h(t )*

*Just draw y(t) and then calculate slope of y(t)*

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