Q: If the power spectral density of stationary random process is a sine-squared function of frequency, the shape of its autocorrelation is

Since autocorrelation function and power spectral density bears a Fourier transform relation, then since required in frequency domain will five rectangular convolutions in time domain thus it is triangular function.

Q: A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω/m, if the line is distortion less, the attenuation constant (in Np/m) is

Distortion less a = RG and Z0 = RG → .

Q: Consider a stable and causal system with impulse response h(t) and system function H(S). Suppose H(S) is rational, contains a pole at S = - 2, and does not have a zero at the origin. The location of all other poles and zero is unknown for each of th…

Statement 1 is false, since f{h(t)e3t} corresponds to the value of the Laplace transform of h(t) at s = 3. If this converges, it implies that s = - 3 is in the ROC. A casual and stable system must always have its ROC to the right of all its poles. However, s = - 3 is not to the right of the pole at s = - 2. Statement 2 is false, because it is equivalent to stating that H(0) = 0. This contradicts the fact that H(s) does not have a zero at the origin. Statement 3 is false. If h(t) is of finite duration, then if its Laplace transform has any points in its ROC, ROC must be the entire s-plane. However, this is not consistent with H(s) having a pole at s = - 2. Statement 4 is false. If it were true, then H(s) has a pole at s = - 2, it must also have a pole at s = 2. This is inconsistent with the fact that all the poles of a causal and stable system must be in the left half of the s-plane.

Q: During transmission over a communicate channel, bit errors occur independently with probability . If a block of 3 bits are transmitted, the probability of at most one bit error is equal to

Probability of no-error + probability one error .

Q: Denominator polynomial of a transfer function of certain network is: s3 + s2 + 2s + 24 Then the network is:

Routh array There is negative number present in first column. Thus network is unstable.

Q: In the circuit shown, in switch S is open for a long time and is closed at t = 0. The current i(t) for t ≥ 0+ is

i(f) = 0.5, i(i) = 0.75 i(t) = Vr + (ii - ij)e-1/p = 0.5 - 0.125e-1000t .

Q: Find Vx Vy Vz

Apply Mesh analysis Apply KVL to mesh 2 -2 + Vy + 1 = 0 ∴ Vy = 1 Apply KVL to mesh 1 ∴ -8 + Vx + 2 = 0 ∴ Vx = 6 V Apply KVL to mesh 3 -1 + Vz -2 = 0 ∴ Vz = 3 V.

Q: Consider the common emitter amplifier shown below with the following circuit parameters: β = 100, gm = 0.3861 A/V, r0 = ∞ rp = 259 Ω, Rs = 1 kΩ, RB = 93 kΩ, RC = 250 Ω, RL = 1 kW, C1 = ∞ and C2 = 4.7mF. The resistance seen by the source Vs is

Zs = Rs + (RB || Brs) rc = 2.475 = 1.258 kV

Question 1

If x1[n] x1(z) with ROC = R1 and x2[n] x2(z) with ROC = R2 then ROC for x1[n] + x2[n] will be __________ (where Ri → Region of convergence and x1[n] and x2[n] are causal).

Accepted Answer

R1 ∩ R2, Suppose R1 for x1(n) be Then ROC for x1(n) + x2(n) R1 ∩ R2 (R1 < R2) Then ROC for x1(n) + x2(n) R1 ∩ R2(R1 < R2)

Question 2

If the power spectral density of stationary random process is a sine-squared function of frequency, the shape of its autocorrelation is

Accepted Answer

Since autocorrelation function and power spectral density bears a Fourier transform relation, then since required in frequency domain will five rectangular convolutions in time domain thus it is triangular function.

Question 3

A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω/m, if the line is distortion less, the attenuation constant (in Np/m) is

Accepted Answer

Distortion less a = RG and Z0 = RG → .

Question 4

Consider a stable and causal system with impulse response h(t) and system function H(S). Suppose H(S) is rational, contains a pole at S = - 2, and does not have a zero at the origin. The location of all other poles and zero is unknown for each of th…

Accepted Answer

Statement 1 is false, since f{h(t)e3t} corresponds to the value of the Laplace transform of h(t) at s = 3. If this converges, it implies that s = - 3 is in the ROC. A casual and stable system must always have its ROC to the right of all its poles. However, s = - 3 is not to the right of the pole at s = - 2. Statement 2 is false, because it is equivalent to stating that H(0) = 0. This contradicts the fact that H(s) does not have a zero at the origin. Statement 3 is false. If h(t) is of finite duration, then if its Laplace transform has any points in its ROC, ROC must be the entire s-plane. However, this is not consistent with H(s) having a pole at s = - 2. Statement 4 is false. If it were true, then H(s) has a pole at s = - 2, it must also have a pole at s = 2. This is inconsistent with the fact that all the poles of a causal and stable system must be in the left half of the s-plane.

Question 5

During transmission over a communicate channel, bit errors occur independently with probability . If a block of 3 bits are transmitted, the probability of at most one bit error is equal to

Accepted Answer

Probability of no-error + probability one error .

Question 6

Denominator polynomial of a transfer function of certain network is: s3 + s2 + 2s + 24 Then the network is:

Accepted Answer

Routh array There is negative number present in first column. Thus network is unstable.

Question 7

In the circuit shown, in switch S is open for a long time and is closed at t = 0. The current i(t) for t ≥ 0+ is

Accepted Answer

i(f) = 0.5, i(i) = 0.75 i(t) = Vr + (ii - ij)e-1/p = 0.5 - 0.125e-1000t .

Question 8

Find Vx Vy Vz

Accepted Answer

Apply Mesh analysis Apply KVL to mesh 2 -2 + Vy + 1 = 0 ∴ Vy = 1 Apply KVL to mesh 1 ∴ -8 + Vx + 2 = 0 ∴ Vx = 6 V Apply KVL to mesh 3 -1 + Vz -2 = 0 ∴ Vz = 3 V.

Question 9

The inverse of given Laplace transform is

Accepted Answer

s = x2 - ex x(t) = cos t.

Question 10

Consider the common emitter amplifier shown below with the following circuit parameters: β = 100, gm = 0.3861 A/V, r0 = ∞ rp = 259 Ω, Rs = 1 kΩ, RB = 93 kΩ, RC = 250 Ω, RL = 1 kW, C1 = ∞ and C2 = 4.7mF. The resistance seen by the source Vs is

Accepted Answer

Zs = Rs + (RB || Brs) rc = 2.475 = 1.258 kV

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