Q1:

A bipolar signal is +A volts for 1 and –A volts for 0. The signal is effected by AWGN with PSD of n/2 =10^-5w/Hz. The bit rate of the system is 7.26 kbps. Then the value of A (in V) so that the probability of error P_e = 10^-4 is …………………..

Given Q (x) = 10^-4 when V = 3.71

Q2:

A symmetric three-level midrise quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

If the probability density function is divided into three regions as shown in the figure the value of ‘a’ in the figure is

Q3:

Consider the binary channel show in figure which of the following statement s is/ are correct if MAP detection is used.

i. Y₀ is detected as X₀

ii. Y₁ is detected asX₁

iii. Y₀ is detected as X₁

iv. Y₁ is detected as X₀

P

Q4:

Determine probability of error when MAP decoding is used if $P(m_0)=0.7;P(m_1)=0.3;P(\frac{r_0}{m_0})=0.9;P(\frac{r_1}{m_0})=0.1;P(\frac{r_0}{m_1})=0.4;P(\frac{r_1}{m_1})=0.6$

Q5:

A binary source in which 1s occurs 3 times as often as 0s. then the average information in bits/symbol will be.

Q6:

A source produces 4 symbols with probability 1/2, 1/4, 1/8 and 1/8 for this source a practical coding scheme has an average code word length of 2 bits/symbols. The efficiency of the code is

Q7:

A BSC has a transition probability of 1/8.If binary transmitted symbol “X” is such that P(X = 0) = 9/10, then probability of error of an optimum receiver will be

Q8:

An event has two possible outcome with probability $P_1=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,and{P}_2=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$64$}\right.$the rate of information with 16 outcomes per second is.

Q9:

Which of the following is/are not a property/ properties of a power spectral density function $S_X(\omega )$?

Q10:

The auto –correlation function of an energy signal has:

1) No symmetry

2) Conjugate Symmetry

3) Odd Symmetry

4) Even symmetry

Q11:

The ACF of a rectangular pulse of duration T is

Q12:

Which one of the following gives the average value or expectation of the function g(x) of the random variable X? {Given f(x) is the probability density function}

Q13:

The auto-correlation function R_x($\tau$) of a random process has the property that R_x(o) is equal to.  

Q14:

If the power spectral density of stationary random process is a Sinc-squared function of frequency, the shape of its auto-correlation is.

Q15:

The PSD of a signal x(t) is given as 8$\pi$δ($\omega$). Then x(t) is given by