## 41. A binary symmetric channel (BSC) has a transition probability of $$\frac{1}{8}.$$ If the binary transmit symbol X is such that $$P\left( {X = 0} \right) = \frac{9}{{10}},$$ then the probability of error for an optimum receiver will be

## 42. Choose the correct one from among the alternatives a, b, c, dafter matching an item from **Group 1** with the most appropriate item in **Group 2**.

**Group 1**
**Group 2**
1. FM
P. Slope overload
2. DM
Q. H-law
3. PSK
R. Envelope detector
4. PCM
S. Capture effect
T. Hilbert transform
U. Matched filter

**Group 1**with the most appropriate item in

**Group 2**.

Group 1 |
Group 2 |

1. FM | P. Slope overload |

2. DM | Q. H-law |

3. PSK | R. Envelope detector |

4. PCM | S. Capture effect |

T. Hilbert transform | |

U. Matched filter |

## 43. A source emits bit 0 with probability $$\frac{1}{3}$$ and bit 1 with probability $$\frac{2}{3}.$$ The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R as

\[\begin{gathered}
{f_{R|0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{4},}&{ - 3 \leqslant r \leqslant 1} \\
{0,}&{{\text{otherwise;}}}
\end{array}} \right. \hfill \\
{f_{R|1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{6},}&{ - 1 \leqslant r \leqslant 5} \\
{0,}&{{\text{otherwise;}}}
\end{array}} \right. \hfill \\
\end{gathered} \]

The minimum decision error probability is

\[\begin{gathered} {f_{R|0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \leqslant r \leqslant 1} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ {f_{R|1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \leqslant r \leqslant 5} \\ {0,}&{{\text{otherwise;}}} \end{array}} \right. \hfill \\ \end{gathered} \]

The minimum decision error probability is

## 44. The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion

$$x\left( t \right) = 5{\left( {\frac{{\sin 2\pi 1000t}}{{\pi t}}} \right)^3} + 7{\left( {\frac{{\sin 2\pi 1000t}}{{\pi t}}} \right)^2}$$

would be

$$x\left( t \right) = 5{\left( {\frac{{\sin 2\pi 1000t}}{{\pi t}}} \right)^3} + 7{\left( {\frac{{\sin 2\pi 1000t}}{{\pi t}}} \right)^2}$$

would be

## 45. The number of bits in a binary PCM system is increased from n to n + 1. As a result, the signal to quantization noise ratio will improve by a factor

## 46. A signal is sampled at 8 kHz and is quantized using 8-bit uniform quantizer. Assuming SNR_{q} for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is

_{q}for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is

## 47. The Nyquist sampling interval, for the signal sin c(700t) + sin c(500t) is

## 48. The bit stream 01001 is differentially encoded using 'Delay and Ex-OR' scheme for DPSK transmission. Assuming the reference bit as a '1' and assigning phases of '0' and 'π' for 1's and 0's respectively, in the encoded sequence, the transmitted phase sequence becomes

## 49. For a given data rate, the bandwidth B_{p} of a BPSK signal and the bandwidth B_{0} of the OOK signal are related as

_{p}of a BPSK signal and the bandwidth B

_{0}of the OOK signal are related as