*Choose the correct alternative from the following (10 x 2)*

1. A band-pass filter will

(a) pass frequencies each side of a band

(b) attenuate low frequencies but not high frequencies

(c) attenuate frequencies on each side of a band

(d) attenuate high frequencies but not low frequencies

2. If each pulse of the sequence to be detected is in ⸺ shape, the pulse can be detected without ISI

(a) Sine

(b) Cosine

(c) Sinc

(d) None of the mentioned

3. A pulse shaping filter should satisfy two requirements. They are

(a) Should be realizable

(b) Should have proper roil off factor

(c) Both of the mentioned

(d) None of the mentioned

4. If a noiseless channel band-limited to 5 kHz sampled every 1 mSec, what wilt be the value of sampling frequency?

(a) 250 samples/sec

(b) 500 samples/sec

(c) 800 samples/sec

(d) 1000 samples/sec

5. In the channel coding theorem, channel capacity decides the ⸺ permissible rate at which error-free transmission is possible.

(a) Maximum

(b) Minimum

(c) Constant

(d) None of the above

6. The relation between the probability of bit error and probability of symbol error in M-ary orthogonal signalling is

(a) M/M - 1

(b) 2M/M - 1

(c) (M/2)/M - 1

(d) M/M + 1

7. Which of the following is Poisson’s equation

(a) ∇

^{2}V = -ρ/∈(b) ∇

^{2}V = -4πσ(c) ∇

^{2}V = -4πρ(d) ∇

^{2}V = 08. ⸺ is defined as the process by which some characteristics of a carrier are varied in accordance with a modulating wave.

(a) Modulation

(b) Demodulation

(c) De-multiplexing

(d) None of these

9. For M equally likely messages, M >> 1 if the rate of information R > C, the probability of error is

(a) Arbitrarily small

(b) Close to unity

(c) Not predictable

(d) Unknown

10. The information rate R for given average information H = 2.0 for analog signal and limited to B Hz is

(a) 8 B bits/scc

(b) 4 B bits/scc

(c) 2 B bits/scc

(d) 16B bits/scc

### Answers

1. (c) The bandpass filter allows signals falling within a certain frequency band set up between two points to pass through while blocking both the lower and higher frequencies either side of this frequency band.

2. (c) The sinc shaped pulse is the ideal Nyquist pulse. If each pulse in the sequence to be detected is in sinc shape the pulses can be detected without ISI.

A sinc pulse

3. (b)

- A pulse-shaping filter should provide the desired roll-off and should be realizable, that is the impulse response needs to be truncated to a finite length.
- A pulse-shaping filter is used in communication channels to manipulate a waveform or pulses to have the desired shape in the time domain.
- A pulse-shaping filter can be a physical circuit, but normally it’s a mathematical function that is used as a signal processing algorithm.
- The goal of using a pulse shaping filter is to transfer digital data through a bandwidth-limited channel by converting it to an equivalent modulated analog signal.

4. (d)

5. (a) The channel capacity of a given channel is the highest information rate (in units of information per unit time) that can be achieved with arbitrarily small error probability.

6. (c) The relationship between the probability of bit error and probability of symbol error is (M/2)/M-1 in M-ary orthogonal signalling.

7. (a)

8. (a) In analog modulation, a continuously varying sine wave is used as a carrier wave that modulates the message signal or data signal. A carrier wave has three defining properties, which are amplitude, frequency and phase.

9. (b) If R > C, the error probability increases towards Unity. It means if the information rate R exceed a specific value C, the error probability will approach towards unity M increases.

10. (b)

The signal should be sampled at frequency 2B Hz.

Hence, information rate = 2 (2B) = 4B bits/s.

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