8/10/2019 Assignment ADC

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1. Show that a band limited signal of finite energy which has no frequency components higher than

fmHz is completely described by specifying values of the signals at instants of time separated by

1/2fm seconds and also show that if the instantaneous values of the signals are separated by

intervals larger than fmseconds, they fail to describe the signal. A bandpass signal has spectral

range that extends from 20 to 82 kHz.

Find the acceptable range of sampling frequency fs*2.

A bandlimited signal x(t) is sampled by a train of rectangular pulsed of width

and period T.

(i)Find an expression for the sampled signal.

(ii)Determine the spectrum of the sampled signal and sketch it.

3. What is aliasing and how it is reduced?

4. A PCM system uses a uniform quantizer followed by a v bit encoder. Show that rms signal to

quantization noise ratio is approximately given as (1.8 + 6v) dB.

5. A television signal having a bandwidth of 4.2 MHz is transmitted using binary PCM system. Given

that the number of quantization level is 512. Determine:

(i)Code word length

(ii)Transmission bandwidth

(iii)Final bit rate

(iv)Output signal to quantization noise ratio.6. The information in an analog signal voltage waveform is to be transmitted over a PCM system

with an accuracy of 0.1% (full scale). The analog voltage waveform has a bandwidth of 100 Hz

and an amplitude range of10 to + 10 volts.

(i)Find the minimum sampling rate required.

(ii)Find the number of bits in each PCM words.

(iii)Find minimum bit rate required in the PCM signal.

(iv)Find the minimum absolute channel bandwidth required for the transmission of the PCM

signal.

7. A delta modulator system is designed to operate at five times the Nyquist rate for a signal

having a bandwidth equal to 3 kHz bandwidth. Calculate the maximum amplitude of a 2 kHz

input sinusoidal signal for which the delta modulator does not have slope over load. Given thatthe quantizing step size is 250 mV. Also, derive the formula that you use.

8. A low pass signal of 3 kHz bandwidth and amplitude over 5 volts to + 5 volts range is sampled

at Nyquist rate and converted to 8-bit PCM using uniform quantization. The mean squared value

of message signal is 2 Volts-squared. Determine the following:

(i)the normalized power for quantization noise.

(ii)The bit transmission rate.

(iii)The signal to quantization noise ratio in dB.

(iv)Derive the expression used in (i) and (ii)

9. If a voice frequency signal is sampled at the rate of 32,000 samples/sec and characterized by

peak value of 2 Volts, determine the value of step size to avoid slope overload. What is

quantization noise power Nq and corresponding SNR? Assume bandwidth of signal as 4 kHz.

10. Explain Delta modulation in detail with suitable diagram. Also, explain ADM and compare its

performance with DM.

11.What is the slope overload distortion and granular noise in delta modulation and how it is

removed in ADM.

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12.Explain Differential pulse code modulation.

13.Derive Power Spectral Density (PSD) of NRZ Polar Format.

14.Derive Power Spectral Density (PSD) of the Manchester Format.

15.Explain Eye Diagram.

16.Explain the Nyquist criteria for distortionless baseband binary transmission.

17.Explain ISI. Give Nyquist criterion for zero ISI raised cosine spectrum.

18.Find out the power spectral density of NRZ and AMI signal format.

19.Draw and explain Eye pattern diagram.

20.

Explain Gram-Schmidt orthogonalization procedure, with a suitable example.

21.Verify whether two signals are orthogonal over one time period of the signal with smallest

frequency signal:

X1(t) = Cos 2ft and X2(t) = Sin 2ft

X1(t) = Cos 2ft and X2(t) = Cos (2ft + /3)X1(t) = Cos 2ft and X2(t) = Cos (4ft + /4)X1(t) = Sin 4ft and X2(t) = - Cos (ft /6)

22.Explain correlation receiver and Maximum Likelihood detection process.

23.

Discuss properties of the Matched Filter. Explain how SNR maximization and minimization ofaverage symbol error probability can be achieved using a Matched Filter receiver?