Tutorial-1 (ECE 5^th Sem)         Subject: Digital Communication

Topic Covered: PCM, Sampling and SNR                                                      Date:05- 08-2016

Q.1. A television signal having a bandwidth of 4.2 MHz is transmitted using binary PCM system. Given that the number of quantization levels is 512. Determine:

a) Code word  length

b) Transmission bandwidth

c) Final bit rate

d) Output signal to quantization noise ratio.

Q.2. The bandwidth of an input signal to the PCM is restricted to 4  KHz input signal varies in amplitude form -3.8V to + 3.8V and has the average power of 30 mV. The required signal to noise  ratio is given as 20 dB. The PCM modulator produces binary output. Assuming uniform quantization.

a) Find the number of bits required per sample.

b) Output of 30 such PCM coders are time multiplexed. What would be the minimum required transmission bandwidth for this multiplexed signal?

Q.3.  The information in an analog signal voltage  waveform is to be transmitted over PCM system with an accuracy of +0.1%(full scale). The analog voltage waveform has a bandwidth of 100Hz and an amplitude range of -10 to +10 volts.

a) Find the minimum sampling rate required.

b) Find the number of bits in each PCM word.

c) Find minimum bit rate required in the PCM signal.

d) Find the minimum absolute channel bandwidth required for the transmission of the PCM signal.

Q.4. A PCM system uses a uniform quantizer followed by a 7-bit binary encoder. The bit rate of the system is equal to 50x10⁶ bits/sec.

a) What is the maximum message signal bandwidth for which the system operates satisfactorily?

b) Calculate the output signal to quantization noise ratio when a full load sinusoidal modulating wave of frequency 1 MHz is applied to the input.

Q.5. The information in analog waveform with maximum frequency f_m=3kHz is to be transmitted overran M-level PCM system where the number of quantization levels is M=16. The quantization distortion is specified not to exceed 1% of peak to peak analog signal.

a) What would be the maximum number of bits per sample that should be used in this PCM system?

b) What is the minimum sampling rate and what is the resulting bit transmission rate?

Q.6.  A signal having bandwidth equal to 3.5kHz is sampled, quantized and coded by a PCM system. The coded signal is then transmitted over a transmission channel of supporting a transmission rate of 50 k bits/sec. Determine the maximum signal to noise ratio that can be obtained by this system.

The input signal has peak to peak value of 4 volts and rms value of 0.2 V.

Q.7. A signal x(t) is uniformly distributed in the range + x_max . Evaluate maximum signal to noise ratio for this signal.