Q1.a)i) The process of quantisation introduces an error or noise component into the quantised signal. Derive an equation for the mean-squared quantisation error in terms of the quantization interval ‘a’.
ii) Hence show that the peak signal-to-quantisation noise ratio (SQNR) is
SQNR = ( 6n + 4.8 ) dB
Where 2 n is the number of quantisation levels.
b)i) Linear quantisation is used prior to binary PCM encoding of an analogue baseband signal which has a uniform probability density function. The signal-to-quantisation noise ratio must be no less than 35 dB. How many binary bits are required to code each quansation level?
ii) If the bit rate is 104 bits per second, what should be the maximum bandwidth of the analogue signal prior to sampling?
Q2.a)i) Explain how nonlinear quantisation can be used to reduce the number of levels required to quantise a signal.
ii) Explain why logarithmic quantisation is preferred.
iii) What types of signal is most suitable to be processed by non-linear quantisation?
b) Sketch the A-law companding curved. Explain why companding is used in voice transmission systems.
c) Show that the dynamic range of the logarithmic portion of the A-law compander is 38.8 dB and that the improvement in signal to quantisation noise ratio realized for small signals, compared with linear quantisation , is 24 dB.
d) For an 8-bit A-law companded PCM system, calculate the SQNR obtainable and the PCM bit rate. Assume the sampling frequency is 8 KHz.
Q3.a) Explain (qualitatively) how Differential Pulse Code Modulation (DPCM) can reduce the transmission bandwidth required.
b) Explain what is delta modulation. Why it is particularly suited to speech signals?
c) For an input sinusoid of frequency 1 kHz, estimate and compare the signal-to-error ratios of a linear PCM coder using a sampling rate of 2.5 kHz and 7 bits per sample quantisation with a single-integration delta modulator producing the same gross bit rate.
BASEBAND REGERATOR / ERROR PROBABILITY / LINE CODE
Q4.a) Digital transmission systems provide better received signal quality compare to analogue transmission systems when implementing a long distance communication link. Explain briefly why this is so.
b) A PCM transmission link employed 8 bit coding and uses baseband regenerator as repeater. Determine the Signal-to-Noise ratio obtainable at the receiver assuming no bit error occurred.
c) An analogue transmission system required amplifiers to be spaced every 2 km apart. Assume the Signal-to-Noise ratio of the amplifier is 65 dB, determine the maximum distance of the link before the quality of the received signal is lower than the PCM link above.
d) A RF binary PSK system operates with phase states separated by 180o. The bit rate is 2.0 Mbit/s and the noise power spectral density at the input to an ideal matched filter detector is 1.0 pW/Hz. If the transmission loss between transmitter and detector is 40 dB, what power must be transmitted to achieve a probability of bit error of 1( 10-6 ?
For binary PSK , Pe = ½ [1- erf(Eb/No)1/2]
Error function tables are provided.
Q5.a) Draw a simplified block diagram of a PCM regenerative repeater.
b) An ideal 18 – section, copper cable, PCM link employs unipolar , NRZ, rectangular pulses on each section and a center point detection process at each repeater. The probability of error versus SNR for this transmission and detection scheme is given by
If all sections were identical, and operated with a section SNR of precisely 18 dB, what would be the overall probability of error for the entire link?
Q6.(a) Sketch the typical, long term, spectrum of a speech waveform. Show on your sketch the bandwidth normally considered sufficient for telephone quality transmission.
(b) i) If the voice signal in part (a) is to...