Digital Comm Tutorial
PCM CODING/COMPANDING
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
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