1. A PCM system samples an analog signal 20,000 times per second. The quantizer has 512 levels.
The resulting digital signal is encoded using Multilevel Line Coding with 8 distinct levels.
a) What is the system's bit rate?
b) What is the system's baud (signal) rate?
c) What is the minimum bandwidth required to transmit this signal?
OR
A PCM encoder receives an analog signal with a maximum frequency of 15 kHz and a peak-to-peak
voltage of 4 V. The required SNR (Signal-to-Quantization Noise Ratio) is at least 36 dB.
a) What is the minimum required sampling rate?
b) Determine the number of quantization levels needed.
Calculate the resulting bit rate of the PCM signal.
c) If the PCM bit stream is transmitted using a line coder with 2 levels, what is the minimum
bandwidth required?
2. An analog signal ranges from -5V to +5V. We use a uniform quantizer with 8 levels.
a) What is the step size?
b) What is the maximum quantization error?
c) If the signal value is 3.2V, which quantization level is it assigned to, and what is the
quantization error?
OR
An analog signal with a maximum frequency of 4 kHz is to be digitized using Delta Modulation. The
signal is given by the equation:
m(t) = 2 sin(8000πt). The DM system uses a sampling rate of 40,000 samples/sec.
a. Calculate the minimum step size Δ required to avoid slope overload
b. If the step size is set to 0.5, will the system experience slope overload for this signal? Justify
your answer mathematically.
3. A Delta Modulator is designed for an audio signal with a bandwidth of 3.2 kHz and a maximum
amplitude of 2 V. The sampling rate is chosen to be 8 times the Nyquist rate.
a. What is the sampling frequency (f_s)?
b. Calculate the step size (Δ) needed to prevent slope overload for a worst-case input signal of
maximum amplitude and frequency.
c. Calculate the maximum average SNR (in dB) for this DM system if the input signal is a
sinusoid with amplitude A.
4. A speech signal with a bandwidth of 3.1 kHz is to be transmitted digitally. Compare the required
bandwidth for two systems:
a) A Delta Modulation system with a sampling rate of 64 kHz.
b) A PCM system that samples at the Nyquist rate and uses 8 bits per sample.
Assume both systems use a binary line code (e.g., NRZ-L) for transmission.
