Instructions: Answer all questions. Each question carries equal marks. Try to answer before checking the solution.
Basic Concepts (Questions 1-10)
1. What does PCM stand for?
Pulse Code Modulation
2. What are the three main steps in PCM?
Sampling, Quantization, and Encoding
3. Who developed PCM and in what year?
Alec Reeves in 1937
4. What is the purpose of sampling in PCM?
To convert a continuous-time signal into a discrete-time signal by measuring the signal's amplitude at regular intervals
5. What does quantization do in the PCM process?
Converts continuous-amplitude samples into discrete amplitude values
6. What is the final step in PCM that creates the digital output?
Encoding (converting quantized samples to binary code)
7. Name two common applications of PCM.
Digital audio (CDs), digital telephony, computer audio interfaces, digital video, medical imaging (any two)
8. What is the main advantage of PCM over analog transmission?
Better noise immunity (or any other advantage: regeneration capability, flexibility, security, easier storage)
9. What is the primary disadvantage of PCM?
Requires larger bandwidth than analog transmission (or complexity, quantization noise)
10. What type of signal is the input to a PCM system?
Analog signal (continuous in both time and amplitude)
Sampling Theory (Questions 11-18)
11. State the Nyquist theorem.
A signal can be exactly reconstructed if the sampling frequency is greater than twice the highest frequency component in the signal (fs > 2 × fmax)
12. What is the minimum sampling rate for a signal with maximum frequency of 12 kHz?
Greater than 24 kHz (2 × 12 kHz)
13. What happens if a signal is sampled below the Nyquist rate?
Aliasing occurs, making it impossible to reconstruct the original signal accurately
14. What is the standard sampling rate for CD-quality audio?
44.1 kHz
15. Why is the CD sampling rate 44.1 kHz when human hearing only goes up to about 20 kHz?
To provide a safety margin above the Nyquist rate (2 × 20 kHz = 40 kHz) and account for filter imperfections
16. What is the sampling rate used in digital telephony (PCM)?
8 kHz
17. What is the maximum audio frequency that can be accurately represented with an 8 kHz sampling rate?
4 kHz (Nyquist frequency = fs/2)
18. What is the purpose of an anti-aliasing filter in PCM systems?
To remove frequency components above half the sampling rate to prevent aliasing
Quantization and Encoding (Questions 19-26)
19. How many quantization levels are there in an 8-bit PCM system?
256 levels (28)
20. What is the standard number of bits per sample in CD-quality audio?
16 bits
21. What is quantization error?
The difference between the actual analog value and the quantized digital value
22. Calculate the SQNR for a 12-bit PCM system.
6.02 × 12 + 1.76 = 74 dB
23. What is the relationship between the number of bits and dynamic range in PCM?
Each additional bit increases dynamic range by approximately 6 dB
24. What is the binary code for quantization level 5 in a 4-bit PCM system?
0101 (5 in binary)
25. What is the difference between linear and nonlinear PCM?
Linear PCM has uniform quantization steps, while nonlinear PCM has non-uniform steps (often used in telephony)
26. What is companding in PCM systems?
A process of compression before quantization and expansion after reconstruction to improve SQNR for small signals
Calculations and Advanced Concepts (Questions 27-30)
27. Calculate the bit rate for a mono PCM system with 16 kHz sampling rate and 12 bits per sample.
16,000 × 12 × 1 = 192,000 bits/sec (192 kbps)
28. What is the bit rate of CD-quality stereo audio (44.1 kHz, 16-bit)?
44,100 × 16 × 2 = 1,411,200 bits/sec (1.411 Mbps)
29. What is the difference between PCM and DPCM?
DPCM (Differential PCM) encodes the difference between current sample and predicted value from previous samples, reducing bit rate
30. Why is 8-bit PCM with μ-law companding often used in digital telephony instead of linear PCM?
It provides better sound quality for voice signals at lower bit rates by having smaller quantization steps for small signals (which are more common in speech) and larger steps for loud signals