Your project involves implementing and analyzing a Pulse Code Modulation (PCM) system using MATLAB. Here’s a detailed breakdown of the tasks based on your project description:

Task Breakdown:

1. Analog Signal Analysis and PCM Conversion:

   • Generate a sinusoidal analog signal with a frequency of 20 Hz.
   • Quantize the signal using a quantizer with 16 levels (each level encoded with 8 bits).
   • Sample the analog signal at the Nyquist rate, calculate the PCM signal, and determine its bit rate analytically and programmatically.

2. Nyquist Rate vs. Twice Nyquist Rate Sampling:

   • Repeat the above task using a sampling rate that is twice the Nyquist rate.
   • Compare the results with respect to:
     • Quality of the sampled signal.
     • Bit rate of the PCM signal.

3. Custom MATLAB Function for Bit Rate Computation:

   • Develop a function to compute the bit rate ($R_b$) given:
     • Sampling rate ($F_s$).
     • Number of quantization levels ($L$).
   • Test this function with:
     • $F_s = 100 \, \text{Hz}, L = 64$.
     • $F_s = 1000 \, \text{Hz}, L = 256$.
     • $F_s = 10,000 \, \text{Hz}, L = 1024$.

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Would you like a MATLAB script or guidance for any specific part of the project? If needed, I can draft detailed code snippets and provide explanations for:

• Signal generation and plotting.
• PCM signal construction and bit rate computation.
• Comparison analysis between Nyquist and twice Nyquist sampling rates.

5 Questions You Might Explore:

1. What is the impact of increasing the sampling rate beyond twice the Nyquist rate on the PCM signal's accuracy?
2. How does the number of quantization levels affect the PCM signal and bit rate?
3. Can the MATLAB function handle other user-defined values for $F_s$ and $L$?
4. What techniques could improve signal quality without increasing the bit rate?
5. How does this project relate to real-world applications of PCM in communication systems?

Tip:

Always validate your MATLAB results with theoretical calculations to ensure accuracy.