Digital Signal Conversion: PCM Sampling, Quantization, and A-Law Encoding
Pulse Code Modulation (PCM) Fundamentals
1. Sampling Process
Samples are taken for the analog signal, measuring its amplitude (voltage). The process involves the following steps:
- The telephone signal has a voice frequency range of 300–3400 Hz. It passes through a low-pass filter, considering the signal from 0 to 4 kHz.
- A sample is taken instantaneously, and the amplitude value is retained for measurement.
- According to Nyquist's theorem, we need a sampling frequency ($f_s$) twice the maximum signal frequency ($f_s \ge 2f_{max}$). For a 4 kHz signal, this results in a sample every 125 $\mu$s (microseconds), corresponding to $f_s = 8,000$ samples/second.
- This process yields a train of Pulse Amplitude Modulated (PAM) pulses.
2. Quantization and Companding
The...