1. Professor: Dr. Miguel Alonso Jr.
PCM
Professor: Dr. Miguel Alonso Jr.

2. Outline Sample and Hold, and Sampling Frequency Quantization
Dynamic Range and SNR Calculations
Amplitude Companding
D to A and A to D

3. Introduction
Concerned with the transfer of information in digital form
Advantages:
Noise Performance
Ability to process signal at the source and destination DSP
PCM is the most common technique used today in Digital Communications for representing an analog signal by a digital word.
PCM is a technique for converting analog signals into a digital representation

5. Sample and Hold, and Sampling Frequency
The first step is to sample and hold the analog input
PAM:
Natural, not good for sampling
Flat-top PAM
Sampling frequency must meet the Nyquist Criteria because of Aliasing
Fs ≥ 2*Fmax

6. Quantization
Once the signal has been sampled, the binary conversion process can begin
In PCM systems, the sampled signal is segmented into different voltage levels, with each level corresponding to a different binary number.
This process is called quantization
Converted to the closest binary value provided in the digitizing system
At each sampling interval, the analog amplitude is quantized into the closest available quantization level

7. Resolution
q = Vmax / 2n
Quantization error or Noise results when the analog signal being sampled lies in between two quantization levels
Example:
3 volt 40Hz Sine wave sampled in a 4-bit PCM system
Fs = ?
Q=?, Fclock = ?

8. Dynamic Range and SNR calculations
Dynamic range for a PCM system is defined as the ration of the maximum input or output voltage level to the smallest voltage level that can be quantized and/or reproduced by the converters
Vfs/q
DR = Vmax/Vmin = 2n
DRdB = 20*log10 Vmax/Vmin
DRdB = 20*log10 2n

9. SNRdB for a PCM system
SNRdB = *n
Signal to quantization noise
SNRq(dB) = 10log 3*(2n)2
Example: A digitizing system specifies 55dB of dynamic range. How many bits are required to satisfy the DR spec? What is the SNRdB ? What is SNRq(dB) ?