PCM

Professor: Dr. Miguel Alonso Jr.

Outline

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

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

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

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

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 = ?

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

SNRdB for a PCM system SNRdB = 1.76 + 6.02*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) ?