Download Lecture 7

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) ?