Transcript Figure 1–1 Communication system.

Lecture on Analog to Digital Conversion
Definitions
• Digital source produces a finite set of possible values.
• Analog source produces a infinite set of possible values.
• Signal is a measurable quantity (e.g., voltage) which bears
information.
• Noise is a measurable quantity which carries undesired
interference.
Why Digital?
•
•
•
•
•
Less expensive circuits
Privacy and security
Small signals (less power)
Converged multimedia
Error correction and reduction
Why Not Digital?
• More bandwidth
• Synchronization in electrical circuits
• Approximated information
Analog to Digital Conversion
• Sampling: Obtaining values at discrete points in time.
• Quantization: Non-linear transformation that maps continuous
values to discrete values.
Analog Signal
- Continuous time
- Continuous value
Sample
Quantize
- Discrete time
- Continuous value
Digital Signal
- Discrete time
- Discrete value
Sampling
Definition. Sampling is a process of evaluating signal w(t) at a discrete set of points,
t1 ,t2 ,t3 ,t4 , .... in time.
w(t)
t1 t2
t3 t4 t 5
t
Nyquist Sampling Theorem (in Plain Language)
Signal w(t) bandlimited to B hertz may be represented over the interval -   t   by
sampling at frequency f s where f s  2 B. If w(t) is sufficiently smooth, then w(t) can be
  n 

completely reconstructed from the samples  w   , n  ...  3, 2, 1, 0,1, 2 ,3, ... .
  f s 

“sampler”
ws(t)
w(t)
ws(t)
w(t)
t1 t2
t3 t4 t5
t
t1 t2
t3 t4 t5
t
Gated Samples
Gated Sample and Hold
Impulse Samples
Sample and Hold
Quantization
V
output w2(t)
-V
V
input w1(t)
-V
Region of operation
For M=2n levels, step size :
 = 2V /2n = V(2-n+1)
Quantization Error, e
V
output w2(t)
-V
V
input w1(t)
-V
/2
-/2
Error, e
input w1(t)


Error is symmetric
around zero.
0
Average error power :
   3 
  
V
2
 n 1 2
1
2
2

V

2
V 2 2n


2
2
2


e ( s )ds   x dx  



2
2V V
0

3  12
12
3




Suppose the input signal is a triangula r wave between  V and  V .

2
V2
Then the average signal power is
.
3
S
    22 n
 N out


Noise
Types of Noise
• Quantizing noise (during A/D conversion)
• Environment noise (e.g., EM interference)
• Filtering noise (low pass filtering at decoder)
Types of Quantization Noise
• Overload noise (input too large)
• Random noise (input too small)
• Granular noise (non uniform error jump)
• Hunting noise (too long of quite time)
signal to noise ratio
S
2
   3M
N
M : quantization levels
2
S
Let M  2n     M 2  2n  22 n
N
S
S
2n

10
log

10
log
2
 20 n log 2  6.02 n
 
 
 N dB
 N out
 
 
This equation states that for each bit added to the ADC scheme, about 6-dB is gained
in the signal-to-noise ratio.
Non-uniform Quantizer
Used to reduce quantization error and increase the dynamic range
when input signal is not uniformly distributed over its allowed
range of values.
allowed
values
values
for most
of time
input
time
Digital to Analog Converter Circuit
Analog to Digital Converter Circuit