Transcript Sampling of Analog Signal

Digital Coding of
Analog Signal
Electronics Engineering Department,
Sardar Vallabhbhai National Institute of Technology,
Surat-395007.
Prepared By:
Amit Degada
Teaching Assistant
Goal of Today’s lecture.
• Something More about the practical
Approach
• Delta Modulation De-merits
• SNR Calculation for DM
• Comparison of DM, DPCM and PCM
• Adaptive delta Modulation
Integrator
• Integrator is nothing but a RC Low Pass
filter.
Characteristic of Quantizer
If the Difference is
positive increase the
Voltage by step-size
σ, Vice-Versa.
• Quantizer is 1 bit Quantizer.
• Its simply a Voltage Comparator.
Noise in DM
• The key to effective use of DM is proper selection of
step size σ and sampling Freq/Sampling Time.
• They must be chosen in a such a way that stair-case
approximation is close to message signal.
• We can know he max frequency at which the signal is
changing
Noise in DM
• To account fastest possible change
we have to increase the sampling
frequency as well as step size.
• But Sampling Freq  Bandwidth
&
Larger the step Size  Quantization
Error
Noise in DM
• Ideally the slope of both Quantized signal and
Message signal must match.
• It requires that
m ax
dm ( t )

dt

………..(7)
Ts
Suppose
m ( t )  A cos  t
Hence,

m (t )
m ax
So
A m ax 
 A   f s
 fs

………..(8)
………..(9)
Noise in DM
The maximum Amplitude that we can
follow for message signal can be given by
A m ax
V oice 
 fs *
r
………..(10)
Where,
 r  2   800 Rad
*
This equation is proved by de jagger.
U may see, F. De. Jagger, “ Delta Modulation, a method of
PCM transmission by 1 bit code”, Phillips Res. Rep. No 7 pp
442-466, 1952
Noise in DM
Thus the maximum Amplitude that we can use without causing
the slope overload can be found at frequency 800Hz.
•Fortunately, Voice signal spectrum decays with frequency.
•Decreases as 1/ω up to 2000 Hz and beyond that by 1/ω2
•Hence Single Integration up to 2000Hz and Double for Beyond it
• Double Integrator Can be Built By 2 Cascade RC with time constant
1/200Pi (100 Hz to 2KHz) and 1/4000pi(>2KHz) respectively.
Noise in DM
Slope overload
The name slope overload comes due to quantized signals
fails to follow the slop of message signal.
The DM With Fixed step size is Linear Delta Modulation
(LDM)
Noise in DM
• What would happen if we keep the step
size larger?
This would results into considerable Overshoot. This is Known as
Hunting or Granular Noise.
It is analogous to Quantization Noise.
Noise in DM
• The error d(t) caused by Hunting Lies in the range of
(-σ,+σ).
where,
σ=Step-Size.
• So Finding the Granular Noise Power,
 
2
 
2

1

2


2
3
 d
2
Signal To Noise Ratio
• Granular Noise has Power Spectral Density in the range of
well-beyond the fs.
• Band-limiting LPF can remove it.
• Ideally Noise Power will be well-below the above equation.
• To Compute Noise power we assume that PSD is uniform
and in the range of 0 to fs Hz. (Experimentally Proved)
• σ3/3 is total noise power, which is uniformly distributed
over the range of fs, the Power within Signal Bandwidth B
is,
 2   B 
No  
 
 3   fs 
And
So  m ( t )
2
Signal To Noise Ratio
Suppose mp is the Signal Peak
Hence,
 
mp 
 fs
r
 rm p
………..(12)
fs
So SNR becomes
So
………..(11)

3 fsm
No
2
(t )
………..(13)
2
 B
Manipulating all equations
3
2
150  B T  m ( t )

2  B 
No
 mp2
 
So
For Single Integration
Where,
5
*
2
 B T  m (t )
 5.34 

No
B

 mp2
So
For Double Integration
B T  fs / 2
Signal To Noise Ratio (PCM)
In General,
So
 c (2)
2n
No
Where,
But
 3m 2 (t )

2

mp
c
3

 [ln(1   )] 2

B T  fs / 2
Finally
&
So
No
 c (2)
………..(14)
Uncompressed
Compressed ………..(15)
B T  n.B
2 BT
B
………..(16)
………..(17)
Comparison Between DM and PCM
Thank You