ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation....
Transcript of ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation....
![Page 1: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/1.jpg)
ANALOG COMMUNICATION (204189)
PULSE ANALOG MODULATION
Unit 6
1
![Page 2: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/2.jpg)
Objectives • Builds the concepts of Pulse Analog Modulation.
• Understand the difference between analog modulation and pulse analog modulation.
• Figures out building a time division multiplexing signal.
• Introduces Sampling and hence reconstruction.
• Familiarizes the words such as Nyquist rate, Nyquist interval, and states the Nyquist Theorem.
• Construction of different types of Pulse Modulated signals.
• Presents Pulse Code Modulation technology and
• Links pulse analog communication and digital communication. 2
![Page 3: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/3.jpg)
Books
1. Communication Systemes Simon Haykin 4th Edition Wiley Publications 2. Principles of Communication Systems Herbert Taub Donald Schilling Goutam Saha Third Edition Tata-McGraw-Hill Publications
NPTEL Lecture Series
3
![Page 4: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/4.jpg)
Introduction(1)
• All the Modulation schemes discussed so far – has carrier – a sinusoidal signal. • A non-sinusoidal signal is used as the carrier. That is a Pulse Signal. V(t)
t
4
![Page 5: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/5.jpg)
Introduction(2)
• The Pulses carry the information present in the message signal. • Advantages
t
V(t)
5
![Page 6: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/6.jpg)
Introduction(3)
Temp
t Pressure
t
t
Volume
t
Mux
6
![Page 7: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/7.jpg)
Band-Limited and Time-Limited Signals
Band limited signals : A signal x(t) is said to be band limited if there exists a highest frequency “B” Hz, such that X(f) = 0 ; ІfІ > B
Time limited signals : A signal x(t) is said to be time limited if it exists over certain finite duration of time, i.e. x(t) = 0 ; t ≤ t1 and t ≥ t2
t1 t
v(t)
t2
7
![Page 8: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/8.jpg)
Band-Limited and Time-Limited Signals(4)
• A time-limited signal is the one that is non-zero only for a finite length of time interval.
T t
v(t) x(t)
t
8
![Page 9: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/9.jpg)
Band-Limited and Time-Limited Signals(5)
• A time - limited signal cannot be also band limited.
t
f(t)
ω
F(ω)
9
![Page 10: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/10.jpg)
Band-Limited and Time-Limited Signals(6)
• A band - limited signal cannot be also time-limited.
t
f(t)
ω
F(ω)
10
![Page 11: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/11.jpg)
11
![Page 12: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/12.jpg)
Band-Limited and Time-Limited Signals(3)
Mention which is a band limited signal?
1 3
2 4
12
![Page 13: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/13.jpg)
Narrowband signals and systems
Narrowband signals : Narrowband signals has frequency components within only a small band “B”. Modulation can produce narrowband signals. Narrowband affects transmission bandwidth, design of receiver and transmitter.
Narrowband systems : Modulators, filters, transmitters, receivers that process narrowband signals, are called Narrowband systems.
13
![Page 14: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/14.jpg)
Sampling Rate(1)
A Sine Wave
A Sine Wave Sampled at I time per cycle And reconstructed
If a sine wave has frequency of 1Hz,
Then, Nyquist rate = 2Hz
But, if we will keep sampling rate = 1Hz,
Then, recovered signal might be as
shown as blue horizontal line, from
which it is not at all possible to recover
or estimate the original signal.
14
![Page 15: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/15.jpg)
Sampling at 2 times per cycle
Sampling at 1.5 times per cycle
If a sine wave has frequency
of 1Hz, Then, Nyquist rate =
2Hz
But, if we will keep sampling
rate = 1.5 Hz or 2Hz,
Then, recovered signal might
be as shown as red (1st case)
or green (2nd case) as shown,
from which it is very hard to
recover or estimate the
original signal.
Sampling Rate(2)
15
![Page 16: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/16.jpg)
Sampling At Many Times Per Cycle
Sampling Rate(3)
16
If a sine wave has frequency
of 1Hz, Then, Nyquist rate =
2Hz
But, if we will keep sampling
rate >> 2Hz i.e. sampling
many times per cycle,
Then, recovered signal will be
as shown by red dotted
outline, from which it is
possible to recover or
estimate the original signal.
![Page 17: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/17.jpg)
Fourier Transform of a Strictly Band-limited Signal
g(t)
t f
Analog signal
G(f)
G(0)
Spectrum of g(t)
W -W
17
![Page 18: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/18.jpg)
Sampling theorem :
• Sampling process is described in time domain.
g(t)
t
Analog signal
g(t) δ
t
Ts
Instantaneously sampled version of analog signal
Ts: Sampling Period 1/Ts = fs Sampling frequency
18
Let, g(t) be a band limited signal whose highest frequency component is W.
Let, the signal is periodically sampled at every Ts seconds i.e. Ts>>(1/2W),
Then, these samples g(nTs) uniquely determines the signal and original signal may be
recovered from these samples with no distortion.
The time Ts is the sampling time.
![Page 19: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/19.jpg)
Sampling Process
g(t)
t
Analog signal: g(t) Instantaneously sampled version of analog signal
t
gδ(t)
g(t) = ∑ g(n Ts) δ(t-nTs) δ n = -∞
∞
= g(0) δ(t) + g(Ts) δ(t-Ts) +g(2Ts) δ(t-2Ts)+…. 𝒈𝜹(t)
𝛿𝑇(𝑡)
t
19
Let, g(t) be a band limited signal whose highest frequency component is W.
δT(t) is a sampling signal with frequency fS.{ where, fS >> 1/(2W)}and
gδ(t) is a sampled signal.
After multiplication of g(t) and δT(t) in time domain, we generate sampled signal gδ(t).
Multiplication in time domain results into convolution in frequency domain.
Sampling signal
![Page 20: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/20.jpg)
Application of Fourier Transform Property (Sampling theorem and low pass signal)
• Frequency convolution property: Multiplication of two functions in time domain is equivalent to convolution in frequency domain.
g(t)
t 𝛿𝑇(𝑡) =
𝛿𝜔(ω)
t
Gδ(f)
Gδ(0)
f
Spectrum of sampled g(t)
-2w 2w w -w
G(f)
G(0)
f w
Sampled version of analog signal
F R E Q U E N C Y fs
3w -3w
𝑑𝑡
Ts
+ 2𝑑𝑡
Ts
{ cos 2π 𝑡
Ts
+ cos 2× 2π 𝑡
Ts
+ _ _ _ _ _ _ }
gδ(t) = g(t) 𝑑𝑡
Ts
+ 2𝑑𝑡
Ts
{ g(t) cos 2π(2W)t + g(t) cos 2× 2π(2W)t + _ _ _ _ }
4w -4w
20
![Page 21: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/21.jpg)
Different Possible Versions of Periodic Spectrum
Establish the relation between fs and w.
fs = 2w
fs > 2w
fs < 2w
I
f -2w 2w w -w fs 2fs
Gδ(f)
f w -w 2fs fs -2fs -fs
2 Gδ(f)
f w -w fs 2fs
3 Gδ(f)
21
![Page 22: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/22.jpg)
Reconstruction (1)
Channel
Ideal f -2w 2w w -w
fs 2fs
g(t)
t
f -2w 2w w -w fs 2fs
Gδ(f)
Pass it through a LPF
LPF: ideal frequency response
1. fs = 2w
w f
T.f
G(f)
G(0)
f w -w
22
![Page 23: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/23.jpg)
Reconstruction (2) G(f)
G(0)
f
g(t)
t
2. fs > 2w
f w -w 2fs fs -2fs -fs
Channel
Ideal f w
2fs fs -2fs -fs
Pass it through a LPF
LPF: practical frequency response w f
T.f
w -w
23
![Page 24: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/24.jpg)
Guard band
If fs=8KHz, W= 3.3KHz Then, Guard band = (fs-W) – W
= fs- 2W
= (8KHz-2*3.3KHz) = 1.4 KHz
24
![Page 25: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/25.jpg)
G(f)
G(0)
f
g(t)
t
Reconstruction (3)
3. fs < 2w
f w -w fs 2fs
Channel
Ideal
Not possible to reconstruct the original signal
w -w
ALIASING
f
25
Here, we find the overlap between spectrum of g(t) and spectrum of DSBSC centered around
fS. Hence, no filtering action will allow recovery of g(t). This phenomenon is called as
Aliasing in frequency domain.
![Page 26: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/26.jpg)
Nyquist criteria
Nyquist rate : When the sampling rate becomes exactly Equal to ‘2w’ samples per second, for a given bandwidth Of ‘w’ Hz, then it is Nyquist rate. Nyquist interval: Time interval between any two adjacent Samples when sampling rate is Nyquist rate.
26
![Page 27: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/27.jpg)
Nyquist Theorem
• A band limited signal of finite energy, which has no frequency components higher than W or fm Hz, is completely described by specifying the values of the signal at instants of time separated by 1/2w or 1/2fm seconds.
• A band limited signal of finite energy, which has no frequency components higher than W or fm Hz, may be completely recovered from the knowledge of its samples taken at the rate of 2W or 2fm samples per second.
• 2W or 2fm sps: Nyquist Rate; 1/2w or 1/2fm : Nyquist interval
27
![Page 28: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/28.jpg)
Sampling of Band pass signal If m(t) has highest frequency fM and lowest frequency 0 Hz, then fs ≥ 2fM.
case (i) fL = n.fs ; where, n = integer n=2(here) ; fs=2(fM-fL)
If m(t) has highest frequency fM and lowest frequency fL Hz, then fs need not be greater than 2(fM-fL). e.g. If spectral range of signal extends from 10.0 MHz to 10.1MHz, then fs= 2(fM-fL) = 2(10.1-10.0) = 0.2MHz. To establish the sampling theorem for bandpass signals, select sampling frequency as fs=2(fM-fL) provided that fM or fL is a harmonic of fs.
28
![Page 29: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/29.jpg)
case (i) fL = n.fs ; where, n = integer n=2(here) ; fs=2(fM-fL)
0 fs
0
PS NS
M(w)
F{m(t)S(t)}
fM
-fs 2fs -2fs 2.5fs -2.5fs
2fs -2fs 2.5fs -2.5fs fL -fL -fM
3fs -3fs
f
f
If “ F{ m(t)S(t) }” is passed thr’ sharp cutoff BPF from fL to fM, signal m(t) will be recovered exactly.
29
![Page 30: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/30.jpg)
case (ii) fL ≠ n.fs ; fM and fL are not harmonics of fs ; To find fs which will give no overlaps.
PS NS
M(jw)
0 fM fL -fL -fM
f
{ -fL+ (N-1)fs } { -fM+ N.fs }
f
F{m(t)S(t)}
30
![Page 31: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/31.jpg)
-fL+ (N-1)fs ≤ fL -fM+ N.fs ≥ fM
(N-1)fs ≤ 2fL N.fs ≥ 2fM
Let, fM-fL≡ B , k ≡ fM/B (N-1)fs ≤ 2(fM-B) N.fs ≥ 2fM
fs ≤ 2B( 𝑘−1
𝑁−1 ) fs ≥ 2B(
𝑘
𝑁 )
This means that sampling frequency should be in between above two fs values to avoid the overlap. As fs >> 2B ; k>>N Band pass sampling theorem :- A band pass signal with highest frequency fM and bandwidth B, can be recovered from it’s samples through band pass filtering, by sampling it with frequency fs = 2 fM / k , where k is the largest integer not exceeding fM/B.
31
![Page 32: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/32.jpg)
Numericals :
32
![Page 33: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/33.jpg)
Pulse amplitude modulation and concept of time division multiplexing :
m1(t)
m2(t) m2(t)
m3(t) m1(t) Filter1
Filter2
Filter3 m3(t)
commutator decommutator
Communication channel
Transmission of no. of band limited signals over single Communication channel
33
![Page 34: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/34.jpg)
Interlacing of two baseband signals :
Channel 1
Channel 2
Ts
Ts
m1(t)
m2(t)
Sample of m1(t)
Sample of m2(t)
t
These samples are inputs to the corresponding filters in decommutator. 34
![Page 35: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/35.jpg)
Maximum no. of signals can be multiplexed = N = fc / fM where, fc => channel bandwidth fM => baseband signal bandwidth i.e. m1(t), m2(t), …… are bandlimited to fM. * The instantaneous samples at the transmitting end will have infinitesimal energy, thus have infinitesimal peak value after transmission, which can be lost in background noise. * Thus more reasonable sampling will be natural sampling.
35
![Page 36: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/36.jpg)
Types of sampling
36
![Page 37: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/37.jpg)
Natural sampling :
m(t)
S(t)
m(t)S(t) = 𝝉
𝐓𝒔
m(t) + 2τ
Ts
{m(t) c1cos 2π 𝑡
Ts
+ m(t) c2cos 2× 2π 𝑡
Ts
+ _ _ _ _ _ _ }
S0(t) = τ
Ts
m(t) Passed thr’ LPF
τ
S(t) = τ
Ts
+ 2τ
Ts
{ c1cos 2π 𝑡
Ts
+ c2cos 2× 2π 𝑡
Ts
+ _ _ _ _ _ _ } , cn=sin (
𝑛𝜋𝜏
𝑇𝑠)
(𝑛𝜋𝜏
𝑇𝑠)
37
m(t)S(t)
![Page 38: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/38.jpg)
If ‘N’ signals are to be multiplexed,
then the maximum pulse width τ=𝑇𝑠
𝑁
If τ ↑, output so(t) ↑ ; where S0(t) = 𝜏
𝑇𝑠
m(t)
But with ↑ in τ, crosstalk ↑
because guard band between adjacent pulse ↓.
So, τ << 𝑻𝒔
𝑵 .
Natural sampling is not generally used, but instead Flat top sampling is used which simplifies the circuitry for sampling operation.
38
![Page 39: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/39.jpg)
Flat top sampling : A Flat top pulse has a const. amplitude equal to sample value of signal at the beginning of the pulse. A gate pulse at G1 briefly closes the sampling switch and the capacitor holds the sampling voltage until discharged by a pulse applied at G2.
39
![Page 40: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/40.jpg)
x(t)
xδ(t) = x(t) s(t)
S(t) = xδ(t) *h(t) S(f) = xδ(f) H(f) = fs 𝑋 𝑓 − 𝑛𝑓𝑠 𝐻(𝑓)∞
𝑛=−∞
h(t)
40
![Page 41: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/41.jpg)
Aperture effect : The high frequency roll off characteristic of H(f) acts as low pass filter and attenuates upper portion of message spectrum. This loss of high frequency content is called as Aperture effect. The aperture effect can be compensated by (i) selecting pulse width τ very small i.e. “ τ<<Ts “. (ii) using equalizer circuit Recovering of x(t) : PAM signal Reconstruction filter Equalizer Equalizer compensates aperture effect and also compensates the attenuation caused by reconstruction filter.
41
![Page 42: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/42.jpg)
Forms of Pulse Modulation
• PAM, PWM ad PPM Analog Modulation schemes.
• A parameter of the pulse is varied in accordance with message signal • PAM- Amplitude – Analog Width - Discrete • PWM – Width- Analog Amplitude – discrete • PPM – Position – Analog Amplitude - Discrete
42
![Page 43: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/43.jpg)
PWM and PPM Generation
Message input
Sawtooth
PWM output
PWM input
Inverter Differentiator Positive edge triggered pulse generator
PPM output
+
-
43
Comparator
![Page 44: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/44.jpg)
Pulse Width Modulation and Pulse Position Modulation
44
t
t
t
t
PWM o/p
inverted PWM
differentiated o/p
PPM o/p
Message input
Sawtooth waveform
t
![Page 45: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/45.jpg)
Pulse Code Modulation(1)
• Digital Scheme
• PCM is a method of converting an analog into digital signals. • PAM, Quantization, Unique code word
45
![Page 46: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/46.jpg)
Pulse Code Modulation (2)
6.4
5.0
3.05
1.25
0.4
6.0
4.4
5.0
2.6
7 6 5 4 3 2 1 0
111 110 101 100 011 010 001 000
110 101 011 001 000 011 101 100 110 Encoding
46
6 5 3 1 0 3 5 4 6 Quantization
![Page 47: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/47.jpg)
PCM generation
47
![Page 48: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/48.jpg)
PCM Generation and Reception
Sampler Quantizer Encoder
Quantizer Filter Decoder
Ch
ann
el
Message signal
48
![Page 49: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/49.jpg)
49
Threshold
t
t
Triangular w/f of same amplitude
Triangular w/f of same slope
PWM output
Flat top sampled signal
Recovered message signal
Message signal
PWM generation (From PAM signal) and detection
![Page 50: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/50.jpg)
50
PWM from PPM
PWM pulses
Clock pulses
PPM pulses
PWM pulses
PPM pulses
Clock pulses
Q R
S
R
S S S S
R R R
![Page 51: ANALOG COMMUNICATION€¦ · Objectives •Builds the concepts of Pulse Analog Modulation. •Understand the difference between analog modulation and pulse analog modulation.](https://reader034.fdocuments.in/reader034/viewer/2022050515/5f9ef6be36131522af35a6e5/html5/thumbnails/51.jpg)
51
PPM Demodulation
Clock pulses
PPM pulses
Recovered message signal
Lines having same slope