ANALOG COMMUNICATIONS IV Sem. Prepared by Mr. T. Nagarjuna ECE Department
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1 ANALOG COMMUNICAIONS IV Sem Prepared by Mr.. Nagaruna ECE Department
2 UNI I SIGNAL ANALYSIS AND LI SYSEMS
3 Classifiation of Signals Deterministi & Non Deterministi Signals Periodi & A periodi Signals Even & Odd Signals Energy & Power Signals
4 Deterministi & Non Deterministi Signals Deterministi signals Behavior of these signals is preditable w.r.t time. here is no unertainty with respet to its value at any time. hese signals an be expressed mathematially. For example xt = sin3t is deterministi signal. Non Deterministi or Random signals Behavior of these signals is random i.e. not preditable w.r.t time. here is an unertainty with respet to its value at any time. hese signals an t be expressed mathematially. For example hermal Noise generated is non deterministi signal.
5 Periodi and Non-periodi Signals Given xt is a ontinuous-time signal x t is periodi if xt = xt+ₒ for any and any integer n Example xt = A oswt xt+ₒ = A os[w t+ₒ+ = A oswt+wₒ= Aoswt+2 = A oswt For non-periodi signals xt xt+ₒ A non-periodi signal is assumed to have a period = Example of non periodi signal is an exponential signal
6 Even and Odd Signals A signal xt is said to be, Even if, xt=x t Odd if, xt= x t xt= x t
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8 Signal Energy and Power
9 Fourier transform of Standard Signals
10 Systems
11 LI System
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13 Convolution
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15 Correlation of signals
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17 Relation between Convolution and orrelation
18 UNI-II AMPLIUDE AND DOUBLE SIDE BAND SUPPRESSED CARRIER MODULAION Introdution to ommuniation system, need for modulation, frequeny division multiplexing; Amplitude modulation, definition; ime domain and frequeny domain desription, single tone modulation, power relations in amplitude modulation waves; Generation of amplitude modulation wave using,square law and swithing modulators; Detetion of amplitude modulation waves using square law and envelope detetors; Double side band modulation: Double side band suppressed arrier time domain and frequeny domain desription; Generation of double side band suppressed arrier waves using balaned and ring modulators; Coherent detetion of double side band suppressed arrier modulated waves; Costas loop; Noise in amplitude modulation, noise in double side band suppressed arrier.
19 Basi analog ommuniations system Baseband signal eletrial signal Input transduer ransmitter Modulator EM waves modulated signal ransmission Channel Carrier Output transduer Baseband signal eletrial signal Reeiver Demodulator EM waves modulated signal
20 ypes of Analog Modulation Amplitude Modulation AM Amplitude modulation is the proess of varying the amplitude of a arrier wave in proportion to the amplitude of a baseband signal. he frequeny of the arrier remains onstant Frequeny Modulation FM Frequeny modulation is the proess of varying the frequeny of a arrier wave in proportion to the amplitude of a baseband signal. he amplitude of the arrier remains onstant Phase Modulation PM Another form of analog modulation tehnique whih we will not disuss
21 Amplitude Modulation Carrier wave Baseband signal Modulated wave Amplitude varyingfrequeny onstant
22 Advantages of Modulation Redution of antenna size No signal mixing Inreased ommuniation range Multiplexing of signals Possibility of bandwidth adustments Improved reeption quality
23 ypes of Modulation
24 AM Modulation/Demodulation Soure Channel Sink Modulator Demodulator Baseband Signal with frequeny fm Modulating Signal Bandpass Signal with frequeny f Modulated Signal f >> fm Voie: Hz GSM Cell phone: 900/1800MHz Original Signal with frequeny fm CSULB May 22,
25 Amplitude Modulation he amplitude of high-arrier signal is varied aording to the instantaneous amplitude of the modulating message signal mt. o s 2 f t o s t C a rrie r S ig n a l: o r m t : o s 2 f t o s t M o d u la tin g M e ssag e S ig n a l: o r m m h e A M S ig n a l: s t [ A m t ] o s 2 f t A M CSULB May 22,
26 * AM Signal Math Expression * Mathematial expression for AM: time domain S t 1 k o s t o s t A M m expanding this produes: S t o s t k o s t o s t A M using : os A os B 1 2 os A B os A B m S t o s t o s t o s t k k A M 2 m 2 m In the frequeny domain this gives: Carrier, A=1. Amplitude k/2 k/2 frequeny lower sideband f-fm f f+fm upper sideband CSULB May 22,
27 AM Modulators Square Law Modulator
28 Swithing Modulator
29 Envelope Detetor
30 Square Law Demodulator
31 DSBSC Modulation
32 Balaned Modulator
33 Ring Modulator
34 Coherent Detetor
35 COSAS LOOP
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38 SSBSC Modulation
39 UNI-III SSB-SC AND VSB
40 Frequeny Disrimination Method
41 Phase Disrimination Method
42 Coherent Detetor
43 Consider the following SSBSC wave having a lower sideband. st=a m A /2 os*2πf f m t] he output of the loal osillator is t=a os2πf t From the figure, we an write the output of produt modulator as vt=stt Substitute st and t values in the above equation. vt=a m A /2 os[2πf f m t]a os2πf t =A m A 2 /2 os[2πf f m t]os2πf t =A m A 2 /4 {os[2π2f f m t]+os2πf m t} =A m A 2 /4 {os[2π2f f m t]+os2πf m t} vt=a m A 2 /4 os2πf m t+a m A 2 / 4 os[2π2f f m t] vt=a m A 2 /4 os2πf m t+a m A 2 / 4 os[2π2f f m t] In the above equation, the first term is the saled version of the message signal. It an be extrated by passing the above signal through a low pass filter.
44 herefore, the output of low pass filter is v 0 t=a m A 2 /4 os2πf m t v 0 t=a m A 2 /4 os2πf m t Here, the saling fator is A 2 /4.
45 VSBSC MODULAION
46 Bandwidth of VSBSC Modulation i.e., Bandwidth of VSBSC Modulated Wave = f m + f v Advantages: he following are the advantages of VSBSC modulation. Highly effiient. Redution in bandwidth when ompared to AM and DSBSC waves. Filter design is easy, sine high auray is not needed. he transmission of low frequeny omponents is possible, without any diffiulty. Possesses good phase harateristis. Disadvantages: Following are the disadvantages of VSBSC modulation. Bandwidth is more when ompared to SSBSC wave. Demodulation is omplex. Appliations: he most prominent and standard appliation of VSBSC is for the transmission of television signals. Also, this is the most onvenient and effiient tehnique when bandwidth usage is onsidered.
47 Generation of VSBSC
48 he output of the produt modulator is pt=a os2πf tmt Apply Fourier transform on both sides Pf=A /2 *Mf f +Mf+f ] he above equation represents the equation of DSBSC frequeny spetrum. Let the transfer funtion of the sideband shaping filter be Hf. his filter has the input pt and the output is VSBSC modulated wave st. he Fourier transforms of ptand st are Pf and Sf respetively. Mathematially, we an write Sfas Sf=PfHf Substitute Pf value in the above equation. Sf=A /2 *Mf f +Mf+f ]Hf he above equation represents the equation of VSBSC frequeny spetrum.
49 Demodulation of VSBSC
50 Comparison of AM
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52 Unit-4 Angle Modulation Basi onepts, frequeny modulation: Single tone frequeny modulation, spetrum analysis of sinusoidal frequeny modulation wave, narrow band frequeny modulation, wide band frequeny modulation, transmission bandwidth of frequeny modulation wave, phase modulation, omparison of frequeny modulation and phase modulation; Generation of frequeny modulation waves, diret frequeny modulation and indiret frequeny modulation, detetion of frequeny modulation waves: Balaned frequeny disriminator, Foster Seeley disriminator, ratio detetor, zero rossing detetor, phase loked loop, omparison of frequeny modulation and amplitude modulation; Noise in angle modulation system, threshold effet in angle modulation system, pre-emphasis and de-emphasis.
53 Phase Modulation PM phase modulation signal s t A o s 2 f t k m t p t k m t, k : p h ase sen sitiv ity p p in stan tan o u s freq u en y f t f i k p 2 d m t dt
54 Frequeny Modulation FM frequeny modulation signal s t A o s 2 f t 2 k m d f 0 k f : fre q u e n y s e n s itiv ity in s ta n ta n o u s fre q u e n y f t f k m t i f t a n g le t 2 f d i t 0 i Assume zero initial phase 2 f t 2 k m d f t 0
55 FM Charateristis Charateristis of FM signals Zero-rossings are not regular Envelope is onstant FM and PM signals are similar
56 Relations between FM and PM F M o f m t P M o f m d t 0 P M o f m t F M o f d m t dt
57 FM/PM Example ime/frequeny
58 Frequeny Modulation FM frequeny modulation signal s t A o s 2 f t 2 k m d f 0 k f : fre q u e n y s e n s itiv ity in s ta n ta n o u s fre q u e n y f t f k m t i f t a n g le t 2 f d i t 0 i Assume zero initial phase 2 f t 2 k m d f t 0 m t A o s 2 f t f f k A o s 2 f t m m i f m m f i d 2 k A o s 2 f d f m m d d f t d t 2 d t 2 d t t 1 f 2 k A f m o s 2 f m 2 L e t t
59 Frequeny deviation Δf Frequeny Deviation differene between the maximum instantaneous and arrier frequeny Definition: f k A k m a x m t f m f Relationship with instantaneous frequeny sin g le-to n e m t ase: f f f o s2 f t i m g en eral ase: f f f f f i Question: Is bandwidth of st ust 2Δf? No, instantaneous frequeny is not equivalent to spetrum frequeny with non-zero power! St has spetrum frequeny with non-zero power.
60 Modulation Index Indiate by how muh the modulated variable instantaneous frequeny varies around its unmodulated level message frequeny m a x k m t a A M e n v e lo p e :, 1 F M fre q u e n y: A m a x k m t f f m t Bandwidth a t m d t Re t A os w t k f a t sin w t k 2 f 2! a 2 t os w t k 2 f 3! a 3 t sin w t...
61 Narrow Band Angle Modulation Definition k f a t 1 Equation t A os w t k f m t sin w t Comparison with AM Only phase differene of Pi/2 Frequeny: similar ime: AM: frequeny onstant FM: amplitude onstant Conlusion: NBFM signal is similar to AM signal NBFM has also bandwidth 2W. twie message signal bandwidth
62 Example
63 Blok diagram of a method for generating a narrowband FM signal.
64 Wideband FM signal Wide Band FM m t A o s 2 f t Fourier series representation m s t A o s 2 f t sin 2 f t m m s t A J o s 2 f n f t n m n A S f J f f n f f f n f n m m 2 n J n : n-th o rd e r B e ssel fu n tio n o f th e firs t k in d
65 Example
66 Bessel Funtion of First Kind If is s m a ll, th e n 1,, 2 0 fo r a ll n n n n n n J J J J J n J
67 Spetrum of WBFM Chapter 5.2 Spetrum when mt is single-tone s t A o s 2 f t sin 2 f t A J o s 2 f n f t m n m n A S f Example 2.2 J f f n f f f n f n m m 2 n
68 Spetrum Properties 1. freq u en ies: f, f f, f 2 f,, f n f, m m m fo r all n. h eo retially in fin i te b an d w id th. 2. F o r << 1 N B F M, freq u en y: f, f f m J 1, J J, J 0 fo r all n n A 3. M ag n itu d e o f f n f : J, d ep en d o n m n 2 4. C a rrie r f m a g n itu d e J a n b e 0 fo r so m e A v e ra g e p o w e r: P A J A 2 2 n n
69 Bandwidth of FM Fats FM has side frequenies extending to infinite frequeny theoretially infinite bandwidth But side frequenies beome negligibly small beyond a point pratially finite bandwidth FM signal bandwidth equals the required transmission hannel bandwidth Bandwidth of FM signal is approximately by Carson s Rule whih gives lower-bound
70 Carson s Rule Nearly all power lies within a bandwidth of For single-tone message signal with frequeny f m B 2 f 2 f 2 1 f m m For general message signal mt with bandwidth or highest frequeny W B 2 f 2W 2 D 1 W w h e re D f is d e v ia tio n ra tio e q u iv a le n t to, W f m ax k m t f
71 ECE 4371 Fall 2008
72 ECE 4371 Fall 2008
73 ECE 4371 Fall 2008
74 ECE 4371 Fall 2008
75 ECE 4371 Fall 2008
76 FM demodulation
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87 Frequeny Response
88 Unit-V Reeivers and Sampling heorem
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90 Super heterodyne Reeiver
91 FM superheterodyne Rx
92 AGC
93 Sampling heorem
94 Continuous to Disrete-ime Signal Converter x t C/D xn= x n Sampling rate
95 C/D System x t st x s t Conversion from impulse train to disrete-time sequene xn= x n
96 Sampling with Periodi Impulse train x t x t t t xn xn n n
97 Sampling with Periodi Impulse train We want to restore x t from xn. What ondition has to be plaed on the sampling rate? x t x t t t xn xn n n
98 C/D System x t st x s t Conversion from impulse train to disrete-time sequene xn= x n n s t t n n x s t x t s t n x t t n n n n x n t n
99 C/D System X s 1 X * S Conversion from 2 x s t impulse train to disrete-time sequene s s x t st S 2 k, 2 k xn= x n n s t t n n x s t x t s t n x t t n n n n x n t n
100 C/D System * 2 1 S X X s k S s k s 2, 2 s : Sampling Frequeny k s s k X X 2 * 2 1
101 C/D System k s s k X X 2 * 2 1 k s k X * 1 k s k X 1 k s s k X X 1
102 Band-Limited Signals Band-Limited 1 X N N Band-Unlimited Y
103 X 1 k k Sampling s of Band-Limited ssignals s X, 2 Band-Limited 1 X 3 s Sampling with Higher Frequeny 2 s N 2/ N S s s 2 s 3 s Sampling with Lower Frequeny 2/ S 6 s 4 s 2 s 2 s 4 s 6 s
104 X s 1 X k Reoverability k s, s 2 Band-Limited 1 X 3 s Sampling with Higher Frequeny 2 s N 2/ N S s > 2 N s s 2 s 3 s Sampling with Lower Frequeny 2/ S s < 2 N 6 s 4 s 2 s 2 s 4 s 6 s
105 X 1 k scase 1: s > 2 k N X s, s 2 N 1 X N 2/ S 3 s 3 s 2 s 2 s s s 2 s 3 s 1/ X s s s 2 s 3 s
106 X 1 k scase 1: s > 2 k N X s, s 2 Passing X s through a lowpass filter with utoff frequeny N < < s N, the original signal an be reovered. N 1 2/ X N S X s is a periodi funtion with period s. 3 s 3 s 2 s 2 s s s 2 s 3 s 1/ X s s s 2 s 3 s
107 X s 1 k X k s, s 2 Case 2: s < 2 N 1 X N N 2/ S 6 s 4 s 2 s 2 s 4 s 6 s 1/ X s 6 s 4 s 2 s 2 s 4 s 6 s
108 X s 1 k X k s, s 2 Case 2: s < 2 N No way to reover the original signal. N 1 2/ X N S X s is a periodi funtion with period s. 6 s 4 s 2 s 2 s 4 s 6 s 1/ X s 6 s 4 s 2 s 2 s 4 s 6 s
109 Nequist Rate Band-Limited 1 X N N Nequist frequeny N he highest frequeny of a band-limited signal Nequist rate = 2 N
110 Nequist Sampling heorem Band-Limited 1 X N N s > 2 N Reoverable s < 2 N Aliasing
111 1 C/D X System X s k k s x t st x s t Conversion from impulse train to disrete-time sequene xn= x n n s t t n n x s t x t s t n x t t n n n n x n t n
112 X s Continuous-ime Fourier ransform 1 k X k s x t st x s t Conversion from impulse train to disrete-time sequene xn= x n X s n n s t t n n X n e n x s t x t s t n x t t n n n n x n t n
113 1 CF X vs. DF s k X k s x t st x s t Conversion from impulse train to disrete-time sequene xn= x n X s n X n e X e n n xn x n e n
114 1 CF X vs. DF s k X k s x t st x s t Conversion from impulse train to disrete-time sequene xn= x n X s X n X n e X e n n s xn X e x n e X e X s n
115 CF vs. DF s X e X k s s k X X 1 k k X e X 2 1
116 1 CF X e vs. DF X k 2 k 1 X 1/ X s s 2 s 1/ Xe s
117 CF vs. DF X Amplitude saling & Repeating e 1 1 k X X 2 k Frequeny saling s 2 s 1/ 1/ X s Xe s s
118 Key Conepts x t CF X Sampling C/D t ICF / / Retrieve One period xn F Xe n IF
119 X e X / / 1 Interpolation t d e X t x / / 2 1 t d e e X / / 2 1 t n n d e e n x / / 2 t n n d e e n x / / 2 n t n d e n x / / 2 n t n t n x n / ] / sin[
120 Interpolation x t n x n sin[ t t n n / / ] xn n t x t x n t n n
121 Ideal D/C Reonstrution System xn Covert from x s t x r t sequene to impulse train Ideal Reonstrution Filter H r
122 Obtained from sampling x t using an ideal C/D system. Ideal D/C Reonstrution System xn Covert from x s t x r t sequene to impulse train Ideal Reonstrution Filter H r H r x s t x n t n n / /
123 x t x n sin Ideal D/C Reonstrution System r / t n n / t n xn Covert from x s t x r t sequene to impulse train Ideal Reonstrution Filter H r X s X e X r H r X e
124 Ideal D/C Reonstrution System x r t n x n sin / / t t n n x t C/D xn D/C x r t In what ondition x r t = x t?
125 he Model x t C/D xn Disrete-ime System yn D/C y r t x t Continuous-ime System y r t
126 he Model x t C/D xn H e Disrete-ime System yn D/C y r t x t Continuous-ime H eff System y r t
127 LI Disrete-ime Systems yn y r t D/C Disrete-ime System x t C/D xn H e X e X e Y Y r H r k k X e X 2 1 r r e Y H Y r e X e H H k r k X e H H 2 1
128 LI Disrete-ime Systems yn y r t D/C Disrete-ime System x t C/D xn H e X e X e Y Y r H r k r r k X e H H Y 2 1 X e H Y r / 0 /
129 LI Disrete-ime Systems Continuous-ime System x t y r t H eff X e H Y r / 0 / X X H Y r eff r e H H eff / 0 /
130 Example:Ideal Lowpass Filter H eff H 0 e / / X x t C/D xn He Disrete-ime 1 System yn D/C Y r y r t H eff 1 0 / /
131 Example:Ideal Lowpass Filter Continuous-ime System x t y r t 1 H eff e H e H H eff / 0 /
132 Example: Ideal Bandlimited Differentiator x t Continuous-ime System y d t x t dt H / H eff 0 /
133 Example: Ideal Bandlimited Differentiator H eff x t Continuous-ime System y d t x t dt H / H eff 0 /
134 Example: Ideal Bandlimited Differentiator H eff x t Continuous-ime System y d t x t dt H e /,
135 Impulse Invariane H e H /, x t Continuous-ime LI system h t, H y t x t C/D xn Disrete-ime LI System hn He yn D/C y t What is the relation between h t and hn?
136 Impulse Invariane, / H e H e X n x X t x n x n x k k X e X 2 1, 1 X e X
137 Impulse Invariane, / H e H e H n h H t h n h n h, 1 H e H n h n h, H e H
138 Impulse Invariane h n h n x t Continuous-ime LI system h t, H y t x t C/D xn Disrete-ime LI System hn He yn D/C y t What is the relation between h t and hn?
ENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University
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