Principles of Communications ECS 332

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1 Principles of Communications ECS 332 Asst. Prof. Dr. Prapun Suksompong 5. Angle Modulation Office Hours: BKD, 6th floor of Sirindhralai building Wednesday 4:3-5:3 Friday 4:3-5:3

2 Example 5.5: FM vs. PM Figure 32 m t Carrier: Acos 2πf t φ x PM t x FM t 2

3 x PM t Acos 2πf t φ k m t Phase Modulation Figure 32 m t =, t t, t t After time t, the message jumps to the value. same Acos 2πf t φ skipped Acos 2πf t φ 9 Acos 2πf t φ Here the phase modulator uses k 9 x PM t = Acos 2πf t φ, Acos 2πf t φ 9, t t t t After time t, the phase is skipped ahead (advanced) by 9. x FM t 3

4 f t f k m t Frequency Modulation Figure 32 Higher value m t Acos 2πf t φ When the message m t is, the x FM t has the same frequency as the carrier signal. When the message m t is, the frequency of x FM t is higher than the frequency of the carrier signal. x PM t x FM t 4 Higher frequency

5 Example 5.6: FM vs. PM Figure 33 m t Acos 2πf t φ x PM t x FM t 5

6 f t f k m t Frequency Modulation Figure 33 m t Acos 2πf t φ x PM t It should be evident that the frequency is changing. x FM t 6

7 f t f k m t Frequency Modulation Figure 33 m t The time at which m t is at its maximum value Acos 2πf t φ corresponds to the time at which x FM t has maximum x PM t frequency. x FM t 7

8 f t f k m t Frequency Modulation Figure 33 m t The time at which m t is at its minimum value Acos 2πf t φ corresponds to the time at which x FM t has minimum x PM t frequency. x FM t 8

9 f t f k m t Frequency Modulation Figure 33 m t is increasing Acos 2πf t φ x PM t The time interval during which m t corresponds to the time interval during which x FM t has increasing frequency. x FM t 9

10 f t f k m t Frequency Modulation Figure 33 m t The time interval during which m t is decreasing Acos 2πf t φ corresponds to the time interval during which x FM t has decreasing x PM t frequency. x FM t

11 x PM t Acos 2πf t φ k m t Phase Modulation Figure 33 m t In, the phase varies in proportion with. When and hence the phase of Acos change 2πf t φ continuously, it is difficult to see the connection with the actual plot of. x PM t x FM t

12 x PM t Acos 2πf t φ k m t Phase Modulation Figure 33 m t One may notice here that, in this example, is similar to Except that the graph is shifted. However, it Acos is still 2πf not t φ clear (visually) how the graph of is related to. x PM t x FM t 2

13 AM, FM, and PM Figure 34 m t x AM t x FM t x PM t 3

14 x AM t A m t cos 2πf t φ Amplitude Modulation Figure 34 m t x AM t In, the envelope varies in proportion to. x FM t 4

15 f t f k m t Frequency Modulation Figure 34 m t m t is increasing in this region x AM t f t is increasing in this region x FM t In, the frequency varies in proportion to. x PM t 5

16 x PM t Acos 2πf t φ k m t Phase Modulation Figure 34 Sudden drop in the value of m t m t m t is increasing in this region x AM t x FM t In, the phase varies in proportion to. Higher but constant frequency. Why? x PM t 6 Sudden change in the phase

17 Instantaneous Frequency Sinusoidal signal: g t Acos 2πf t φ Frequency f Generalized sinusoidal signal: Frequency? g t Acos t Observation: Frequency value may vary as a function of time. instantaneous frequency Why do we need to find the instantaneous frequency? Analyze Doppler effect (or Doppler shift) Implement frequency modulation (FM) where the instantaneous frequency will follow the message m t. 7

18 Instantaneous Frequency 2 t t x t cos 2 x() t.5 Figure t At t = 2, frequency =? 4 8

19 Instantaneous Frequency 2 t t x t cos 2 x() t.5 Figure By matching the terms with cos 2πf t, you may guess that f t t t At t = 2, f = t 2 = 4 Hz? Correct? 4

20 Instantaneous Frequency 2 t t x t cos 2 Figure 36 x() t cos( 2 4 t) By matching the terms with cos 2πf t, you may guess that f t t t At t = 2, f = t 2 = 4 Hz? Correct?

21 Instantaneous Frequency 2 t t x t cos 2 x() t cos( 2 4 t).5.5 Figure t 4 Hz is too low!!! x() t cos( 2 4 t) t 2

22 Instantaneous Frequency 2 t t x t cos 2 x() t cos( 2 2 t).5.5 Figure zoom in t 2 Hz fits better. x() t cos( 2 2 t) t 2 Hz?

23 First-order (straight-line) approximation/linearization How does the formula f t φ t work? Technique from Calculus: first-order (tangent-line) approximation/linearization

24 First-order (straight-line) approximation/linearization How does the formula f t t work? Technique from Calculus: first-order (tangent-line) approximation/linearization When we consider a function t near a particular time, say, t t, the value of the function is approximately t t t t t t t t t t Therefore, near t t, cos slope slope constant t cos t t t t t Now, we can directly compare the terms with cos 2πf t φ

25 First-order (straight-line) approximation/linearization For example, for t near t = 2, t 2 3t t 2 2 t 2 2 t 2 6 t 2 t πt 2 2π 2 t 2π

26 First-order (straight-line) approximation/linearization For example, for t near t = 2, t 2 3t t 2 2 t 2 2 t 2 6 t 2 t πt 2π 2 t 2π

27 First-order (straight-line) approximation/linearization For example, for t near t = 2, t 2 3t t 2 2 t 2 2 t 2 6 t 2 t πt 2π 2 t 2π

28 Same idea Suppose we want to find. Let. Note that Approximation: 5.9 is near MATLAB:. >> sqrt(5.9) ans =

29 Phase Modulation Figure 33 m t When and hence the phase of change continuously, it is difficult to see the connection Acos 2πf t φ with the actual plot of. x PM t 29 New Fact: In varies in proportion with the slope of., the instantaneous x FM frequency t

30 Phase Modulation Figure 37 m t d m t dt Acos 2πf t φ x PM t f t d f k m t dt 3 New Fact: In proportion with the slope of., the instantaneous x FM frequency t varies in

31 Phase Modulation Figure 37 m t The time at which d the slope of m t m t dt is at its maximum Acos 2πf t φ value corresponds to the time at which x PM t has maximum x PM t frequency. 3 New Fact: In varies in proportion with the slope of., the instantaneous x FM frequency t

32 Phase Modulation Figure 37 m t The time at which d the slope of m t m t dt is at its minimum Acos 2πf t φ value corresponds to the time at which x PM t has minimum x PM t frequency. 32 New Fact: In varies in proportion with the slope of., the instantaneous x FM frequency t

33 Phase Modulation Figure 37 m t The time interval d during which the m t dt slope of m t is Acos 2πf t φ increasing corresponds to the time interval during which x PM t has x PM t increasing frequency. 33 New Fact: In varies in proportion with the slope of., the instantaneous x FM frequency t

34 Elements of digital commu. sys. Message Transmitter Information Source Recovered Message Destination Source Encoder Remove redundancy (compression) Source Decoder Channel Encoder Add systematic redundancy to combat errors introduced by the channel Receiver Channel Decoder Digital Modulator Map digital sequence to analog signal Digital Demodulator Channel Transmitted Signal Received Signal Noise & Interference 34

Channel Encoder Add systematic redundancy

channel Receiver Channel Decoder Digital

35 Digital Modulation/Demodulation Message Transmitter Information Source Recovered Message Destination Source Encoder Remove redundancy (compression) Source Decoder Channel Encoder Add systematic redundancy to combat errors introduced by the channel Receiver Channel Decoder Digital Modulator Map digital sequence to analog signal Digital Demodulator Channel Transmitted Signal Received Signal Noise & Interference 35

36 Digital Version Use digital signal to modulate the amplitude, frequency, or phase of a sinusoidal carrier wave. Think of m(t) as a train of scaled (rectangular) pulses. The modulated parameter will be switched or keyed from one discrete value to another. Three basic forms: amplitude-shift keying (ASK) frequency-shift keying (FSK) phase-shift keying (PSK) 36

37 Keying? To key = to enter or operate on (data) by means of a computer keyboard or telephone keypad she keyed in a series of commands A telegraph key is a switching device used primarily to send Morse code. 37

38 Binary ASK, FSK, and PSK m m t 38 [Carlson & Crilly, 29, Fig 4.- p 649]

39 Simple ASK: ON-OFF Keying (OOK) cos 2πf t Digital Modulator?.8.6 f c = 4 Hz.4.2 Bit rate = bps t T 2T 3T 4T 5T Seconds t 39 [ASK_playTones_Demo.m]

40 Simple ASK : ON-OFF Keying Smoke signal 4

Simple ASK: ON-OFF Keying (OOK) cos 2πf t Bit stream Digital Modulator?.8.6 f c = 4 Hz Bit rate = bps.4.2 -.2 -.4 t -.6 -.

41 Simple ASK: ON-OFF Keying (OOK) cos 2πf t Bit stream Digital Modulator?.8.6 f c = 4 Hz Bit rate = bps t Seconds T 2T 3T 4T 5T f c = Hz.5 Bit rate = 2 bps t Seconds [ASK_playTones_Demo.m]

42 ASK: Higher Order Modulation 4 3 Digital Modulator? Seconds f c = Hz Symbol rate = 2 symbols per second Bit rate = 4 bps

43 FSK M = 4 f f f f f c,,, 3,6,9,2 [Hz] s t cos 2πf t s t cos 2πf t s t cos 2πf t s t cos 2πf t [FSK_playTones_Demo.m]

44 FSK Digital Modulator? M = 4 f f f f f c,,, 3,6,9,2 [Hz] [ ] f [ ] Hz Seconds [FSK_playTones_Demo.m]

45 FSK Digital Modulator? M = 4 f f, f, f, f, 2,3, 4 [Hz] c [ ] f [ ] Hz Seconds [FSK_playTones_Demo.m]

46 FSK 2 5 = (random) bits Digital Modulator? R s = 5 Bit rate = bps Magnitude Seconds Frequency [Hz]

47 47 Digits of

48 48 Digits of

49 Digits of 49

50 Figure 42 Five Frequencies cos 2πf t cos 2πf t cos 2πf t cos 2πf t cos 2πf t Seconds Each tone lasts /R s sec. Rate = R s frequency-changes per second 5

51 Spectrum of Five Frequencies (/5).5 Hz 2 Hz 3 Hz 4 Hz 5 Hz cos 2πf t cos 2πf t cos 2πf t cos 2πf t cos 2πf t -.5 R s = Seconds.8 Magnitude Frequency [Hz]

52 Spectrum of Five Frequencies (2/5).5 Hz 2 Hz 3 Hz 4 Hz 5 Hz cos 2πf t cos 2πf t cos 2πf t cos 2πf t cos 2πf t -.5 R s = Seconds..8 Magnitude Frequency [Hz]

53 Cos vs. Cos Pulse x t cos 2π t x t cos 2π t,.4 t.6,, otherwise Seconds Seconds..8 Magnitude.3.2. Magnitude Frequency [Hz] Frequency [Hz] 53

54 Figure 43 Cosine Pulse cos 2π t,.5 t.6, x t, otherwise..5 x(t) t [s].5.4 X(f) f [Hz]

55 Figure 44 Spectrum of Five Frequencies (3/5).5 Hz 2 Hz 3 Hz 4 Hz 5 Hz cos 2πf t cos 2πf t cos 2πf t cos 2πf t cos 2πf t -.5 R s = Seconds.3 Magnitude Frequency [Hz]

56 Fourier Transform Pairs (2) Time Domain Frequency Domain j 2 ft j2 ft g t G f e df G f g t e dt sinc( x) sin x x

57 Spectrum of Five Frequencies (4/5) Hz 2 Hz 3 Hz 4 Hz 5 Hz R s = Seconds Magnitude Frequency [Hz]

58 Spectrum of Five Frequencies (5/5).5 Hz 2 Hz 3 Hz 4 Hz 5 Hz cos 2πf t cos 2πf t cos 2πf t cos 2πf t cos 2πf t -.5 R s = Seconds 95.8 Magnitude Frequency [Hz]

ECE5713 : Advanced Digital Communications

ECE5713 : Advanced Digital Communications Bandpass Modulation MPSK MASK, OOK MFSK 04-May-15 Advanced Digital Communications, Spring-2015, Week-8 1 In-phase and Quadrature (I&Q) Representation Any bandpass