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Lecture 1.7. AM FM PM OOK BPSK FSK

Lecture 1.7. AM FM PM OOK BPSK FSK. AM, FM, and Digital Modulated Systems Amplitude Modulation (AM) Double Sideband Suppressed carrier (DSSC) Assymetric Sideband Signals Single sideband signals (SSB). Bandpass Signaling Review. Where. Where.

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Lecture 1.7. AM FM PM OOK BPSK FSK

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  1. Lecture 1.7.AM FM PMOOK BPSK FSK

  2. AM, FM, and Digital Modulated Systems • Amplitude Modulation (AM) • Double Sideband Suppressed carrier (DSSC) • Assymetric Sideband Signals • Single sideband signals (SSB)

  3. Bandpass Signaling Review Where Where • The modulated bandpass signal can be described by Modulation Mapping function:Convert m(t) →g(t) Ref :Table4-1 • The voltage spectrum of the bandpass signal is • The PSD of the bandpass signal is

  4. Amplitude Modulation • The Complex Envelope of an AM signal is given by Ac indicates the power level of AM and m(t) is the Modulating Signal • Representation of an AM signal is given by • Ac[1+m(t)] In-phase component x(t) • If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated • Envelope detection can be used if % modulation is less than 100%.

  5. Amplitude Modulation An Example of a message signal m(t) Waveform for Amplitude modulation of the message signal m(t)

  6. Amplitude Modulation B An Example of message energy spectral density. Carrier component together with the message 2B Energy spectrum of the AM modulated message signal.

  7. AM – Percentage Modulation • Definition: The percentage of positive modulation on an AM signal is • The percentage of negative modulation on an AM signal is • The percentage of overall modulation is If m(t) has a peak positive values of +1 and a peak negative value of -1 AM signal  100% modulated

  8. AM Signal Waveform % Positive modulation= 50% % Negative modulation =50% Overall Modulation = 50% Amax = 1.5Ac Amin = 0.5 Ac

  9. AM – Percentage Modulation Under modulated (<100%) 100% modulated Over Modulated (>100%) Envelope Detector Can be used Envelope Detector Gives Distorted signal

  10. AM – Normalized Average Power The normalized average power of the AM signal is If the modulation contains no dc level, then The normalized power of the AM signal is Discrete Carrier Power Sideband power

  11. AM – Modulation Efficiency • Definition : The Modulation Efficiency is the percentage of the total power of the modulated signal that conveys information. Only “Sideband Components” – Convey information Modulation Efficiency: Highest efficiency for a 100% AM signal : 50% - square wave modulation Normalized Peak Envelope Power (PEP)of the AM signal: Voltage Spectrum of the AM signal: Unmodulated Carrier Spectral Component Translated Message Signal

  12. Carrier Power Sideband power Spectrum  Modulation Efficiency  Double Side Band Suppressed Carrier (DSBSC) • Power in a AM signal is given by • DSBSC is obtained by eliminating carrier component • If m(t) is assumed to have a zero DC level, then Power  • Disadvantages of DSBSC: • Less information about the carrier will be delivered to the receiver. • Needs a coherent carrier detector at receiver

  13. DSBSC Modulation B An Example of message energy spectral density. No Extra Carrier component 2B Energy spectrum of the DSBSC modulated message signal.

  14. LSSB USSB Single Sideband (SSB) Modulation • An upper single sideband (USSB) signal has a zero-valued spectrum for • A lower single sideband (LSSB) signal has a zero-valued spectrum for • SSB-AM – popular method ~ BW is same as that of the modulating signal. Note: Normally SSB refers to SSB-AM type of signal

  15. –Hilbert transform of m(t)  Where and H(f) j f -j Single Sideband Signal • Theorem :A SSB signal has Complex Envelopeand bandpass form as: Upper sign (-)  USSB Lower sign (+)  LSSB Hilbert Transform corresponds to a -900phase shift

  16. Using Recall from Chapter 4 Single Sideband Signal Proof: Fourier transform of the complex envelope Upper sign  USSB Lower sign  LSSB Upper sign  USSB If lower signs were used  LSSB signal would have been obtained

  17. Single Sideband Signal

  18. SSB - Power The normalized average power of the SSB signal Hilbert transform does not change power. SSB signal power is: Power of the modulating signal Power gain factor The normalized peak envelope (PEP) power is:

  19. Generation of SSB SSB signals have bothAM and PM. The complex envelope of SSB: For the AM component, For the PM component, Advantages of SSB • Superior detected signal-to-noise ratio compared to that of AM • SSB has one-half the bandwidth of AM or DSB-SC signals

  20. Generation of SSB • SSB Can be generated using two techniques • Phasing method • Filter Method • Phasing method This method is a special modulation type of IQ canonical form of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)

  21. Generation of SSB • Filter Method The filtering method is a special case in which RF processing (with a sideband filter) is used to form the equivalent g(t), instead of using baseband processing to generate g(m) directly. The filter method is the most popular method because excellent sideband suppression can be obtained when a crystal oscillator is used for the sideband filter. Crystal filters are relatively inexpensive when produced in quantity at standard IF frequencies.

  22. Weaver’s Method for Generating SSB.

  23. Generation of VSB

  24. AM, FM, and Digital Modulated Systems • Phase Modulation (PM) • Frequency Modulation (FM) • Generation of PM and FM • Spectrum of PM and FM • Carson’s Rule • Narrowband FM

  25. AM and FM Modulation (a) Carrier wave. (b) Sinusoidal modulating signal. (c) Amplitude-modulated signal. (d) Frequency modulated signal.

  26. Angle Modulation • Advantages: • Constant amplitude means Efficient Non-linear Power Amplifiers can be used. • Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high. • Disadvantages: • Usually require more bandwidth than AM • More complicated hardware

  27. ∆θ is related to the peak modulating voltage by: Where Where ∆θis the peak phase deviation • The Phase Modulation Indexis given by: • The Frequency Modulation Indexis given by: ∆F Peak Frequency Deviation B Bandwidth of the modulating signal Modulation Index • The Peak Phase Deviationis given by:

  28. Spectrum of Angle modulated signal Where Spectra of Angle modulated signals • Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f). • But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained. • To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

  29. Then Where is the phase Modulation Index. which is periodic with period Spectrum of PM or FM Signal with Sinusoidal Modulating Signal • Assume that the modulation on the PMsignal is Same θ(t) could also be obtained if FM were used where and The peak frequency deviation would be The Complex Envelope is:

  30. Spectrum of PM or FM Signal with Sinusoidal Modulating Signal Where Which reduces to Is a special property of Bessel Functions or Using discrete Fourier series that is valid over all time, g(t) can be written as Jn(β) – Bessel function of the first kind of the nth order Taking the fourier transform of the complex envelopeg(t), we get

  31. Bessel Functions of the First Kind J0(β)=0 at β=2.4, 5.52 & so on

  32. Bessel Functions of the First Kind

  33. Frequency spectrum of FM • The FM modulated signal in time domain Observations: • From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of c± nm. • By analogy with AM modulation, these frequency components are called sidebands. • We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands. • The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

  34. Spectra of an FM Signal with Sinusoidal Modulation • The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands 1.0 f BT

  35. Spectra of an FM Signal with Sinusoidal Modulation J0(1.0) 1.0 J1(1.0) J2(1.0) f BT

  36. Spectra of an FM Signal with Sinusoidal Modulation 1.0 f BT

  37. Carson’s rule • Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted. • Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side. (1+b)fm

  38. For sinusoidal modulation Note: When β =0 i.e. baseband signals Carson’s rule • Therefore the Bandwidth required is given by β – phase modulation index/ frequency modulation index B – bandwidth of the modulating signal • Carson’s rule :Bandwidth of an FM signal is given by

  39. AM, FM, and Digital Modulated Systems • Binary Bandpass Signalling Techniques • OOK • BPSK • FSK

  40. Binary Bandpass Signaling techniques • On–Off keying (OOK) [amplitude shift keying (ASK)] - Consists of keying (switching) a carrier sinusoid on and off with a unipolar binary signal. • - Morse code radio transmission is an example of this technique. • - OOK was one of the first modulation techniques to be used and precedes analog communication systems. • Binary Phase-Shift Keying (BPSK) - Consists of shifting the phase of a sinusoidal carrier 0o or 180o with a unipolar binary signal. - BPSK is equivalent to PM signaling with a digital waveform. • Frequency-Shift Keying (FSK) - Consists of shifting the frequency of a sinusoidal carrier from a mark frequency (binary 1) to a space frequency (binary 0), according to the baseband digital signal. - FSK is identical to modulating an FM carrier with a binary digital signal.

  41. Binary Bandpass Signaling techniques

  42. On-Off Keying (OOK) Carrier Cos(2fct) OOK output Acm(t)Cos(2fct) Message m(t) • Also known as Amplitude Shift Keying (ASK) • The complex envelope is • The OOK signal is represented by • The PSD of this complex envelope is given by where m(t) has a peak value of So that s(t) has an average normalized power of

  43. On-Off Keying (OOK) 1 0 1 0 1 0 1 Message m(t) Unipolar Modulation m(t) Bipolar Modulation s(t) OOK signal Tb – bit period ; R – bit rate

  44. On-Off Keying (OOK) • PSD of the bandpass waveform is given by • Null-to-Null bandwidth is and absolute bandwidth is • The Transmission bandwidth is Where B is the baseband bandwidth

  45. Binary output Envelope Detector OOK in Detection of OOK • Non-Coherent Detection • Coherent Detection with Low-pass filter Binary output LPF OOK in

  46. Binary Phase Shift Keying (BPSK) Message: m(t) Carrier:Cos(2fct) BPSK output AcCos(2fct+Dpm(t)) -90 Phase shift 1 0 1 0 1 0 1 Message m(t) Unipolar Modulation m(t) Bipolar Modulation s(t) BPSK output Generation:

  47. Binary Phase Shift Keying (BPSK) • The BPSK signal is represented by let pilot carrier term data term • The level of the pilot carrier term is set by the value of the peak deviation • The digital modulation index ‘h’ is given by 2∆θ – maximum peak-to-peak deviation during time Ts • If Dp is small, then there is little power in data term & more in pilot term • To maximize performance (minimum probability of error) Optimum case : BPSK signal :

  48. Binary Phase Shift Keying (BPSK) • The complex envelope for this BPSK is given by • The PSD for this complex envelope is given by • PSD of the bandpass waveform is given by Average normalized power of s(t) : Null-to-Null BW PSD of optimum BPSK

  49. Binary Phase Shift Keying (BPSK) If Dp /2 Pilot exists fc 2R = 2/Tb Power Spectral Density (PSD) of BPSK:

  50. Frequency Shift Keying (FSK) Message: m(t) Cos(2f1t) FSK output AcCos(2f1t+1) or AcCos(2f2t+2) Osc. f1 Cos(2f2t) Osc. f2 • Discontinuous FSK : • The discontinuous-phase FSK signal is represented by for t during a binary ‘1’ signal for t during a binary ‘0’ signal

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