![Signals and Systems
13-10
TRANSPARENCY
13.15
Demodulation of an
amplitude-modulated
signal with a
sinusoidal carrier.
[Transparency 13.10
repeated]
TRANSPARENCY
13.16
Effect of loss of
synchronization
in phase in a
synchronous
sinusoidal amplitude
modulation/demodu-
lation system.
Cos (WC
t + 0c)
Y (W)
j2i
1 el6
C(I
- 11 (W,- M) W. (W.+ WM) W
ciw)
re~lI
Weit
W(W)
-2jO I~O
- w, I W M2 L
cos (ct + 0c)
(oe - +c)]x(t)
Lowpass filter
cos (oct + 4c)
w(t) = x(t) Cos(Wmt + 6,) cos (ot +
= [cos (0c ~ oc)]x(t) +-I- x(t) cos (2wct + Oc+ #c)
lowpass component](https://image.slidesharecdn.com/lec13modulation-250425144147-f0324159/85/signals-and-systems-lec-13-modulation-pdf-10-320.jpg)
signals and systems lec 13 modulation.pdf
- 1. 13 Continuous-Time Modulation In this lecture, we begin the discussion of modulation. This is an important concept in communication systems and, as we will see in Lecture 15, also pro- vides the basis for converting between continuous-time and discrete-time sig- nals. In its most general sense, modulation means using one signal to vary a parameter of another signal. In communication systems, for example, if a channel is particularly suited to transmission in a certain frequency range, the information to be transmitted may be embedded in a carrier signal matched to the channel. The mechanism by which the information is embedded is modu- lation; that is, the information to be transmitted is used to modulate some pa- rameter of the carrier signal. In sinusoidal frequency modulation, for example, the information is used to modulate the carrier frequency. In sinusoidal ampli- tude modulation, the carrier is sinusoidal at a frequency that the channel can accommodate, and the information to be transmitted modulates the ampli- tude of this carrier. Furthermore, in communication systems, if many differ- ent signals are to be transmitted over the same channel, a technique referred to asfrequencydivision multiplexingis often used. In this method each sig- nal is used to modulate a carrier of a different frequency so that in the com- posite signal the information for each of the separate signals occupies non- overlapping frequency bands. The modulation property for Fourier transforms applies directly to am- plitude modulation, that is, the interpretation in the frequency domain of the result of multiplying a carrier signal by a modulating signal. From the modula- tion property we know that for amplitude modulation the spectrum of the modulated output is the convolution ofthe spectra of the carrier and the mod- ulating signal. When the carrier is either a complex exponential or a sinu- soidal signal, the spectrum of the carrier is one or a pair of impulses and the result ofthe convolution is then to shift the spectrum of the modulating signal to a center frequency equal to the carrier frequency. Modulation with a single complex exponential and with a sinusoidal signal are closely related. With a complex exponential carrier, demodulation, i.e., recovery of the original modulating signal, is relatively straightforward, basically involving modulating a second time with the complex corjugate signal. With sinusoidal 13-1
- 2. Signals and Systems 13-2 amplitude modulation, demodulation consists of modulating again with a si- nusoidal carrier followed by lowpass filtering to extract the original signal. This form of demodulation is typically referred to as synchronous demodula- tion since it requires synchronization between the sinusoidal carrier signals in the modulator and demodulator. However, by adding a constant to the modu- lating signal or equivalently injecting some carrier signal into the modulated output, a simpler form of demodulator can be used. This is referred to as asynchronousdemodulationand typically results in a less expensive demod- ulator. However, the fact that a carrier signal is injected into the modulated signal represents an inefficiency of power transmission. Suggested Reading Section 7.0, Introduction, pages 447-448 Section 7.1, Continuous-Time Sinusoidal Amplitude Modulation, pages 449- 459 Section 7.2, Some Applications of Sinusoidal Amplitude Modulation, pages 459-464 Section 7.3, Single-Sideband Amplitude Modulation, pages 464-468
- 3. Continuous-Time Modulation 13-3 SINUSOIDAL AMPLITUDE MODULATION SINUSOIDAL FREQUENCY MODULATION TRANSPARENCY 13.1 Sinusoidal amplitude and frequency modulation with a sinusoidal carrier. TRANSPARENCY 13.2 Block diagram of amplitude modulation and some examples of commonly used carrier signals. A A A t
- 4. Signals and Systems 13-4 TRANSPARENCY 13.3 Spectra associated with amplitude modulation with a complex exponential carrier. xt 1- x(t) CMt 4 ( ff X(w) *CMI~ YGw) x(t) - t + OG 43. 2e0* Iz I I W Y~w) y(t) + 3M (WC - WM 4 1w. +"M)i C(w) 21e-ws t 0-twot + .) liwe X(w) ~WM WM 00s (w~t + 6,) TRANSPARENCY 13.4 Representation of amplitude modulation with a complex exponential carrier in terms of amplitude modulation with two sinusoidal carriers with a 90*phase difference. xKt) X y(t) X() -- M WM y"w) y(t) lY(C)+ Y* (-w)j Rejy(t) (Y() - Y*(-w) jIm jy(t)} Re jy(t)} IMl" o
- 5. Continuous-Time Modulation 13-5 ejwct X y(t) Ideal lowpass filter H(w) WO CO e jct w(t) X f(t) TRANSPARENCY 13.5 The use of amplitude modulation with a complex exponential carrier to implement bandpass filtering with a lowpass filter. X(o) TRANSPARENCY 13.6 Spectra associated with the system in Transparency 13.5. (-we - WO 0 ) (-Wd1 + WO) Y(o) W(o) F- - (JO I F(w) A-
- 6. Signals and Systems 13-6 TRANSPARENCY 13.7 Equivalent frequency response associated with the system in Transparency 13.5. TRANSPARENCY 13.8 Representation of amplitude modulation with a complex exponential carrier in terms of amplitude modulation with two sinusoidal carriers with a 90* phase difference. (71 (-Wc - Wo 0 ) (-wc + wO) H, (W) 2 wo H2(F 2 7 -------------
- 7. Continuous-Time Modulation 13-7 c(t) = cos (WCt + Oe) ei(wt +0) + e et +60 2 2 X(C,) C(o) we Ie IweJC 1 YC ) C-je l(Welo TRANSPARENCY 13.9 Spectra associated with amplitude modulation with a sinusoidal carrier. Cos (Wct + 0,) I10 0 12 10 WC (- -M) (- + WpM)W C(W) tie tWeW W(W) i-2j9,I I 1 2jOC TRANSPARENCY 13.10 Demodulation of an amplitude-modulated signal with a sinusoidal carrier. - COM
- 8. Signals and Systems 13-8 TRANSPARENCY 13.11 Block diagram of sinusoidal amplitude modulation and demodulation. MODULATOR x(t) y(t) cos (wet + 0C) DEMODU LATOR y(t) H(w) 2 -W w w Lowpass filter cos (oct +Oc) WM < w < (2oc m COS Wat TRANSPARENCY 13.12 Block diagram for frequency division multiplexing. Cos Wc t Xc(W x(t) Ya (t) Xa (t) Xb (t) COS ob t Yb (t) w(t)
- 9. Continuous-Time Modulation 13-9 X, (W) -wM WM (A Xb (W) -wM W ( X ( M M M L (A.) W(W) Ar7inK> - Wa K>r7~~A Wa Lb Mc L TRANSPARENCY 13.13 Spectra illustrating frequency division multiplexing. TRANSPARENCY 13.14 Demultiplexing and demodulation of a frequency division multiplexed signal. - C Demultiplexing - Bandpass filter COS Wat Demodulation Lowpass filter Xa (t) -Wb -Cb
- 10. Signals and Systems 13-10 TRANSPARENCY 13.15 Demodulation of an amplitude-modulated signal with a sinusoidal carrier. [Transparency 13.10 repeated] TRANSPARENCY 13.16 Effect of loss of synchronization in phase in a synchronous sinusoidal amplitude modulation/demodu- lation system. Cos (WC t + 0c) Y (W) j2i 1 el6 C(I - 11 (W,- M) W. (W.+ WM) W ciw) re~lI Weit W(W) -2jO I~O - w, I W M2 L cos (ct + 0c) (oe - +c)]x(t) Lowpass filter cos (oct + 4c) w(t) = x(t) Cos(Wmt + 6,) cos (ot + = [cos (0c ~ oc)]x(t) +-I- x(t) cos (2wct + Oc+ #c) lowpass component
- 11. Continuous-Time Modulation 13-11 TRANSPARENCY 13.17 A simple system and associated waveform for an asynchronous demodulation system. y(t) - IA + x(tI cos wCt Cos ('t AT A A NA~ ~NA AAAW4-A- TRANSPARENCY 13.18 Modulator associated with asynchronous sinusoidal amplitude modulation. For such a system the carrier must be irjected into the output. This transparency shows time waveforms for the asynchronous modulation system. IY--V.N,Lv -yyV. vA
- 12. Signals and Systems 13-12 TRANSPARENCY 13.19 Frequency spectra associated with an asynchronous modulation system. y(t) - A+ x(t)I cos oct cos (",t iTA irA 1 2 X(W) TRANSPARENCY 13.20 Single-sideband modulation in which only the upper sidebands are retained. Y(W) sideband sideband sideband sideband Y, (w) -C W ~W M W M -we
- 13. Continuous-Time Modulation 13-13 v (t) 11 2 c W H(w) -Loc cW 1 - - A 2 TRANSPARENCY 13.21 Single-sideband modulation in which only the lower sidebands are retained. TRANSPARENCY 13.22 The use of a highpass filter to obtain a single-sideband signal.
- 14. MIT OpenCourseWare http://ocw.mit.edu Resource: Signals and Systems Professor Alan V. Oppenheim The following may not correspond to a particular course on MIT OpenCourseWare, but has been provided by the author as an individual learning resource. For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.