Download Pattern Recognition & Signal Modulation: Amplitude & Angle Modulation, Demodulation and more Slides Signals and Systems Theory in PDF only on Docsity! ECE 8443 – Pattern RecognitionECE 3163 – Signals and Systems • Objectives: Generalized Fourier Transform Analog Modulation Amplitude Modulation Angle Modulation Demodulation and Demultiplexing • Resources: Wiki: The Fourier Transform Celier: Generalized Fourier Transform MIT 6.003: Lecture 15 Wiki: Amplitude Modulation RE: AM Demodulation Wiki: Electromagnetic Spectrum Wiki: 700 MHz Auction LECTURE 12: SIGNAL MODULATION AND DEMODULATION Audio:URL: ECE 3163: Lecture 12, Slide 1 • Consider a DC or constant signal: • Compute its Fourier Transform: • Unfortunately, the limit is not finite, and the integral does not converge. • Consider an alternate approach based on an impulse function: • Apply the duality property: • This is known as the Generalized Fourier transform. It allows us to extend the Fourier transform to some additional useful signals such as periodic signals: The Fourier transform of a periodic signal is a train of impulse functions (and is a line spectrum). Generalized Fourier Transform 1)(0,1)(,00)( tdtt F k k k tjkω k tjω )δ(ω-kωcωXectx )πδ(ω-ωe 0 0 2)( 2 0 0 t-,x(t) 1 2/2/ 2/ 2/ 2/ 2/ 1 lim 1 limlim)1()( TjTj T T T tj T T -T tj T - tj ee j e j dtedtejX 2)(1)( txttx F ECE 3163: Lecture 12, Slide 4 Amplitude Modulation Using a Sinusoid ECE 3163: Lecture 12, Slide 5 Synchronous Demodulation of Sinusoidal AM • Assumptions: = 0 (for now), Local oscillator is synchronized with the carrier. In practice, synchronization is achieved using a phase- locked loop (PLL). ECE 3163: Lecture 12, Slide 6 • We can easily derive the properties of the demodulated signal: • The low-pass filter removes the high-frequency replica of x(t), leaving only the “baseband” component. • Suppose there is a phase difference between the transmitter and the receiver: The mismatch in phase appears as a scale factor that can be ignored. • If there is a time-varying phase difference (due to drift): If the phase difference varies slowly in time, the net result is simply a time- varying amplitude change, which distorts the signal (slightly). • What happens if the receiver is exactly 90 out of phase? Synchronous Demodulation in the Time Domain )2cos( 2 1 2 1 )()(cos)()cos()()( 2 ttxttxttytw ccc )2cos( 2 1 )cos( 2 1 )( )cos()cos()()cos()()( ttx tttxttytw c ccc ))(2cos( 2 1 ))(cos( 2 1 )()( ttttxtw c ECE 3163: Lecture 12, Slide 9 Double-Sideband Vs. Single-Sideband Modulation • Since x(t) and y(t) are real, from conjugate symmetry, both lower sideband (LSB) and upper sideband (USB) signals carry exactly the same information. • Double-sideband (DSB) occupies 2M bandwidth in > 0, even though all the information is contained in M. • Single-sideband (SSB) occupies M bandwidth in > 0. • Of course, SSB requires slightly more complicated hardware, so it was originally only used in applications where bandwidth was very limited (e.g., transcontinental telephone lines). • Analog television signals, which are being obsoleted in February 2009, use a variant of SSB. Single-Sideband Modulation
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ECE 3163: Lecture 12, Slide 10
ECE 3163: Lecture 12, Slide 11 Frequency Division Multiplexing • Used in many communications systems including broadcast radio and cell phones.
