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EE345S Real-Time Digital Signal Processing Lab Fall 2006 Analog Sinusoidal Modulation Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Lecture 9 Single-Carrier Modulation Methods • Analog communication Transmit/receive analog waveforms Amplitude Modulation (AM) Freq. Modulation (FM) Phase Modulation (PM) Quadrature Amplitude Mod. Pulse Amplitude Modulation m(t ) Signal Processing Carrier Circuits TRANSMITTER Digital communication Same but treat transmission and reception as digitized Amplitude Shift Keying (ASK) Freq. Shift Keying (FSK) Phase Shift Keying (PSK) QAM PAM Transmission Medium s(t) CHANNEL Carrier Circuits r(t) Signal Processing mˆ (t ) RECEIVER 9-2 Radio Frequency (RF) Modem • Message signal: stream of bits • Digital sinusoidal modulation in digital signaling • Analog sinusoidal modulation in carrier circuits for upconversion to RF Error Correction m[k ] Signal Processing Digital Signaling Carrier Circuits TRANSMITTER D/A Converter Transmission Medium s(t) CHANNEL Carrier Circuits r(t) Signal Processing mˆ [ k ] RECEIVER 9-3 Modulation • Modulation: some characteristic of a carrier signal is varied in accordance with a modulating signal • For amplitude, frequency, and phase modulation, modulated signals can be expressed as s(t ) A(t ) cos(2 f c t (t )) A(t) is real-valued amplitude function fc is carrier frequency (t) is real-valued phase function • See Modulation handout (Appendix I) 9-4 Review Amplitude Modulation by Cosine • Multiplication in time: convolution in Fourier domain (let 0 = 2 f0): y t f t cos 0 t Y 1 F 0 0 2 • Sifting property of Dirac delta functional xt t xt d xt xt t t0 t0 xt d xt t0 • Fourier transform property for modulation by a 1 1 cosine Y F 0 F 0 2 2 9-5 Review Amplitude Modulation by Cosine • Example: y(t) = f(t) cos(0 t) Assume f(t) is an ideal lowpass signal with bandwidth 1 Assume 1 << 0 lower sidebands F() ½F 0 1 Y() ½F 0 ½ -1 0 1 -0 - 1 0 -0 + 1 0 0 - 1 0 0 + 1 Y() is real-valued if F() is real-valued • Demodulation: modulation then lowpass filtering • Similar derivation for modulation with sin(0 t) 9-6 Amplitude Modulation by Sine • Multiplication in time is convolution in Fourier domain y t f t sin 0 t Y 1 F j 0 0 2 • Sifting property of the Dirac delta functional xt t xt d xt xt t t0 t0 xt d xt t0 • Fourier transform property for modulation by a j j sine Y F F 2 0 2 0 9-7 Amplitude Modulation by Sine • Example: y(t) = f(t) sin(0 t) Assume f(t) is an ideal lowpass signal with bandwidth 1 Assume 1 << 0 lower sidebands F() j ½F 0 1 Y() j -1 0 1 -j ½F 0 ½ 0 - 1 -0 - 1 0 0 0 + 1 -0 + 1 -j ½ Y() is imaginary-valued if F() is real-valued • Demodulation: modulation then lowpass filtering 9-8 Amplitude Modulated (AM) Radio • Double sideband large carrier (DSC-LC) Carrier wave varied about mean value linearly with baseband message signal m(t) s(t ) Ac 1 k a m(t ) cos( 2 f c t ) Ac cos( 2 f c t ) Ac k a m(t ) cos( 2 f c t ) ka is the amplitude sensitivity, ka > 0 Modulation factor is = ka Am where Am is maximum amplitude of m(t) • Envelope of s(t) has about same shape as m(t) if | ka m(t) | < 1 for all t fc >> W where W is bandwidth of m(t) 9-9 Amplitude Modulation • Disadvantages – Redundant bandwidth is used – Carrier consumes most of the transmitted power • Advantage – Simple detectors (e.g. AM radio receivers for cars) • Receiver uses a simple envelope detector – Diode (with forward Rs resistance Rf ) in series – Parallel connection of + capacitor C and load vs(t) – resistor Rl Rf C Rl 9 - 10 Amplitude Modulation (con’t) • Let Rs be source resistance • Charging time constant (Rf + Rs) C must be short when compared to 1/ fc, so (Rf +Rs) C << 1/ fc • Discharging time constant Rl C – Long enough so that capacitor discharges slowly through load resistor Rl between positive peaks of carrier wave – Not so long that capacitor voltage will not discharge at max rate of change of modulating wave 1/fc << Rl C << 1/W 9 - 11 Other Amplitude Modulation Types • Double sideband suppressed carrier (DSB-SC) s(t ) Ac m(t ) cos(2 f c t ) • Double sideband variable carrier (DSB-VC) s(t ) Ac m(t ) cos(2 f c t ) cos(2 f c t ) • Single sideband (SSB): Remove either lower sideband or upper sideband by – Extremely sharp bandpass or highpass filter, or – Phase shifters using a Hilbert transformer 9 - 12 Quadrature Amplitude Modulation • Allows DSB-SC signals to occupy same channel bandwidth provided that the two message signals are from independent sources s(t ) Ac m1 (t ) cos(2 f c t ) Ac m2 (t ) sin( 2 f c t ) A(t ) cos(2 f c t (t )) A(t ) Ac m (t ) m (t ) 2 1 2 2 m2 (t ) (t ) arctan m1 (t ) • Two message signals m1(t) and m2(t) are sent Ac m1(t) is in-phase component of s(t) Ac m2(t) is quadrature component of s(t) 9 - 13 Frequency Modulated (FM) Radio • Message signal: analog audio signal • Transmitter – Signal processing: lowpass filter to reject above 15 kHz – Carrier circuits: sinusoidal modulatation from baseband to FM station frequency (often in two modulation steps) • Receiver – Carrier circuits: sinusoidal demodulation from FM station frequency to baseband (often in two demodulation steps) – Signal processing: lowpass filter to reject above 15 kHz m(t ) Signal Processing Carrier Circuits TRANSMITTER Transmission Medium s(t) CHANNEL Carrier Circuits r(t) Signal Processing mˆ (t ) RECEIVER 9 - 14 Frequency Modulation • Non-linear, time-varying, has memory, non-causal t s (t ) Ac cos i (t ) Ac cos 2 f c t 2 k f m(t ) dt 0 • For single tone message m(t) = Am cos(2 fm t) f i (t ) 2 f c t sin( 2 f m t ) where f k f Am fm 1 d Instantaneous f i (t ) i (t ) f c f cos( 2 f m t ) frequency 2 dt • Modulation index is = f / fm << 1 => Narrowband FM (looks like double-sideband AM) >> 1 => Broadband FM 9 - 15 Carson's Rule • Bandwidth of FM for single-tone message at fm – Narrowband: BT 2 f m BT 2f – Wideband: • Carson’s rule for single-tone FM: BT 2 f m (1 ) FM Radio f fm Peak freq. deviation (F) Peak message freq. (W) Deviation ratio (D) Bandwidth BT = 2 fm (1+ ) Station Spacing 75 kHz 15 kHz 5 180 kHz 200 kHz • For a general message signal, fm = W TV Audio 25 kHz 15 kHz 1.66 80 kHz 6 MHz 9 - 16