Signal Processing and Linear Systems-B.P.Lathi copy

# Moreover this very property allows us t o reduce t he

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Unformatted text preview: t frequency ( at l east over a small band). This scheme suffers from t he fact t hat t he slope of H (w) of a t uned circuit is linear only over a small band, a nd therefore causes considerable distortion in t he o utput. T his fault can partially be corrected by a balanced discriminator t hat uses two resonant circuits, one t uned above a nd t he o ther t uned below We. These days, a p hase-locked l oop ( PLL), whose performance is s uperior to any of t he m ethods discussed here (especially in t he large noise environment) has become very popular as a demodulator of angle modulated signals because of its reasonable cost. More discussion a bout m odulation a nd d emodulation of angle modulated signals appears in reference 4. A Historical Note I n t he twenties, broadcasting was in its infancy. However, t here was a constant search for techniques t hat would reduce noise (static). Now, since t he noise power is p roportional t o t he m odulated signal bandwidth (sidebands), a ttempts were focused on finding a modulation scheme to reduce t he b andwidth. I t was rumored t hat a new method h ad b een discovered for eliminating sidebands (no sidebands, no bandwidth!). T he c oncept of FM, where t he c arrier frequency would be varied in proportion to t he message m (t), a ppeared quite intriguing. T he c arrier frequency w(t) would be varied with time so t hat w(t) = We + k m(t), where k is a n a rbitrary c onstant. T he c arrier frequency will remain within t he b and from We - kmp t o 4 Continuous-Time Signal Analysis: T he Fourier Transform 300 + k mp. T he s pectrum, centered a t We, would have a bandwidth 2 kmp, which is controlled by t he a rbitrary c onstant k. B y using a n a rbitrarily small k, we could make t he i nformation bandwidth arbitrarily small. This was a passport t o communication heaven. Unfortunately, t he e xperimental results showed t hat s omething was seriously wrong somewhere. T he F M b andwidth was found t o b e always greater t han ( at b est e qual to) t he AM b andwidth. In some cases, its bandwidth was several times t hat of AM. Careful a nalysis by Carson showed t hat t he F M b andwidth could never be smaller t han t hat of AM; a t b est equal t o t hat of AM. Unfortunately, Carson did n ot recognize t he c ompensating advantage of F M in its ability t o s uppress noise. W ithout any justification, he states, " Thus, F M introduces inherent distortion a nd has no compensa.ting advantages whatsoever."5 I n his later p aper he says: " In fact, as more a nd m ore schemes are analyzed a nd t ested, and as t he essential n ature of t he problem i s clearly perceivable, we a re unavoidably forced t o t he conclusion t hat s tatic, like t he poor, will always be with us.,,6 This opinion of one o f t he a blest mathematicians o f t he day in t he communication industry set back t he development of FM. T he nois€-suppressing advantage of F M was later proved by Major Edwin H. A rmstrong 7 , a b rilliant engineer whose contributions to t he field o f r adio systems are comparabl...
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## This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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