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

# T he o nly difference is t hat t he c arrier is s ine

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Unformatted text preview: odulated Signals. I n Eq. (4.86), we see t hat a n arrowband angle (or exponential) modulated signal (NBEM) consists of a carrier t erm a nd a DSB-SC t erm whose carrier has a 71' / 2 p hase shift. Hence, we c an readily generate this signal using t he procedure discussed in Sec. 4.7. W ideband modulation (WBEM) can be obtained from NBEM by passing the N BEM signal through a nonlinear device. Consider, for example, a nonlinear device whose input x (t) a nd t he o utput y(t) are related by y(t) = x 2 (t). I f t he i nput is a n angle modulated signal cos [wet + k1/J(t)J, t hen t he o utput y(t) is given by y(t) = cos 2 [wet = 1 + k1/J(t)J 1 2' + 2' cos [2w et + 2k1/J(t)J I f we pass this signal through a bandpass filter centered a t 2w e , t he o utput is z (t) = 1 2' cos [2w et + 2k1/J(t)J Observe t hat t he second order of nonlinearity has doubled t he c arrier frequency as well as t he effective value of k w ithout causing any distortion. In a similar way, we c an show t hat a n n th-order of nonlinearit.y increases n-fold t he carrier frequency as well as the effective value of k. T his fact allows us t he convert t he N BEM into WBEM. This is t he indirect method of generating angle modulated signal. We c an also generate angle modulated signal by a direct method, which uses a v oltage c ontrolled o scillator ( VeO). T he o utput of a VCO is a c onstant 4.'8 Angle Modulation 299 a mplitude sinusoid, whose instantaneous frequency is directly proportional to an input voltage m (t). Clearly, a VCO is a n F M generator. As d emonstrated earlier, FM generator, with minor modification, can be used t o g enerate any other form of angle modulation. Demodulation We shall discuss here demodulation of FM waves. As explained earlier, FM demodulator, with some minor modification, can be used for demodulation of any other form of angle modulation. Because t he i nstantaneous frequency of F M wave is proportional t o t he b aseband signal m (t), a n F M d emodulator is a device whose o utput is proportional t o frequency of t he i nput signal. Thus, t he gain H (w) of a n ideal FM demodulator is of t he form q w + C2. An ideal differentiator has this property. I f t he i nput t o a n ideal differentiator is a n angle modulated signal x (t) = cos [wet + k1/J(t)J, t he o utput y(t) is given by y(t) = d x(t) d t"- = -[we = [we . + k1/J(t)J sin [wet + k1/J(t)J + k~(t)J sin [wet + k1/J(t) + 71'J T he o utput is also a n angle modulated signal, whose envelope is We + k~(t). Hence, a n ideal differentiator followed by a n envelope detector will result in t he o utput we+k~(t). After blocking t he dc, we o btain t he desired o utput k~(t). Recall t hat for t . F M, 1/J(t) = J m (a)da. Hence, 1/J(t) = m (t). A nother device t hat c an be used as a n F M demodulator is a t uned circuit, whose resonant frequency is selected either above o r below the carrier frequency of t he F M signal t o b e demodulated. T he frequency response of a t uned circuit (below t he r esonant frequency) is a pproximately linear with t he i npu...
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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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