Fraryeneyan
Spectra of FMFM spectra contains thecarrierfrequencyplussideband componentswhose amplitudes depend ontheBessel functions (of the first kind)I is the modulation index, f, the carrielfrequency,fthe modulatorfrequencyJo(1)J.3(I)=-J3()Ji(r)amplitudeJ2(1)J-2(I)J3()f2fmfe+fmfe+3fmJemfa-fmfe+2fmfrequencyJ.()=-J(I)
Spectra of FM • FM spectra contains the carrier frequency plus sideband components whose amplitudes depend on the Bessel functions (of the first kind). • I is the modulation index, fc the carrier frequency, fm the modulator frequency
Bessel function of the firstkind of orders 0 ～ 31.00.8orderoorder1order20.6order30.4epnde0.2-0.2-0.41015205modulationindexJ。(I) corresponds to order 0Ji (I) corresponds to order 1
Bessel function of the first kind of orders 0 ~ 3 J0(I) corresponds to order 0, J1(I) corresponds to order 1,
Spectra of FMBesselfunctions look like dampedsine waves, where the order of thefunction is given by the subscriptA property of Bessel functions:J-i(I) = J;(I)*(-1)iC library for Bessel functions:jn(order, I)
Spectra of FM • Bessel functions look like damped sine waves, where the order of the function is given by the subscript • A property of Bessel functions: J-i(I) = Ji(I) * (-1)i • C library for Bessel functions: jn(order, I)
Properties of Formant FM SpectraNegative frequencies fold up tocorresponding positive harmonicfrequencies400100200300500600700-1008009001000110012004frequency
Properties of Formant FM Spectra • Negative frequencies fold up to corresponding positive harmonic frequencies