Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

:2.74 FREQUENCY MODULATION, Volume Iwhere m = D/jx. The equation for the frequency-modulated wavebecomese = E sin {at + S (t) } = E sin at cos S(t) + E cos at sin S (t)(12)Since cos S(t) is symmetrical about the origin, it can be expandedin a cosine series. Similarly, sin S(t) is skew symmetric about theorigin and can be expanded in a sine series. From Figure 8,cos S(t) = cos mdmx (ir — 8)-rrX ^ B1 — x^ 7r^ 8 ^ TTX— 2 &» cos 27rW,u.tm=0(13)where7Ty2 /^ ma;cos m0 cos ndd8 H— / cos (ir — 8) cos nOdd (14)^ .Ar 1 — »Similarly,sin jS(0 = sinrafl= sin-& = sin irmx.nmx(15)g 9 ^ ira;mx (it — 9)1-a;Tra; §§ 7rwherec n s in 2imuim=0(16)2 /" 2f mxc n= — / sin ra0 sin TC0d0 H / sin (ir — 8) sin w0d0. (17)" Jo * J-nx 1 — xWhen these results are substituted intoby(11), the spectrum is given