Sinusoidal Frequency Modulation(FM) Oscillator y(t=A cos(e(t) Amplitude fixed Phase modulation: A(t)=wct+.Bo+ kp c(t) Frequency modulation: dt=;wc+ka(t) x(t) is signal to be …………… instantaneous transmitted Chirp FⅣ x(t=u(t) x(t=tou(t)
Sinusoidal Frequency Modulation (FM) FM x(t) is signal to be transmitted
Sinusoidal Fm (continued) ransmitted power does not depend on x(t): average power=A/2 Bandwidth ofy(t) can depend on amplitude of x(t) Demodulation a) Direct tracking of the phase at (by using phase-locked loop b) Use of an lti system that acts like a differentiator v(t y Envelope detector HG@- Tunable band-limited differentiator, over the bandwidth of y(t) H(j0)≈j 2()s looks like am (wc+ kf()Asin e(t) envelope detection de/ di
Sinusoidal FM (continued) • Transmitted power does not depend on x ( t): average power = A 2/2 • B a n d wid t h o f y ( t) can depend on amplitude of x ( t ) • Demodulation a) Direct tracking of the phase θ( t) (by using phase-locked loop ) b) Use of an LTI system that acts like a differentiator H(j ω) — Tunable band-limi ted differentiator, over the bandwidth of y ( t) … looks like AM envelope detection