flâneur

Wideband FM Signals

dspfirst.gatech.edu · 449 words · saved by 1 readers

Each one of these FM signals is synthesized from the same basic formula: a sine-wave in the argument of a cosine function is used to "modulate" the frequency at the rate fm. x(t)=Acos(2π f c t+ D f cos(2π f m t)) 𝑥 ( 𝑡 ) = 𝐴 cos ⁡ ( 2 𝜋 𝑓 𝑐 𝑡 + 𝐷 𝑓 cos ⁡ ( 2 𝜋 𝑓 𝑚 𝑡 ) ) However, the fundamental idea of instantaneous frequency breaks down in this case because the chirp rate gets too high. Notice that the previous ideas about the frequency content of the FM signal are no longer valid ! If the modulation rate gets too large, then our perception of the sounds changes. However, the change is not necessarily a loss, since the chirps created with high-frequency sine waves in their argument seem to posses a harmonic quality (i.e., the spectrum exhibits a number of isolated spectral lines). This fact is the basis of FM synthesis for various musical instruments.

There are four FM (Frequency Modulation) sounds to study. First listen to each of them without knowing how they differ. Your browser does not support the audio tag. Each one of these FM signals is synthesized from the same basic formula: a sine-wave in the argument of a cosine function is used to "modulate" the frequency at the rate fm. $$x(t) = A \cos( 2\pi f_c t + D_f \cos(2\pi f_m t) )$$ However, the fundamental idea of instantaneous frequency breaks down in this case because the chirp rate gets too high. Sounds in time-frequency domain Let's look at the sounds in the time-frequency…

saved by

related reading