Modulation index is the ratio of the amplitude of modulating signal to that of carrier wave.
\(\mu = \frac{A_m}{A_c}\)
Modulation index is kept low in order to avoid distortion. The low frequency modulating signal is mixed with high-frequency carrier wave, the distortion is restricted due the high-frequency carrier wave for modulation index lying between 0 and 1.
Bandpass filter rejects low and high frequencies and allows a band of frequencies to pass through.
