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In this problem, we explore how the use of FM can overcome nonlinear distortion. Consider a memoryless channel characterized by the nonlinear input–output relationship:
where v_{i}(t) is the input and υ_{0}(t) is the output; α_{1}, α_{2}, and α_{3}, are fixed coefficients. The input is defined by the frequency-modulated signal
The message bandwidth is denoted by W, and the frequency deviation of the FM signal is ∆f.
(a) Evaluate the output υ_{0}(t).
(b) Using the generalized Carson rule, show that if the carrier frequency satisfies the condition
then the effect of nonlinear distortion can be removed by band-pass filtering.
(c) Specify the mid-band frequency and bandwidth of the filter in part (b).
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