The spectrum of a voice signal m (t) is zero outside the interval a < |

The spectrum of a voice signal m (t) is zero outside the interval ƒ_a < | ƒ | < ƒ_b. To ensure communication privacy, this signal is applied to a scramble that consists of the following cascade of components: product modulator, high pass filter, second product modulator, and low-pass filter. The wave applied to the first product modulator has frequency equal top ƒ_c, where that applied to the second product modulator has a frequency equal to ƒ_b + ƒ_c, both of them have unit amplitude,. The high-pass and low-pass filters have the same cutoff frequency at ƒc. Assume that ƒ_c > ƒ_b.

(a) Derive an expression for the scrambler output s (t), and sketch its spectrum.

(b) Show that the original voice signal m (t) may be recovered from s (t) by using an unscramble that is identical to the unit just described.