The spectrum of a voice signal m(t) is zero outside the in- terval fa = |f|< fp. In order to ensure communication privacy, this signal is applied to a scrambler that consists of the following cas- cade of components: a product modulator, a high-pass filter, a second product modulator, and a low-pass filter. The carrier wave applied to the first product modulator has a frequency equal to fe, whereas that applied to the second product modulator has a fre-

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The spectrum of a voice signal m(t) is zero outside the in-
terval fa = |f|<fp. In order to ensure communication privacy, this
signal is applied to a scrambler that consists of the following cas-
cade of components: a product modulator, a high-pass filter,
a second product modulator, and a low-pass filter. The carrier wave
applied to the first product modulator has a frequency equal to f.,
whereas that applied to the second product modulator has a fre-
quency equal to fp + fc; both of them have unit amplitude. The
high-pass and low-pass filters have the same cutoff frequency at f.
Assume that f. >fp.
(а)
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 unscrambler that is identical to the
unit described above.
Transcribed Image Text:The spectrum of a voice signal m(t) is zero outside the in- terval fa = |f|<fp. In order to ensure communication privacy, this signal is applied to a scrambler that consists of the following cas- cade of components: a product modulator, a high-pass filter, a second product modulator, and a low-pass filter. The carrier wave applied to the first product modulator has a frequency equal to f., whereas that applied to the second product modulator has a fre- quency equal to fp + fc; both of them have unit amplitude. The high-pass and low-pass filters have the same cutoff frequency at f. Assume that f. >fp. (а) 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 unscrambler that is identical to the unit described above.
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