The pre-envelop and the envelop of a function f(t) = A cos

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The pre-envelop and the envelop of a function f(t) = A cos (ω_ct)

1. A e^jω_c^t, A
2. A² e^jω_c^t,
  A²
  2 2
3. A·e^−jω_c^t, A
4. A² e^−jω_c^t,
  A²
  2 2

Correct Option: A

Pre-envelop is given by
f_p(t) = f(t) + jf_h(t)
= A cos ω_ct + jA cos (ω_ct – 90°)
= A cos ω_ct + jA sin ω_ct
and the envelop is the magnitude of f_p(t)
|f_pe^jω_c^t(t)| = |Ae^jω_c^t = A

A²	e^jω_c^t,	A²
2	e^jω_c^t,	2

A²	e^−jω_c^t,	A²
2	e^−jω_c^t,	2