Is is possible to transmit rt=a1utcos2Πfct+a2utsin2Πfct+a3utcos4Πfct+a4utcos64Πfct and recover a1 a2 a3 and a4 uniquely back from rt Explain your reasoning

No, it is not possible to recover a1, a2, a3, and a4 uniquely from r(t).

The reason is that r(t) contains multiple frequency components, and each of the four terms (a1u(t)cos(2Πfct), a2u(t)sin(2Πfct), a3u(t)cos(4Πfct), and a4u(t)cos(64Πfct)) contribute to different frequency components.

When we pass r(t) through a filter to extract a specific frequency component, we will obtain a combination of a1, a2, a3, and a4. Therefore, to recover a1, a2, a3, and a4 uniquely, we need to know the frequency components of each term and separate them accordingly.

Without any additional information, it is impossible to determine the exact frequency components of each term, and thus, it is impossible to recover a1, a2, a3, and a4 uniquely from r(t).