Given f(t) = cos ω1t + sin ω2t then fh(t) =?

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Given f(t) = cos ω₁t + sin ω₂t then f_h(t) =?

1. sin ω₁t – cos ω₂t
2. sin ω₁t + cos ω₂t
3. sin ω₂t – cos ω₁t
4. None of these

Correct Option: A

We know that Hilbert transform [f_h (t)] can be obtained by replacing the signal (– 90°) i.e.
f_h (t) = cos (ω₁t – 90°) + sin (ω₂t – 90°)
or f_h (t) = sin ω₁t – cos ω₂t
Hence alternative (A) is the correct choice.