The Hilbert transform of cos ω 1 t + sin ω 2 t is
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The Hilbert transform of cos ω1t + sin ω2t is
A. <p>sin ω<sub>1</sub>t – cos ω<sub>2</sub>t</p>
B. <p>sin ω<sub>1</sub>t + cos ω<sub>2</sub>t</p>
C. <p>cos ω<sub>1</sub>t – sin ω<sub>2</sub>t</p>
D. <p>sin ω<sub>1</sub>t + sin ω<sub>2</sub>t</p>
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Right Answer is: A
SOLUTION
\({\rm{\hat x}}\left( {\rm{t}} \right) = {\rm{x}}\left( {{\rm{t}} - {\rm{\pi }}/2} \right)\)where \(x ̂(t)\)is Hilbert perform of x(t)
therefore, cos (ω1t – π/2) + sin (ω2t – π/2)
sin ω1t – cos ω2t