Yes, this is true. It follows from the fact that the average $$\lim_{T\to\infty} {1\over T}\int_0^T\cos(\lambda_i t+\phi_i)\sum A_i\cos(\lambda_i t+\phi_i)\,dt$$ t+\phi_i)\sum_j A_j\cos(\lambda_j t+\phi_j)\,dt$$ is $A_i/2$. Clearly the average is bounded by the supremum of the function.
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Yes, this is true. It follows from the fact that the average $$\lim_{T\to\infty} {1\over T}\int_0^T\cos(\lambda_i t+\phi_i)\sum A_i\cos(\lambda_i t+\phi_i)\,dt$$ is $A_i/2$. Clearly the average is bounded by the supremum of the function. |
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