Suppose you have a set of real-valued waveforms {s1(t), s2(t),..., sN(t)}, and you want to find...

Suppose you have a set of real-valued waveforms {s₁(t), s₂(t),..., s_N(t)}, and you want to find a basis for the span of their complex envelopes. The obvious approach would be to first downconvert each of the waveforms, and then apply the Gram-Schmidt procedure to the set of complex envelopes. Will we get the same answer if we first apply Gram-Schmidt, and then downconvert? Justify your answer.

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