So....a cosine wave when shown in the frequency domain is represented by a 1/2 magnitude vector at the positive frequency and a 1/2 magnitude vector at the negative frequency. I am surprised by this because I cannot understand why a vector of magnitude 1 at the positive frequency of the cosine wave is wrong? I understand euler's inverse formula that cos ix = e^ix / 2 + e^-ix / 2. When I look at this equation, I see a one positive and negative associated with 1/2 magnitudes but I cannot make the jump from e^ix and e^-ix locating these 1/2 magnitude vectors at the positive x frequency and -x frequency. And again, why would the 1 vector at the positive frequency be wrong?(adsbygoogle = window.adsbygoogle || []).push({});

In about ten signal processing texts I have see this thrown around as if it is self explanatory but I am not getting it. Can someone spell this out for me? Thanks!

-xerxes73

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# Cosine wave represented as 1/2 magnitude vector at positive and negative frequency?

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