<div>I understand complex numbers used to represent rotation, so as to encode frequency in an easy to manipulate form, and I understand that the imaginary part can be disposed of when converting back to real signals and nothing is changed, but there's one bit that is hanging me up:
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<div>Using i is just a convention, a way to keep from mixing the two numbers. The square root of -1 is not really involved in any of it, because it doesn't exist. So why, when you multiply Z1 and Z2, do i*sin(a) and i*sin(b) multiply to -sin(a)sin(b)?
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<div>Also, the decision (this is coming from Miller's "Theory and Techniques") to multiply the complex constant A by the unit-value complex number Zn; this is convenient, but it seems rigged. Instead of letting Z have whatever amplitude it really has, in which case multiplying it (which already seems forced) by itself changes its amplitude, you force it to be 1 and add on the amplitude later. Nothing violated, but it seems artificial, like we fudge the numbers to make it come out right. If it is artificial, and just a way of simplifying sinusoid manipulation, then why even use artificial mathematical operations to explain it?
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<div>I already tried just moving ahead accepting these, but eventually something always throws me.</div>
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<div>One more question... regarding how filters work, is there no intuitive way to express it? No shortcut so that rpole~ and rzero~ will at least make sense in theory before I push through all the math?</div>
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<div>-Chuckk</div>
<div><br clear="all"><br>-- <br>"It is not when truth is dirty, but when it is shallow, that the lover of knowledge is reluctant to step into its waters."<br>-Friedrich Nietzsche, "Thus Spoke Zarathustra"
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