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lecture5 - CSE 471 Media Processing and Multimedia Phasors...

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1 CSE 471 Media Processing and Multimedia Phasors Phasors and phasor math A much more efficient way to analyze manipulations of digital audio
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2 CSE 471 Media Processing and Multimedia Now, some simple questions? What do I get if I add two sinusoids of the same frequency? What do I get if I add two sinusoids that are different frequencies?
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3 CSE 471 Media Processing and Multimedia Sinusoidal math How do we add sinusoids? a 1 cos( ϖ t+ φ 1 )+a 2 cos( ϖ t+ φ 2 ) =a 1 cos( ϖ t)cos( φ 1 )-a 1 sin( ϖ t)sin( φ 1 )+ a 2 cos( ϖ t)cos( φ 2 )-a 2 sin( ϖ t)sin( φ 2 ) And so on, quickly descending into a trigonometry hell even Dante could not conceive There’s got to be a better way!
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4 CSE 471 Media Processing and Multimedia Where does it all come from? x y cos ϖ t Unit circle: radius = 1 Rotation speed: ϖ (radians per second)
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5 CSE 471 Media Processing and Multimedia At the same time… x y cos ϖ t sin ϖ t What if we decided to carry sin ϖ t along as baggage?
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6 CSE 471 Media Processing and Multimedia Complex numbers j=sqrt(-1) c=a+bj is a complex number This is a two dimensional number system Real axis –and- Imaginary axis
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7 CSE 471 Media Processing and Multimedia Imaginary numbers as 2d vectors real imaginary 2 + 3j -3 - 1j z=x+jy magnitude is the vector length R = |z|=sqrt(x 2 +y 2 ) phase is the angle relative to the real axis We can express in polar coordinates
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