EECE 301 Note Set 12a Complex Sinusoids

EECE 301 Note Set 12a Complex Sinusoids - 1/16 EECE 301...

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Unformatted text preview: 1/16 EECE 301 Signals & Systems Prof. Mark Fowler Complex Sinusoids Complex-Valued Sinusoidal Functions 2/16 A sinusoid is completely defined by its three parameters:-Amplitude A (for EEs typically in volts or amps or other physical unit)-Frequency in radians per second-Phase shift in radians T is the period of the sinusoid and is related to the frequency 3/16 Phase shift (often just shortened to phase) shows up explicitly in the equation but shows up in the plot as a time shift (because the plot is a function of time). Q: What is the relationship between the plot-observed time shift and the equation- specified phase shift? A: We can write the time shift of a function by replacing t by t + t o (more on this later, but you should be able to verify that this is true!) Then we get: ) sin( )) ( sin( ) ( o o o t t A t t A t t f + = + = + = So we get that: = t o (unit-wise this makes sense!!!) Frequency can be expressed in two common units:-Cyclic frequency: f = 1/...
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EECE 301 Note Set 12a Complex Sinusoids - 1/16 EECE 301...

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