EE200_Weber_10-7

EE200_Weber_10-7 - EE 200 Frequency Domain Signals are...

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1 EE 200 Frequency Domain Signals are functions with a domain and a range. In this chapter we deal with signals where the domain is time (continuous or discrete) or space. The frequency of signals can be in Hertz (cycles per second) or in cycles per unit distance. Signals can be represented in the frequency domain rather than the time domain, and this has several advantages when dealing with LTI systems.
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2 EE 200 Frequency Decomposition Many real-world signals are very complex and to understand them we can break them down into compositions of simpler signals. Example: Musical sounds can be modeled (sort of) as combinations of pure tones. Each pure tone is a single sinusoidal signal, and the sound we hear is a sum of multiple sinusoids. s ( t ) = sin( f 1 " 2 # t ) + sin( f 2 " 2 t ) + sin( f 3 " 2 t ) + L
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3 EE 200 Frequency Decomposition The “major triad” consisting of a the notes A, C sharp (C#) and E has frequency components at three frequencies: A 440 Hz C# 554 Hz E 659 Hz Our ear hears the sum of all three sinusoids s ( t ) = sin(440 " 2 # t ) + sin(554 " 2 t ) + sin(659 " 2 t )
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4 EE 200 Frequency Decomposition The three sinusoids sum to create a new signal.
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EE200_Weber_10-7 - EE 200 Frequency Domain Signals are...

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