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EE3TP4_17_SinusoidalResponse_v2_Lecture 25

EE3TP4_17_SinusoidalResponse_v2_Lecture 25 - Ch 5...

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Ch. 5 Frequency-Domain Analysis of Systems Our main interest in this chapter is: How do we use the FT to analyze LTI systems? We’ll focus on the zero-state response here… We’ll look first at CT systems using three steps: 1. Find out how sinusoids go through a C-T LTI 2. Because a periodic signal is a sum of sinusoids we use linearity to extend Section 5.1 results to periodic signals. 3. Non-periodic signals also can be viewed as a sum (really an integral) of sinusoids so we can extend the result again! Later we’ll do the same things for D-T systems. In between we’ll look at “Ideal C-T Filters” and “Sampling” to convert C-T signals into D-T signals
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5.1 Response to a sinusoidal input: Previously, using convolution, we saw that it is easy to find how a complex sinusoid goes through a C-T LTI system : h(t) x t = Ae j ω 0 t θ y t = Ae j ω 0 t θ −∞ h τ e 0 τ d τ = H ω 0 We now know that this is the Fourier transform of the system’s impulse response, evaluated at ω = ω 0
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