lecture 7.pptx - Signals and Systems Lecture 7 Frequency domain Models To think about signals and systems in terms of frequency rather than time jt Use

# lecture 7.pptx - Signals and Systems Lecture 7 Frequency...

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Signals and Systems Lecture 7
Frequency- domain Models: To think about signals and systems in terms of frequency rather than time Use of the complex exponential function as the basic signal component. t j e ) e - e ( 2j 1 sin ) e e ( 2 1 cos jsin - cos e jsin cos e j - j j - j j - j
Signal models: If we put θ = ωt ) e - e ( 2j 1 t sin ) e e ( 2 1 t cos t j - t j t j - t j
Ex. t t t t A t o o o o j - j j - j o e 2 e 2 A ) e e ( 2 A Acos x(t) Amplitude 2 A 2 A o o - 0 We represent the signal in terms of amplitude, phase and frequency of its complex exponential components.
Ex. A voltage signal is modelled as the sinusoid. 0.5) 5cos(3t V(t) Express the signal in terms of exponential frequency component and sketch the frequency domain representation of the signal. Sol. ) e e ( 2 5 v(t) 0.5) j(3t - 0.5) j(3t j0.5 - j3t - 0.50 j(3t - j0.5 j3t 0.5) j(3t e e e e e e j3t - j0.5 - j3t j0.5 e ] e 2 5 [ e ] e 2 5 [ v(t) 2 5 -3 3 ω Amplitude 0.5 -0.5 phase ω
System models: The response of a linear system to a sinusoidal input component is itself a sinusoid of the same frequency as the input but, changed amplitude and phase. This means that we can develop a model for the behavior of a system in terms of the effect the system has on the amplitude and phase of sinusoid.
We know that. d ) - x(t ) ( h y(t) - Where h(t) is the unit impulse response of the system  

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