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...

This preview shows page 1 - 8 out of 23 pages.

Signals and Systems Lecture 7
Image of page 1
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
Image of page 2
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
Image of page 3
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.
Image of page 4
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
Image of page 5
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.
Image of page 6
We know that. d ) - x(t ) ( h y(t) - Where h(t) is the unit impulse response of the system  
Image of page 7
Image of page 8

You've reached the end of your free preview.

Want to read all 23 pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes