ECE45 Announcements

 
 

  1. ✤Class starts Tues April 2

  2. ✤A Pre-Test is available on-line in the handout section. This is material you should already know from previous classes. You should review this material before starting ECE45.

  3. ✤MATLAB software is a useful package to understand the application of the theory developed in class, these links contain useful resources to get started with MATLAB:

  4. ✤ http://www.mathworks.com/help/pdf_doc/matlab/getstart.pdf?s_tid=int_tut

  5. ✤ http://web.eecs.umich.edu/~aey/eecs451/matlab.pdf

  6. ✤Review on complex numbers posted on-line

  7. ✤Review on circuits posted on-line

  8. ✤Review on average power posted on-line

  9. ✤The ECE tutoring center in Jacobs Hall 5101 is also available to help you with the material in the class. Walk-ins are welcome M-F 8am-5pm


  1. ✤LECTURE 1. We pointed out the need to review operations with complex numbers, which are essential for this class. We also gave pointers to other review material and material useful to learn MATLAB which will be used in some of the homeworks. We introduced linear systems.  An example of a linear system is any RLC circuit. Linear systems transform sinusoids applied as input to the system into sinusoids at the output. The frequency of the sinusoid does not change, the system only affects the amplitude and phase of the sinusoid. When any linear combination of sinusoids is applied, the output can be computed using the principle of superposition. We started talking about phasors and introduced the phasor method to find the output of the system for any given sinusoidal input.


  1. ✤LECTURE 2. We reviewed the phasor method and introduced the frequency response. The frequency response is a complex number defined as the phasor of the output divided by the phasor of the input and depends on the frequency. It gives the response of the system to any sinusoidal excitation applied at any given frequency. The amplitude of the applied sinusoid is scaled by the magnitude of the frequency response and the phase of the sinusoid is shifted by the phase of the frequency response. 


  1. ✤LECTURE 3. To visualize the frequency response we can plot the magnitude and phase separately. We gave examples of low-pass, high-pass, and band-pass filters using RLC circuits, and plotted the corresponding frequency responses. We introduced Bode plots that provide the asymptotic behavior of the frequency response on a logarithmic scale.


  1. ✤LECTURE 4-5. We discussed Bode plots (amplitude and phase) and gave a general graphical method to be used in the problem sets.


  1. ✤LECTURE 6-7-8. We introduced one of the most important concepts in this class: the Fourier Series. This is a series representation that can be used for periodic signals that have finite energy over a period. Such signals can be represented as the superposition of infinitely many sinusoids. Using superposition, we can then easily find the response of any LTI system of given frequency response to any periodic signal. The Fourier series coefficients of a signal can be found through integration. We discussed several mathematical properties of the Fourier series that can be used to solve problems. We also discussed the practical significance of the series and watched some cool videos introducing the concept of “spectrogram” of a signal.  Check them out again:

  2. ✤https://www.youtube.com/watch?v=tTy-ZNw_sk8

  3. ✤https://www.youtube.com/watch?v=VRAXK4QKJ1Q

  4. ✤https://www.youtube.com/watch?v=3IAMpH4xF9Q


  1. ✤Midterm 1 will cover everything discussed in class up to Fourier series. That is: RLC, LTI, Frequency response, Bode plots, Fourier Series.


  1. ✤ LECTURE 9-10 We generalized the concept of Fourier series introducing the Fourier transform. This is an integral representation of any signal that has finite energy. The signal is represented as the superposition of a continuous “spectrum” of sinusoids of all frequencies. We discussed the relationship with the Fourier series and its application to problems involving linear systems.


  1. ✤LECTURE 11-14 We practiced problems with Fourier Transforms, introduced delta functions and convolution integral. We also had a midterm review session.


  1. ✤ Midterm 1 solutions have been added in the handout section.

  2. ✤ Midterm 2 solutions have been added in the handout section

  3. ✤ There will be extra office hours before the final on Tuesday from 3:30-5:30 in JACOBS 5101C

  4. ✤Check out the “convolution machine” https://www.fit.vutbr.cz/study/courses/ISS/public/demos/conv/