Software Engineering 2MX3

Monday, April 7, 2008

• Block diagrams

Friday, April 4, 2008

• Please see this correction regarding the tutorial

Wednesday, April 2, 2008

• Laplace transforms for describing mechanical systems

Monday, March 31, 2008

• More z-transforms, Laplace transforms

Friday, March 28, 2008

Tutorial notes:

• Page 1
• Page 2
• Page 3
• Page 4 - Correction: Should add poles close to exp(i*pi/5) and exp(-i*pi/5)

Wednesday, March 26, 2008

• Physics of the interactive motion simulator
• Filter networks/banks
• DSL
• Edge detection in images
• Introduction to the z-transform

Monday, March 24, 2008

• PWM implementation
• Sampling and aliasing
• Audio demonstration
• Nyquist-Shannon sampling theorem
• Wagon wheel example
• Mouse clicks and CD players

Monday, March 17th, 2008

• The DFT and Fast Fourier Transform
• More audio demonstrations
• Frequency buckets and approximation

Wednesday, March 12th, 2008

• Summary of the Fourier series and transforms

Monday, March 10th, 2008

• More CTFT and DTFT examples
• Pulse signals, brick wall filters, sinc function

Wednesday, March 5th, 2008

• Filter design

Monday, March 3th, 2008

• Frequency domain and the DTFT
• Audio demonstrations/examples

Friday, February 29th, 2008

Tutorial notes:

• Page 1
• Page 2 - Fourier series coefficients of odd triangle wave
• Page 3
• Page 4
• Fourier series approximation of triangle wave: (PDF) (gnuplot source)
• Same triangle wave decomposed into sinusoids: (PDF) (gnuplot source)

Wednesday, February 27th, 2008

• Computing Fourier series coefficients

Corrections to assignment 5:

• In question 1.3, the signal is x(t) = cos(t) + cos(2t) + sin(3t)

Monday, February 11th, 2008

• Signal filtering using frequency response
• General form of frequency response

Wednesday, February 6th, 2008

• Examples of computing output using frequency response

Monday, February 4th, 2008

• Formal definitions of linearity and time invariance
• Derivation of and how to compute frequency response

Wednesday, January 30th, 2008

• Introduction to complex numbers

Monday, January 28th, 2008

• Block diagram representation of systems

Friday, January 25th, 2008

Corrections to assignment 2:

• In question 2, the system S is y(n) = -y(n - 1) - y(n - 2) + x(n)

Corrections to assignment 1 solutions:

• Output for 1.1:

  n	-2	-1	0	1	2	3	4	5	6	7	8	9	10
  x	0	0	1	0	0	0	0	0	0	0	0	0	0
  y	0	0	0	1	0	-1	-1	0	1	1	0	-1	-1

• Output for 1.2:

  n	-2	-1	0	1	2	3	4	5	6	7	8	9	10
  x	0	0	1	1	1	0	0	0	0	0	0	0	0
  y	0	0	0	1	1	0	-2	-2	0	2	2	0	-2

• Output for 1.3:

  n	-2	-1	0	1	2	3	4	5	6	7	8	9	10
  x	0	0	1	-1	1	-1	1	-1	1	-1	1	-1	1
  y	0	0	0	1	-1	0	-1	1	0	1	-1	0	-1

  Alternatively:

  n	-2	-1	0	1	2	3	4	5	6	7	8	9	10
  x	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1
  y	0	0	0	2	0	0	-2	0	0	2	0	0	-2

• Matrix A in question 3:

  0	0	0	0
  1	0	0	0
  0	1	0	-1
  0	0	1	0

• Matrix C in question 3:

  0

  1

  0

  -1

Wednesday, January 23th, 2008

• Formal definitions of FIRs and IIRs
• Signals as a linear combination of impulses
• Symbolic representation of systems

Monday, January 21th, 2008

• Examples of SISO systems
• Using shift and add to compute the output
• The convolution operator

Friday, January 18th, 2008

• Converting between state equations and impulse response

Wednesday, January 16th, 2008

• Closed form of the impulse response

Monday, January 14th, 2008

• Homogeneity, additivity and linearity
• Superposition of signals
• Time invariance

Friday, January 11th, 2008

• Choosing and computing states from state equations
• Generalized difference equations
• Matrix multiplication review
• SISO and MIMO systems

Wednesday, January 9th, 2008

• Continuous vs. discrete signals, function signatures
• Difference equations (two-point moving average)
• Stability, instability and marginal stability
• Memory, state buffers and state equations
• Impulse and zero initial conditions

Monday, January 7th, 2008

• Definitions of signals and systems
• Examples of signals and systems (servos, PWM, MP3, etc.)
• Finite state machines (even-odd)