Introduction to Fourier Series and Harmonic Analysis

Saturday, 22 November 1997, 9:00 AM - 4:00 PM [CHECK TIME]
Mathematics Building, Room 101

• Removing noise from sounds (Karl Bauer, bauer@math.arizona.edu )
• Periodic functions(Jeff Cunningham, jcunn@math.arizona.edu )
• What does it mean for a function to be periodic?
• Sums and products of periodic functions
• Guessing Fourier coefficients game (Cecilia Fosser, cfosser@math.arizona.edu )
• Fourier's discovery
• Coefficients that are impossible to guess
• Geometric integration
• Integration as signed area
• Integral of some periodic functions is zero
• Integral of other periodic functions is nonzero
• Calculating Fourier coefficients
• Multiplying the Fourier series by a period function
• Isolating terms
• Computing the coefficients
• Introduction to Riemann sums
• Basic concepts
• Doing Riemann sums with a calculator
• Guided exercises
• An earlier example revisited
• Computing Fourier coefficients of a given function
• MATLAB program for computing Fourier series
• Comparing MATLAB results to earlier results
• Touchtones
• Demonstration
• Fourier coefficients of touchtones
• Recognizing touchtones

If you are interested in pursuing any of these topics further, please email the individuals above.

Summary: 1 teachers and 24 students.