Fourier Methods

Buffalo State College, July 8–10, 2019

(One or two set-ups available)

The Fourier transform is a commonly-used tool in mathematical physics, but Fourier analysis has now become a real-time diagnostic capability in experimental physics as well. Fourier Methods is a collection of hands-on electronic skills, and patterns of thinking, which can be used to understand the information content of signals in physics, engineering, communication, and beyond. This Immersion will develop those skills, using a combination of a Fourier-analyzer instrument (Stanford Research Systems SR770), a package of TeachSpin electronic modules, and some hardware experiments to perform and analyze. (see http://www.teachspin.com/fourier-methods.html)

Participants will experience the time-domain and frequency-domain views of various signals, ranging from simple to complex—including chaotic and noise waveforms. They will also learn the metrology of signals, and noise, in the frequency domain; the Fourier picture of recovery of weak sinusoidal signals immersed in noise will illuminate why lock-in detection works, and will also illustrate the meaning of the unit V/√Hz. Participants will acquire skills using the TeachSpin curriculum, and apply them to experiments in acoustic resonance, fluxgate magnetometry, or coupled oscillators.

Participants may bring a laptop, and are welcome (but not required) to bring along a favorite or familiar oscilloscope; the rest of the necessary equipment will be on hand.

Costs of the experiment: to replicate it as it will be used in the Immersion would cost $8k. Some, even many, of its ideas can be replicated at much lower cost, given a digital oscilloscope with FFT capability; of course, that way, lots of objects and systems would have to be improvised.
 

Host and Mentor:

David Van Baak is Professor Emeritus of Physics at Calvin College. His academic career included teaching and developing in the advanced-lab at Calvin College from 1980 through 2014; and since 2005 it has included collaborations with TeachSpin. Since 2014 he has been full time at Teachspin.
The Fourier transform no longer belongs just to theorists! The fast-Fourier-transform algorithm, and real-time data acquisition and digitization, now make the Fourier content of real-life laboratory signals transparently visible in table-top laboratory investigations. His experience with such technologies has included a 1991 ILIP grant for Fourier Methods across the curriculum, and has progressed to involvement with a commercial release of a full Fourier-methods teaching package. If voltmeters and oscilloscopes represent fundamental data-acquisition tools, and if a lock-in amplifier stands for advanced capabilities, then a Fourier analyzer is a wonderful intermediate-level tool for visualization and measurement which physicists ought to acquire and pass along to their students. Quite apart from teaching signal-processing capabilities of remarkable sensitivity and resolution, this Immersion will reinforce the skills of the Fourier way of thinking, and will (ideally) addict each participant with the routine use of a Fourier analyzer in laboratory diagnostics.

Dr. David A. Van Baak, Teachspin, Inc., 2495 Main Street, Suite 409, Buffalo NY 14214-2153. Email: dvanbaak@teachspin.com. Telephone: 716-885-4701.

Please note that the Jonathan F. Reichert Foundation has established a grant program to help purchase apparatus used in Laboratory Immersions. Limitations and exclusions apply, but generally speaking the foundation may support up to 40% of the cost of the required equipment.