H4-01: FOURIER SYNTHESIS

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PURPOSE: To demonstrate Fourier synthesis of complex wave shapes.
DESCRIPTION: Complex waves may be formed using up to twelve harmonics with independently variable amplitudes and phases. Any individual harmonic such as the fundamental (in the photograph above) can be shown on one trace of the oscilloscope, while the sum is shown on the other trace. The wave can be simultaneously seen on the oscilloscope and heard using a loudspeaker with a separate volume control. Digital phase locking of all harmonics allows the frequency to be varied from below 100 Hz to above 1000 Hz while the wave shapes remain fixed, to show that timbre is primarily dependent on harmonic structure, and not on frequency or intensity. Some easily produceable wave shapes are square wave, sawtooth wave, triangular wave and pulse train.
Click on any of the wave shapes displayed below to see and hear an mpeg video containing the synthesis of that wave:

triangular wave	square wave
sawtooth wave	pulse train

Click here to see a video showing all of the above wave shapes as produced by a signal generator.

Click on the images above to see (and hear) the four basic waveshapes as created by a signal generator and as synthesized using our twelve-channel Fourier synthesizer. Each mpg contains about ten seconds of the wave as produced by a standard wave generator followed by ten seconds of the wave as synthesized using the first twelve harmonics. SUGGESTIONS: Practice for most effective use. Click here to view and print a copy of the Fourier Synthesizer instruction sheet in ".docx" format.
See Question of the Week #325 for information on using this demonstration to enhance class involvement.
REFERENCES: Available. (PIRA 3C50.00)
EQUIPMENT: Fourier synthesizer, four-trace oscilloscope, and loudspeaker on scope/TV cart, as photographed.
SETUP TIME: 10 minutes.