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Application of the Fourier Transform

Examples for spectra with last week's example program: From the Fourier transform results a spectrum in constant steps of frequency. For instance, with 22,050 Hz sampling rate and 1024 input samples, the 513 values resulting from the Fourier transform correspond to 0 Hz, 21.5 Hz, 43.1 Hz, 64,6 Hz, and so in steps of 21.5 Hz up to 11,003 Hz and 11,025 Hz. This set of frequencies does not correspond to the human perception of frequency: From 21.5 to 43.1 Hz it's one octave, from 11,003 to 11,025 Hz it's a fraction of a semitone. One can reorganize the frequency scale to conform to musical intervals. However, the lack of frequency resolution at the low end remains.

Electroencephalogram (EEG)

The activity of the brain generates tiny voltages on the scalp. These are easily classifyable using their frequency, which is an ideal application of the Fourier transform. The low-frequency waves (delta and theta) signify sleep, the high-frequency waves (alpha and beta) signify the awake state. If the eyes are closed, beta waves will give way to alpha waves.

EEG waves result from the joint behavior of large regions of neurons. Nonetheless, the voltages on the scalp amout to only 10 to 100 microvolts (millionth part of a volt). Thus, a huge amplification is required to get signals in the usual range of several volts. Schematics and kits are available on the Internet (OpenEEG). Apart from the amplification, the circuitry has to take care of suppressing the powerline frequency that pollutes any measurement of tiny voltages at high resistances. Thus, a strong filter is inserted that cuts all frequencies greater than or equal to 50 Hz (Europe) or 60 Hz (U.S.).

Example for an Actuator: Using the Motor Fader

Motor Faders are employed as volume controls for the (possibly dozens of) tracks of professional music mixing consoles. The sound engineer can use them to set the tracks' levels. The console (of digital audio workstation) records the motion of the faders and can reproduce this motion automatically. Here, the faders are moved through the motors to "display" the mix to the sound engineer. He or she can grab any fader and manually override the automated motion. When the system sense that the user touches a fader, it releases it from the motorized motion.

The motor fader provides six connections:

A simple method to control the motor is to let it turn right at full speed when the lever is too far right from the target position, and to let it turn left at full speed when the lever is too far left. However, this leads to a rattling motion: Starting left, the lever will accerelate and travel past the target position; the motor begins to spin in the other direction, again overshooting, etc. One can cope with this by reducing the speed when the lever approaches the target position. This reduction is done best by pulse width modulation (PWM). The Arduino offers 256-step PWM on several of its digital outputs without further ado. One of these outputs is connected to the on/off (enable) pin of the motor driver.

Electrical devices that contain coils (in particular, motors) generate voltage spikes when they are switched on and off. The L293D contains internal diodes that clamp these spikes in order to protect the digital electronics. On top of that, the L293D allows to conntec two independent supply voltages: one for the logic part and one for the power part. It is a good idea to feed the motor (the power part) from unregulated power, not from the "clean" 5 volts. This keeps spikes out of the digital circuitry (which may otherwise show erratic behavior) and relieves the power regulator from the huge current that a motor will drain.

Electrotactile Displays

If nerve cells are stimulated through electrical current, they send pulses. The other nerve cells (and, thus, the brain) cannot tell these pulses from the regular output of these cells. So one can use electrodes to create tactile sensations on the skin, confuse the user's equilibrium sense or simulate audio signals.