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That looks like a simple waveform generator. The pots are set to create a voltage at a certain time period and the combined settings of all the pots create a wave of a certain shape.
For example, setting the first pot to 0.1v and the second to 0.2v, etc., you'll get a ramp output that ramps up. Setting them opposite to that will give you a ramp down. Setting them to correspond to sin(t) amplitudes will give you a sine wave output, even if offset by some DC value.
The basic operation is such that the 555 gives the counter chip a clock, and the counter counts up and provides a binary count to the one of 16 decoder. Thus, one pot at a time is selected and so only that pot generates the wave amplitude at that point in time. By changing the pot settings you can generate a wide variety of wave shapes, but they will be limited to 16 discrete steps rather than a continuously smooth output. Using some output filtering helps this situation when possible.
In short:
The 555 provides pulses to the counter chip.
The counter chip counts up in binary.
The decoder chip (74154) decodes the binary count into 16 distinct low true outputs.
The inverters invert the outputs of the decoder into high outputs instead of low outputs.
The analog switches enable the pots one at a time.
The pots create the output voltage for that point in time.
Since the pots are biased with 5v, that means any output from 0 to 5v is possible for any point in the waveform.
The output frequency is limited by the max frequency of the chip that has the lowest frequency limit, but because the 7493 chip divides the 555 frequency by 16 that will limit the output frequency by the max of the 555 divided by 16. The exception is if you set up the pots to generate an N*x frequency, but then that limits the analog resolution instead.
A simple example would be if you set up the pots from left to right to values of 0.0v, 0.1v, 0.2v, 0.3v, 0.4v, up to 1.5v. That will cause a ramp output that spans from 0 to 1.5v and then it will jump back down to 0v.
If instead you set the pot values to 0.0, 0.1, 0.2, and when you get to 0.7 you set the next to 0.7, 0.6, 0.5, 0.4, etc., you;ll get an output that ramps up and then ramps back down again.
If you need a true AC output you'll have to reference the output to some positive output offset.
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