A square wave pulse generator is the most commonly used generator. It is mainly used in testing different equipment. It outputs square waves that varies between two levels, with a 50 percent duty cycle.
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Triangular wave generator is a device (for eg NE555 timer) that generates a triangular wave by integrating a square wave. In applications an ICL8038 IC can be used to generate all types of waves.
Yes,schmitt trigger has upper and lower threshold voltage for the reason of noise protection while square wave generator doesn't have these properties.
Timers, oscillators, square wave generator, power supply clocks, system clocks...you name it.
The wording are confusing an op-amp is an op-amp a comparator is another animal. an op-amp can be used as square wave generator by overdriving it but the results are not desirable. However a comparator will be a switch on-off at the set level.
The wave with the maximum RMS value, in comparision with the peak value, is the square wave.