the input and output waveforms the squarewaves generated by the first and second squaring circuits 12 and 13 are described in the frequency domain by a fundamental frequency and odd harmonics decreasing as 1 n where n is the order of the harmonic when two squarewaves with relatively small difference in fundamental frequencies are mixed the associated fundamental frequencies and harmonics beat to produce a fundamental frequency u03b4f and odd harmonics decreasing as 1 n 2 these beat frequencies are the frequency domain description of the desired triangular waveform filtering out the unwanted higher frequencies results in the desired waveform referring now to fig3 sawtooth waveforms can be produced by the addition of an exclusive or gate 16 and a comparator 17 comparator 17 detects the output of low pass filter 15 and changes its output whenever the peak of the desired triangular waveform is detected this output and the output from first squaring circuit 12 are applied to exclusive or gate 16 the output from exclusive or gate 16 changes phase by 180 u00b0 whenever the peak of the triangular waveform is sensed by comparator 17 this results in a 180 u00b0 phase shift in the output from the low pass filter 15 the output from the low pass filter 15 is therefore a sawtooth waveform with a fundamental frequency 2 u03b4f a person skilled in the art would now realize that the exclusive or gate 16 could be placed anywhere after either squaring circuit and in front of the low pass filter 15 and achieve the same results similarly the triangular waveform generator of fig1 may be easily arranged to generate squarewaves or sine waves by employing a conventional squaring circuit or diode shaping circuit in addition squarewaves and sine.