The principle of Fourier transform is to convert a square wave into a triangular wave. In the triangular wave generating circuit, the time constant of the forward integration of the integration circuit is much larger than that of the reverse integration, or the time constant of the reverse integration is much larger than that of the forward integration, so the rising and falling slopes of the output voltage uO are quite different, and sawtooth waves can be obtained.

Square wave integral is triangular wave, and triangular wave differential is square wave. Sine wave can be obtained by integrating triangular wave for many times, and can also be converted by diode network. Sine wave can be converted into square wave by Schmidt trigger or comparator. Square wave is a non-sine wave, which usually appears in electronics and signal processing. An ideal square wave has only two values: high and low.

A signal with a rectangular waveform of current or voltage is a rectangular wave signal, and the ratio of the time occupied by high level in a waveform period is called duty cycle, which can also be understood as the ratio of the effective release time of the circuit to the total release time. A rectangular wave with a duty cycle of 50% is called a square wave, which is divided into zero level and negative low level.

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An ideal square wave can be expressed by Fourier series, which has infinite terms, as follows: Gibbs phenomenon will occur when a square wave is expressed by Fourier series. The ringing phenomenon in non-ideal square wave has been proved to be related to this phenomenon. σ approximation can prevent Gibbs phenomenon, and σ approximation uses Lanczos σ factor to make the sequence converge more ideally.

Sine wave can be obtained by integrating triangular wave for many times, and can also be converted by diode network. Sine wave can be converted into square wave by Schmidt trigger or comparator. ?

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