sågtandsvågor

Sågtandsvågor, also known as sawtooth waves, are a type of non-sinusoidal periodic waveform. Their characteristic shape resembles the teeth of a saw, with a gradual increase or decrease in amplitude followed by a sharp drop or rise. This pattern repeats cyclically. In a positive sawtooth wave, the amplitude increases linearly over time and then abruptly drops back to its minimum value. Conversely, a negative sawtooth wave decreases linearly before a sudden jump back to its maximum.

The mathematical representation of a positive sawtooth wave with amplitude A and period T can be expressed as f(t) = 2A * ((t/T) - floor(t/T + 0.5)) for a wave centered around zero, or f(t) = A * ((t/T) - floor(t/T)) for a wave starting at zero. The term floor(x) represents the greatest integer less than or equal to x. The sharp transitions in a sawtooth wave mean it contains a rich harmonic content, consisting of a fundamental frequency and all its odd harmonics.

Sågtandsvågor are commonly encountered in electronics, particularly in oscilloscopes and sweep generators, where they are used to create a linear sweep across the screen. They also find applications in audio synthesis, creating distinctive timbres, and in some forms of signal processing. The predictability and sharp edges of the waveform make it useful for generating precise timing signals and for analyzing the frequency response of circuits.