Pvågsform

Pvågsform is a theoretical class of waveforms used in signal processing and acoustics. It describes signals formed by a sequence of discrete pulses whose shapes and timing can be programmed to achieve a desired spectral and temporal profile. The term blends P for pulse, våg meaning wave in several Scandinavian languages, and form, signaling a particular waveform shape.

Construction and definition: A Pvågsform consists of pulses Pi centered at times ti with amplitudes Ai and durations Wi. Each pulse uses a shape pi(t) defined over [0, Wi], and the overall signal is S(t) = sum_i Ai pi(t − ti). The shapes may vary from symmetric bells to asymmetric ramps, and ti can be nonuniform to control the spectrum. The design allows a balance between time localization and frequency content.

Properties: This framework provides precise control over time-frequency content; by adjusting the set of pulses, one can approximate complex waveforms with a finite pulse train. It supports nonstationary spectra and rapid onset or offset transients, with bandwidth managed through the pulse shapes and spacing between pulses.

Generation and applications: Pvågsform can be synthesized in digital signal processors by discrete pulse synthesis or by passing a pulse train through shaping filters. In communications, it enables flexible modulation with controlled spectral occupancy; in audio, it can create percussive textures; in testing, it serves to simulate transient signals or sensor responses.

History and terminology: The name arose in theoretical discussions and is not tied to a single standard, with adoption varying by field. Related concepts include pulsed waveforms, impulse trains, and time-localized modulation. See also Waveform, Pulsed signal, Pulse-width modulation.