A pulse wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent each cycle ( period) called the duty cycle and for the remainder of each cycle is low. A duty cycle of 50% produces a square wave, a specific case of a rectangular wave. The average level of a rectangular wave is also given by the duty cycle.
The pulse wave is used as a basis for other waveforms that modulate an aspect of the pulse wave, for instance:
The Fourier series expansion for a rectangular pulse wave with period , amplitude and pulse length is [1]
Equivalently, if duty cycle is used, and :
Note that, for symmetry, the starting time () in this expansion is halfway through the first pulse.
Alternatively, can be written using the Sinc function, using the definition , as
A pulse wave can be created by subtracting a sawtooth wave from a phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is bandlimited, too.
The harmonic spectrum of a pulse wave is determined by the duty cycle. [2] [3] [4] [5] [6] [7] [8] [9] Acoustically, the rectangular wave has been described variously as having a narrow [10]/thin, [11] [3] [4] [12] [13] nasal [11] [3] [4] [10]/buzzy [13]/biting, [12] clear, [2] resonant, [2] rich, [3] [13] round [3] [13] and bright [13] sound. Pulse waves are used in many Steve Winwood songs, such as " While You See a Chance". [10]
A pulse wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent each cycle ( period) called the duty cycle and for the remainder of each cycle is low. A duty cycle of 50% produces a square wave, a specific case of a rectangular wave. The average level of a rectangular wave is also given by the duty cycle.
The pulse wave is used as a basis for other waveforms that modulate an aspect of the pulse wave, for instance:
The Fourier series expansion for a rectangular pulse wave with period , amplitude and pulse length is [1]
Equivalently, if duty cycle is used, and :
Note that, for symmetry, the starting time () in this expansion is halfway through the first pulse.
Alternatively, can be written using the Sinc function, using the definition , as
A pulse wave can be created by subtracting a sawtooth wave from a phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is bandlimited, too.
The harmonic spectrum of a pulse wave is determined by the duty cycle. [2] [3] [4] [5] [6] [7] [8] [9] Acoustically, the rectangular wave has been described variously as having a narrow [10]/thin, [11] [3] [4] [12] [13] nasal [11] [3] [4] [10]/buzzy [13]/biting, [12] clear, [2] resonant, [2] rich, [3] [13] round [3] [13] and bright [13] sound. Pulse waves are used in many Steve Winwood songs, such as " While You See a Chance". [10]