A pulse wave or pulse train is a kind of non-sinusoidal waveform that is similar to a square wave, but does not have the symmetrical shape associated with a perfect square wave. It is a term common to synthesizer programming, and is a typical waveform available on many synths. The exact shape of the wave is determined by the duty cycle of the oscillator. In many synthesizers, the duty cycle can be modulated (sometimes called pulse-width modulation) for a more dynamic timbre. The pulse wave is also known as the rectangular wave, the periodic version of the rectangular function.
The Fourier series expansion for a rectangular pulse wave with period T and pulse time τ is
Note that, for symmetry, the starting time (t = 0) in this expansion is halfway through the first pulse. The phase can be offset to match the accompanying graph by replacing t with t - τ/2.
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.
Famous quotes containing the words pulse and/or wave:
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Hide him in lonely garrets, if you will,—
But his hard, human pulse is throbbing still
With the sure strength that fearless truth endows.”
—Edwin Arlington Robinson (1869–1935)
“Children are as destined biologically to break away as we are, emotionally, to hold on and protect. But thinking independently comes of acting independently. It begins with a two-year-old doggedly pulling on flannel pajamas during a July heat wave and with parents accepting that the impulse is a good one. When we let go of these small tasks without anger or sorrow but with pleasure and pride we give each act of independence our blessing.”
—Cathy Rindner Tempelsman (20th century)