“Pulse wave”的意思、由来-开放百科全书

A pulse wave or pulse train is a kind of non-sinusoidal waveform that includes square waves (duty cycle of 50%) and similarly periodic but asymmetrical waves (duty cycles other than 50%). It is a term common to synthesizer programming, and is a typical waveform available on many synthesizers. 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.^[1]

The pulse wave is also known as the rectangular wave, the periodic version of the rectangular function.

The average level of a rectangular wave is also given by the duty cycle, therefore by varying the on and off periods and then averaging these said periods, it is possible to represent any value between the two limiting levels. This is the basis of pulse width modulation.

The Fourier series expansion for a rectangular pulse wave with period {{math|T}} and pulse time {{math|τ}} is

Note that, for symmetry, the starting time ({{math|t {{=}} 0}}) in this expansion is halfway through the first pulse. The phase can be offset to match the accompanying graph by replacing {{math|t}} with {{math|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. Another way to create one is with a single ramp wave (sawtooth or triangle) and a comparator, with the ramp wave on one input, and a variable DC{{clarify|date=May 2015}} threshold on the other. The result will be a precisely controlled pulse width, but it will not be bandlimited.

The harmonic spectrum of a pulse wave is determined by the duty cycle.^[2]^[3]^[4]^[2]^[3]^[4]^[5]^[6] Acoustically, the rectangular wave has been described variously as having a narrow^[10]/thin^[1]^[7]^[8]^[9]^[10], nasal^[1]^[7]^[8]^[10]/buzzy^[10]/biting^[9], clear^[11], resonant^[11], rich^[7]^[10], round^[7]^[10] and bright^[10] sound. Pulse waves are used in many Steve Winwood songs, such as "While You See a Chance".^[12]

See also

References

1. ^¹²Reid, Gordon (February 2000). "Synth Secrets: Modulation", SoundOnSound.com. Retrieved May 4, 2018.
2. ^Pejrolo, Andrea and Metcalfe, Scott B. (2017). Creating Sounds from Scratch, p.56. Oxford University Press. {{ISBN|9780199921881}}.
3. ^Snoman, Rick (2013). Dance Music Manual, p.11. Taylor & Francis. {{ISBN|9781136115745}}.
4. ^Skiadas, Christos H. and Skiadas, Charilaos; eds. (2017). [https://books.google.com/books?id=CAhEDwAAQBAJ&pg=PT440&dq=%22rectangle+wave%22+harmonics&hl=en&sa=X&ved=0ahUKEwjtw-ye7evaAhVkwYMKHZBSD7oQ6AEILzAB#v=onepage&q=%22rectangle%20wave%22%20harmonics&f=false Handbook of Applications of Chaos Theory], {{unpaginated}}. CRC Press. {{ISBN|9781315356549}}.
5. ^"Electronic Music Interactive: 14. Square and Rectangle Waves", UOregon.edu.
6. ^Hartmann, William M. (2004). Signals, Sound, and Sensation, p.109. Springer Science & Business Media. {{ISBN|9781563962837}}.
7. ^¹²³⁴Souvignier, Todd (2003). Loops and Grooves, p.12. Hal Leonard. {{ISBN|9780634048135}}.
8. ^¹²Cann, Simon (2011). [https://books.google.com/books?id=QTBVDQAAQBAJ&pg=PT20&dq=pulse+wave+sawtooth+wave&hl=en&sa=X&ved=0ahUKEwiJws-y3vDaAhVG5oMKHcQtCFAQ6AEITDAG#v=onepage&q=pulse%20wave%20sawtooth%20wave&f=false How to Make a Noise], {{unpaginated}}. BookBaby. {{ISBN|9780955495540}}.
9. ^¹Aikin, Jim (2004). Power Tools for Synthesizer Programming, p.55-56. Hal Leonard. {{ISBN|9781617745089}}.
10. ^¹²³⁴Hurtig, Brent (1988). Synthesizer Basics, p.23. Hal Leonard. {{ISBN|9780881887143}}.
11. ^¹²Holmes, Thom (2015). Electronic and Experimental Music, p.230. Routledge. {{ISBN|9781317410232}}.
12. ^¹²{{cite web|url=http://www.keyboardmag.com/lessons/1251/synth-soloing-in-the-style-of-steve-winwood/50240|title=Synth Soloing in the Style of Steve Winwood |last=Kovarsky|first=Jerry|date=Jan 15, 2015|website=KeyboardMag.com|publisher=|access-date=May 4, 2018}}