Introduction to Sampling

Inside computers and modern ``digital'' synthesizers, (as well as music CDs), sound is sampled into a stream of numbers. Each sample can be thought of as a number which specifies the position^D.2of a loudspeaker at a particular instant. When sound is sampled, we call it digital audio. The sampling rate used for CDs nowadays is 44,100 samples per second. That means when you play a CD, the speakers in your stereo system are moved to a new position 44,100 times per second, or once every 23 microseconds. Controlling a speaker this fast enables it to generate any sound in the human hearing range because we cannot hear frequencies higher than around 20,000 cycles per second, and a sampling rate more than twice the highest frequency in the sound guarantees that exact reconstruction is possible from the samples.

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Subsections

• Reconstruction from Samples--Pictorial Version
• The Sinc Function
• Reconstruction from Samples--The Math

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Order a Hardcopy of Mathematics of the DFT

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Next: Reconstruction from Samples--Pictorial Version

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.