In order to convert analog signals such as images or sound to digital formats they must be sampled. A sample is simply a representation of a single point in space or time. The more individual points (samples) you have, the more accurately you can reproduce an image or sound. In fact, when samples are close enough together it's sometimes possible to make a digital copy with no perceptible difference between it and the analog original.
Video samples are perhaps the easiest way to understand how sampling works. Each Frame in a digital image (or video frame) is composed of a grid of dots called Pixels. Each pixel represents a particular point in both space and time. On a DVD there are up to 720 pixels across a single horizontal line, which create the illusion of a seamless picture. Likewise you could "draw" a line in time between pixels that occupy the same location in space. The sequence of samples in time then creates the illusion of motion.
Audio samples don't include a spatial component because those effects are created by using multiple signals (channels). Instead it's sampled purely in units of time. However, these samples come far more frequently than frames of video. While video typically requires each point (pixel) to be updated around 24, 25, or 30 times per second, even CD quality audio is sampled approximately 1,500 times as often at 44.1kHz (44,100 samples per second). Higher quality formats from DVD-Video to DVD-Audio and Blu-ray may be sampled at 48kHz, 96kHz, or even as high as 192kHz.
Nyquist-Shannon Sampling Theorem
The basic principles of sampling are based on the work of Claude Shannon, which was in turn based partially on the work of Harry Nyquist. In terms of consumer applications the most important part of their work to know is what's referred to as the Nyquist Frequency. The Nyquist Frequency is twice the frequency of the signal being sampled. In reality it's almost always preferable to Capture with the maximum number of samples possible. If necessary you can downsample later, but upsampling can never add samples without loss.
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