# Digitized Sound

Nearly everything mentioned in the previous tutorials about sound and waveforms applies to digitized sounds or digital waveforms as well. However, because digital waveforms are sampled approximations to continuous functions of time, there are some important differences to be aware of and there is some new terminology to learn. First, digital waveforms are described in terms of their sampling rate in Hertz and sample resolution in bits per sample. The term Hertz, abbreviated Hz, normally means cycles per second when describing waveforms, but it is generalized to samples per second when describing a sampling rate. Each sample in a digital waveform is a measurement of the amplitude of an analog waveform at an instant in time. The sampling rate specifies how many measurements of the analog signal amplitude are made per second by the Analog to Digital Converter (ADC) hardware of the computer. Similarly, when digital waveforms are converted to analog signals (using a Digital to Analog Converter or DAC), sampling rate refers to how many times per second the (DAC) hardware must be updated with a new sample value.

Sample resolution specifies the accuracy of each amplitude measurement made by the ADC hardware. The more bits of resolution, the greater the accuracy. A bit is defined as one binary digit, that is, either the value 0 or the value 1. Thus, when only one bit is used to represent the value of an amplitude measurement, the amplitude must be either 0 or 1. If two bits are used to represent amplitude values, then four possible amplitude values can be represented (0, 1, 2, and 3). More generally, the number of amplitude values that can be reresented by a given number of bits is 2**N where N is the number of bits. Using a large number of bits per sample allows the full amplitude range of an ADC to be partitioned into a large number of very small steps.

In the following figure, the X axis is time in msec and the Y axis is amplitude in arbitrary units. This figure shows an analog sine wave (solid line) is sampled (illustrated by the circle symbols) at a comparatively high rate compared to its frequency and with good sample resolution. 