# .wav Audio Files

## Introduction

WAVE is short for Waveform Audio File Format. WAVE files typically have a .wav extension, so they are commonly referred to as WAV or .wav files. .wav files are a common format for storing audio data, though other types of data are sometimes saved in this format. WAVE files are uncompressed —this results in relatively high quality audio signals, but at the expense of larger file sizes than would result from compressing the data.

The data in .wav files is saved as a series of samples. That is, the original waveform is sampled so that the waveform is represented by a series of points. The basic idea is illustrated in Fig. 1 below. The original waveform in Fig. 1 is represented by the blue line. The sampled points are represented by black dots. We will assume that the points are evenly spaced in time and that they are separated by a time Δt1. The sampled data is shown in Fig. 2(a)—note that we now have no information about the shape of the function between the sampled points. After we have sampled the data, it is common to retain only the data points f1, f2 , f3 ... and the time spacing between the points. It is also common to assume that the value of the function is constant between the sampled points. Figure 2(b) shows the result of these simplifications.

These .wav files can be considered to provide a list of numbers, such as the data points f1, f2, f3 ... shown in Fig. 2, along with some additional information which provides, among other things, the sampling frequency at which the data were recorded. The sampling frequency provides the sampling period of the data (the sampling period is the time spacing between points—Δt in Figs. 1 and 2). The sampling frequency is generally represented in units of Hertz, or Hz. Although the units are the same as those used to represent the frequency of sinusoidal signals, these are not the same thing. The sampling frequency represents the number of samples per second (rather than cycles per second, as in sinusoidal frequencies) so the units of Hertz are somewhat misleading. The sampling frequency is simply the inverse of the sampling period, so that:

${f_s} = \frac{1}{{\Delta t}}$

1Engineers often use the symbol “Δ” to indicate a change in some parameter. Thus, Δt indicates a change in time. In this case, Δt is a time change between samples.

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