Audio Domains: Time and Frequency
Audio data can be represented in one of two domains: the time domain and the frequency domain. Editing audio in a stereo audio editor (like Audacity) or DAW (like Pro Tools) typically takes place in the time domain. When you look at a standard representation of an audio signal in an editor you are looking at amplitude values at various times. A waveform display is actually an x-y (Cartesian) graph. Amplitude is represented on the y-axis, and time is represented on the x-axis, but without any negative values for x because audio always moves forward in time as a physical thing.
You can also describe the spectrum of a sound at any given moment. The spectrum view shows the amplitudes of frequencies present in a sound. This view is also an x-y graph, with amplitude values again being represented in the y-axis, but in this case frequency values are represented on the x-axis. While it is possible to have negative frequencies and negative amplitudes, simple spectrum views will only show positive y and x values.
To understand the concept of domains, you must understand that the domain is the parameter represented on the x axis. The standard waveform view has time represented on the x-axis, and therefore is a time-domain representation of sound. The spectrum view has frequency represented on the x-axis, and therefore is a frequency-domain representation of sound.
In a time-domain representation, frequency information is omitted from the graphed parameters. We may be able to deduce frequency information from the graph by counting zero amplitude crossings, but the parameter itself is not part of the graph parameters. With frequency-domain representation you do not have any information about time.
Converting Domains – The Fourier Transform
To convert from a time domain representation of sound to a frequency domain representation, you use a process called the Fourier Transform. To reverse the process and convert from the frequency domain to the time domain you use an Inverse Fourier Transform.