What is a Frequency Domain?
The Frequency Domain refers to the analytic space in which mathematical functions or signals are conveyed in terms of frequency, rather than time. For example, where a time-domain graph may display changes over time, a frequency-domain graph displays how much of the signal is present among each given frequency band. It is possible, however, to convert the information from a time-domain to a frequency-domain. An example of such transformation is a Fourier transform. The Fourier transform converts the time function into a set of sine waves that represent different frequencies. The frequency-domain representation of a signal is known as the "spectrum" of frequency components.
How does the Frequency Domain work?
The Frequency domain works by allowing a representation of the qualitative behavior of a system, as well as characteristics of the way the system response to changes in bandwidth, gain, phase shift, harmonics, etc. A discipline in which the frequency domain is used for graphical representation is in music. Often audio producers and engineers display an audio signal within a frequency domain in order to better understand the shape and character of an audio signal.
Applications of Frequency Domain
For example, auditory sounds exist between a range of 20-20,000Hz, and some frequencies are harder for the human ear to withstand. The frequency 3,400Hz is a harsh frequency (the sound of babies crying), and the human ear is specifically tuned to respond viscerally to that sound. An audio engineer may reduce the strength of that frequency in the frequency domain using an audio equalizer. By displaying the audio signal in the frequency domain, an engineer can boost and reduce signals to make the sounds more pleasant for the human ear. The Fletcher-Munson curve is a widely used function that lays atop the frequency domain that audio engineers often reference when mixing various frequencies. The function's curve selectively boosts and reduces frequencies to allow the audio engineer to raise the gain of the signal while mitigating the unpleasant sounds.