Frequency Domain and Time Domain Analysis

In our journey through the exploration of sound, we've primarily focused on frequency domain analysis — an approach that considers sounds in terms of their component frequencies. This method has provided valuable insights into the nature of tonal and non-tonal sounds alike. However, as we delve further into the intricacies of audio and sound production, particularly mixing, another perspective becomes equally essential — time domain analysis.

Time domain analysis takes a different approach to understanding sound. Instead of dissecting a sound into its component sine waves (or frequencies), time domain analysis examines the disturbance patterns a sound creates as it travels through a medium — be it air molecules, the human eardrum, a speaker cone, or the electrical signal of an audio cable. This view offers a direct perspective on the energy of the sound at any given moment, a parameter we refer to as its amplitude.

The character of a sound is determined by the continuously changing patterns of its amplitude, otherwise known as its waveform. A waveform is a visual representation of the fluctuations in energy or pressure levels that a sound induces in its medium of propagation over time.

Interestingly, when two or more sounds are combined — as they often are when being played simultaneously through a shared medium — their waveforms or time-domain disturbances amalgamate. This combination occurs in a straightforward manner: the instantaneous amplitude of the resulting sound at any given time is a mathematical summation of the instantaneous amplitudes of each individual sound. This principle underpins the final stage of mixing in audio production, aptly named "summing." Summing essentially blends the separate mixer tracks into one comprehensive "master" track, akin to the way different ingredients are mixed to create a single, delicious dish.

Understanding both frequency and time domain analysis is fundamental to fully grasping the nature of sound. Just as one might appreciate a painting both for its individual colors and for the overall image it forms, sound can be interpreted as a collection of sine waves (frequency domain) or as a pattern of disturbance in a medium (time domain). These dual perspectives complement each other, each providing unique insights beneficial for various applications — from sound synthesis to mixing, mastering, and beyond.