Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. Frequency is a measure of the number of occurrences of a repeating event per unit Time.
A source of light can have many colors mixed together and in different amounts (intensities). A rainbow, or prism, sends the different frequencies in different directions, making them individually visible at different angles. A graph of the intensity plotted against the frequency (showing the amount of each color) is the frequency spectrum of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a flat line. Therefore, flat-line spectrums in general are often referred to as white, whether they represent light or something else.
Similarly, a source of sound can have many different frequencies mixed together. Each frequency stimulates a different length receptor in our ears. When only one length is predominantly stimulated, we hear a note. A steady hissing sound or a sudden crash stimulates all the receptors, so we say that it contains some amounts of all frequencies in our audible range. Things in our environment that we refer to as noise often comprise many different frequencies. Therefore, when the sound spectrum is flat, it is called white noise. White noise is a random signal (or process with a flat Power spectral density. This term carries over into other types of spectrums than sound.
Each broadcast radio and TV station transmits a wave on an assigned frequency (aka channel). A radio antenna adds them all together into a single function of amplitude (voltage) vs. time. The radio tuner picks out one channel at a time (like each of the receptors in our ears). Some channels are stronger than others. If we made a graph of the strength of each channel vs. the frequency of the tuner, it would be the frequency spectrum of the antenna signal.
Analysis means decomposing something complex into simpler, more basic parts. As we have seen, there is a physical basis for modeling light, sound, and radio waves as being made up of various amounts of all different frequencies. Any process that quantifies the various amounts vs. frequency can be called spectrum analysis. It can be done on many short segments of time, or less often on longer segments, or just once for a deterministic function (such as ).
The Fourier transform of a function produces a spectrum from which the original function can be reconstructed (aka synthesized) by an inverse transform, making it reversible. This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and In order to do that, it preserves not only the magnitude of each frequency component, but also its phase. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 This information can be represented as a 2-dimensional vector or a complex number, or as magnitude and phase (polar coordinates). In graphical representations, often only the magnitude (or squared magnitude) component is shown. This is also referred to as a power spectrum. In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density (
Because of reversibility, the Fourier transform is called a representation of the function, in terms of frequency instead of time, thus, it is a frequency domain representation. Frequency domain is a term used to describe the analysis of Mathematical functions or signals with respect to frequency Linear operations that could be performed in the time domain have counterparts that can often be performed more easily in the frequency domain. It is also helpful just for understanding and interpreting the effects of various time-domain operations, both linear and non-linear. For instance, only non-linear operations can create new frequencies in the spectrum.
The Fourier transform of a random (aka stochastic) waveform (aka noise) is also random. Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random. is a one volume manga created by Tsutomu Nihei as a prequel to his ten-volume work Blame!. Some kind of averaging is required in order to create a clear picture of the underlying frequency content (aka frequency distribution). In Statistics, a frequency distribution is a list of the values that a variable takes in a sample. Typically, the data is divided into time-segments of a chosen duration, and transforms are performed on each one. Then the magnitude or (usually) squared-magnitude components of the transforms are summed into an average transform. This is a very common operation performed on digitized (aka sampled) time-data, using the discrete Fourier transform (see Welch method). In Mathematics, the discrete Fourier transform (DFT is one of the specific forms of Fourier analysis. In Physics, Engineering, and applied Mathematics, Welch's method, named after P When the result is flat, as we have said, it is commonly referred to as white noise. White noise is a random signal (or process with a flat Power spectral density.
Sound spectrum is one of the determinants of the timbre or quality of a sound or note. Musical acoustics or music acoustics is the branch of Acoustics concerned with researching and describing the Physics of Music — how sounds In Music, timbre (ˈtæm-bər' like timber, or, from Fr timbre tɛ̃bʁ is the quality of a Musical note or sound that distinguishes different Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies In Music, the term note has two primary meanings 1 a sign used in Musical notation to represent the relative duration and pitch of a Sound; It is the relative strength of pitches called harmonics and partials (collectively overtones) at various frequencies usually above the fundamental frequency, which is the actual note named (eg. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer An overtone is a natural resonance or vibration frequency of a system an A).