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Encyclopedia > Frequency spectrum

Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

Electromagnetic emission spectrum of Iron in the visible region.

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. Iron emission spectrum This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Iron emission spectrum This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... General Name, Symbol, Number iron, Fe, 26 Chemical series transition metals Group, Period, Block 8, 4, d Appearance lustrous metallic with a grayish tinge Atomic mass 55. ...

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. This term carries over into other types of spectrums than sound. For other uses of the term white noise, see white noise (disambiguation). ...

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.

The rotation of the earth has only one frequency and never changes. So the concept of "spectrum" is not particularly useful in that case.

Example of voice waveform and its frequency spectrum
A triangle wave pictured in the time domain (top) and frequency domain (bottom). The fundamental frequency component is at 220 Hz (A2).

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 $begin{matrix} frac{sin (t) }{t} end{matrix},$). Image File history File links Download high resolution version (1046x418, 8 KB) Summary I created this image myself using Matlab tools. ... Image File history File links Download high resolution version (1046x418, 8 KB) Summary I created this image myself using Matlab tools. ... bandlimited triangle wave pictured in time and frequency domains File links The following pages link to this file: Triangle wave Categories: GFDL images ... bandlimited triangle wave pictured in time and frequency domains File links The following pages link to this file: Triangle wave Categories: GFDL images ... A triangle wave is a waveform named for its triangular shape. ...

The Fourier transform of a function produces a spectrum from which the original function can be reconstructed (aka synthesized) by an inverse transform. So it is reversible. In order to do that, it preserves not only the magnitude of each frequency component, but also its phase. 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. The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i. ... Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ... The power spectrum is a plot of the portion of a signals power (energy per unit time) falling within given frequency bins. ...

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. 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. Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ...

The Fourier transform of a random (aka stochastic) waveform (aka noise) is also random. Some kind of averaging is required in order to create a clear picture of the underlying frequency content (aka frequency distribution). 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). When the result is flat, as we have said, it is commonly referred to as white noise. This is a Root page. ... In mathematics, the discrete Fourier transform (DFT), sometimes called the finite Fourier transform, is a Fourier transform widely employed in signal processing and related fields to analyze the frequencies contained in a sampled signal, solve partial differential equations, and to perform other operations such as convolutions. ... In 1967 P.D. Welch wrote a paper titled The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms that appeared in IEEE Trans. ... For other uses of the term white noise, see white noise (disambiguation). ...

Results from FactBites:

 Howstuffworks "How the Radio Spectrum Works" (680 words) In the same way, AM radio is confined to a band from 535 kilohertz to 1,700 kilohertz (kilo meaning "thousands," so 535,000 to 1,700,000 cycles per second). The first radio broadcasts occurred in 1906 or so, and frequency allocation for AM radio occurred during the 1920s (The predecessor to the FCC was established by Congress in 1927.). Television stations were pretty much non-existent until 1946 or so, which is when the FCC allocated commercial broadcast bands for TV.
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