# Frequency Spectrum

The frequency spectrum is characterized by the distribution of amplitudes for each frequency of a wave phenomenon (sound, light or electromagnetic) that is a superposition of waves of various frequencies. The graph of intensity versus frequency of a particular wave is also called the frequency spectrum.

The spectrum of frequencies or spectral decomposition of frequencies can be applied to any concept associated with frequency or wave movements such as colors, musical notes, radio or TV electromagnetic waves and even the regular rotation of the earth.

Summary

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• 1 Light, sound and electromagnetic spectrum
• 2 Spectral analysis
• 4Fuente

Light, sound and electromagnetic spectrum

light source can have many colors mixed together in different amounts (intensities). A rainbow , or transparent prism, deflects each photon based on its frequency at a slightly different angle. That allows us to see each component of the initial light separately. A graph of the intensity of each color deflated by a prism showing the amount of each color is the frequency spectrum of light or light spectrum . When all visible frequencies are equally present, the effect is the “color” white, and the frequency spectrum is uniform, represented by a flat line. In fact, any frequency spectrum that consists of a flat line is called white .hence we speak not only of “white color” but also of “white noise”.

The dark fringes represent the frequencies for which the amplitude of the sound wave is greatest. Similarly, a source of sound waves can be a superposition of different frequencies. Each frequency stimulates a different part of our cochlea (cochlea of ​​the ear).

When we listen to a sound wave with a single predominant frequency, we hear a note. But on the other hand, any whistle or sudden blow that stimulates all the receptors, we will say that it contains frequencies within the entire audible range. Many things in our environment that we qualify as noise frequently contain frequencies from the entire audible range. Thus when a frequency spectrum of a sound, or sound spectrum.

When this spectrum is given by a flat line, we say that the associated sound is white noise. Another example of sound wave frequency spectrum is found in the analysis of the human voice, for example each vowel can be characterized by the sum of sound waves whose frequencies fall on frequency bands, called formant, the human ear is able to distinguish some vowels from others thanks to the fact that it can discriminate said formants, that is, to know part of the spectrum of frequencies present in a sound wave that produces the articulation of said vowel.

Each radio or TV broadcasting station is a source of electromagnetic waves that emits waves close to a given frequency. In general, the frequencies will be concentrated in a band around the nominal frequency of the station, this band is what we call channel. A radio receiving antenna condenses different electromagnetic waves into a single voltage amplitude signal, which can be decoded back into a sound amplitude signal, which is the sound we hear when we turn on the radio. The radio tuner selects the channel, similar to how our receivers in the cochlea select a certain note. Some channels are weak and some are strong. If we make a graph of the intensity of the channel with respect to its frequency, we obtain the electromagnetic spectrum of the receiving signal.

Spectral analysis

Analysis refers to the action of breaking down something complex into simple parts or identifying the simpler parts of that complex thing. As has been seen, there is a physical basis for modeling light, sound or radio waves in superposition of different frequencies. A process that quantifies the various intensities of each frequency is called spectral analysis .

Mathematically, spectral analysis is related to a tool called Fourier transform or Fourier analysis. Given a signal or wave phenomenon of amplitude That is, the signal can be conceived as the Fourier transform of the amplitude. This analysis can be carried out for small time intervals, or less frequently for long intervals, or even the spectral analysis of a deterministic function can be carried out.

In addition, the Fourier transform of a function not only allows a spectral decomposition of the formants of a wave or oscillatory signal, but with the spectrum generated by the Fourier analysis it can even be reconstructed ( synthesize) the original function using the inverse transform. In order to do this, the transform not only contains information about the intensity of a certain frequency, but also about its phase.

This information can be represented as a two-dimensional vector or as a complex number. In graphical representations, often only the modulus squared of that number is represented, and the resulting graph is known as a power spectrum or power spectral density.(SP): It is important to remember that the Fourier transform of a random wave, better said stochastic, is also random. An example of this type of wave is environmental noise.

Therefore, to represent a wave of this type, a certain type of averaging is required to adequately represent the frequency distribution. For such digitized stochastic signals, the discrete Fourier transform is often used. When the result of this spectral analysis is a flat line, the signal that generated the spectrum is called white noise.

##### byAbdullah Sam
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