Information about Frequency Spectrum
Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth.
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. 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. 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.
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.
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.
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An overtone is a natural resonance or vibration frequency of a system.
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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.
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.
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.
Spectrum analysis
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Example of voice waveform and its frequency spectrum
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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
).
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. 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.
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.
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.
Physical acoustics of music
Sound spectrum is one of the determinants of the timbre or quality of a sound or note. 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. an A).See also
FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. A sequel, titled Amplitude was released in 2003.
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White noise is a random signal (or process) with a flat power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth.
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Fourier transform, named in honor of French mathematician Joseph Fourier, is a certain linear operator that maps functions to other functions. Loosely speaking, the Fourier transform decomposes a function into a continuous spectrum of its frequency components
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In statistical signal processing and physics, the spectral density, power spectral density, or energy spectral density is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has
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- See also: Time domain
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Stochastic, from the Greek "stochos" or "aim, guess", means of, relating to, or characterized by conjecture and randomness. A stochastic process is one whose behavior is non-deterministic in that a state does not fully determine its next state.
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NOiSE is a one volume manga created by Tsutomu Nihei as a prequel to his acclaimed ten-volume work, Blame!.
It offers some rather sketchy information concerning the Megastructure's origins and initial size, as well as the origins of Silicon life.
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It offers some rather sketchy information concerning the Megastructure's origins and initial size, as well as the origins of Silicon life.
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In statistics, a frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears.
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discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite-domain discrete-time signals. As with most Fourier analyses, it expresses an input function in terms of a sum of sinusoidal components by determining
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White noise is a random signal (or process) with a flat power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth.
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In music, timbre, or sometimes timber, (from Fr. timbre; IPA /'tæmbəɹ/ as in the first two syllables of tambourine, or /'tɪmbəɹ/, like timber)[1]
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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note has two primary meanings: 1) a sign used in music to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis
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harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.
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Partial may refer to:
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- bias
- overtone
- partial function
- partial algorithm
- Partial derivative
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- "Overtones" redirects here. For the album by Just Jack, see Overtones (album).
An overtone is a natural resonance or vibration frequency of a system.
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electromagnetic (EM) spectrum is the range of all possible electromagnetic radiation. The "electromagnetic spectrum" (usually just spectrum) of an object is the frequency range of electromagnetic radiation with wavelengths from thousands of kilometers down to fractions of
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Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music — how sounds employed as music work.
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Frequency estimation is the process of estimating the complex frequency components of a signal in the presence of noise[1]. The most common methods involve identifying the noise subspace to extract these components.
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