High Frequency Content Measure
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High Frequency Content Measure
In signal processing, the high frequency content measure is a simple measure, taken across a signal spectrum (usually a STFT spectrum), that can be used to characterize the amount of high-frequency content in the signal. The magnitudes of the spectral bins are added together, but multiplying each magnitude by the bin "position" (proportional to the frequency). Thus if ''X''(''k'') is a discrete spectrum with ''N'' unique points, its high frequency content measure is: : \mathrm = \sum_^ i, X(i), In contrast to perceptual measures, this is not based on any evidence about its relevance to human hearing. Despite that, it can be useful for some applications, such as onset detection. The measure has close similarities to the spectral centroid The spectral centroid is a measure used in digital signal processing to characterise a spectrum. It indicates where the center of mass of the spectrum is located. Perceptually, it has a robust connection with the impression of brightness of ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ...
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Spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum. Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the " spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of condition ...
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STFT
The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a ...
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Human Hearing
Hearing, or auditory perception, is the ability to perceive sounds through an organ, such as an ear, by detecting vibrations as periodic changes in the pressure of a surrounding medium. The academic field concerned with hearing is auditory science. Sound may be heard through solid, liquid, or gaseous matter. It is one of the traditional five senses. Partial or total inability to hear is called hearing loss. In humans and other vertebrates, hearing is performed primarily by the auditory system: mechanical waves, known as vibrations, are detected by the ear and transduced into nerve impulses that are perceived by the brain (primarily in the temporal lobe). Like touch, audition requires sensitivity to the movement of molecules in the world outside the organism. Both hearing and touch are types of mechanosensation. Hearing mechanism There are three main components of the human auditory system: the outer ear, the middle ear, and the inner ear. Outer ear The outer ear inclu ...
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Onset Detection
Onset refers to the beginning of a musical note or other sound. It is related to (but different from) the concept of a transient: all musical notes have an onset, but do not necessarily include an initial transient. Onset detection In signal processing, onset detection is an active research area. For example, the MIREX annual competition features aAudio Onset Detection contest Approaches to onset detection can operate in the time domain, frequency domain, phase domain, or complex domain, and include looking for: * Increases in spectral energy * Changes in spectral energy distribution (spectral flux) or phase * Changes in detected pitch - e.g. using a polyphonic pitch detection algorithm * Spectral patterns recognisable by machine learning techniques such as neural networks. Simpler techniques such as detecting increases in time-domain amplitude can typically lead to an unsatisfactorily high amount of false positives or false negatives. The aim is often to judge onsets simil ...
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Spectral Centroid
The spectral centroid is a measure used in digital signal processing to characterise a spectrum. It indicates where the center of mass of the spectrum is located. Perceptually, it has a robust connection with the impression of brightness of a sound. It is sometimes called center of spectral mass. Calculation It is calculated as the weighted mean of the frequencies present in the signal, determined using a Fourier transform, with their magnitudes as the weights: : \mathrm = \frac where ''x(n)'' represents the weighted frequency value, or magnitude, of bin number ''n'', and ''f(n)'' represents the center frequency of that bin. Alternative usage Some people use "spectral centroid" to refer to the median of the spectrum. This is a ''different'' statistic, the difference being essentially the same as the difference between the unweighted median and mean statistics. Since both are measures of central tendency, in some situations they will exhibit some similarity of behaviour. ...
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