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Bandwidth Expansion
Bandwidth expansion is a technique for widening the bandwidth or the resonances in an LPC filter. This is done by moving all the poles towards the origin by a constant factor \gamma. The bandwidth-expanded filter A'(z) can be easily derived from the original filter A(z) by: :A'(z) = A(z/\gamma) Let A(z) be expressed as: :A(z) = \sum_^a_kz^ The bandwidth-expanded filter can be expressed as: :A'(z) = \sum_^a_k\gamma^kz^{-k} In other words, each coefficient a_k in the original filter is simply multiplied by \gamma^k in the bandwidth-expanded filter. The simplicity of this transformation makes it attractive, especially in CELP coding of speech, where it is often used for the perceptual noise weighting The process of weighting involves emphasizing the contribution of particular aspects of a phenomenon (or of a set of data) over others to an outcome or result; thereby highlighting those aspects in comparison to others in the analysis. That i ... and/or to stabilize the LPC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandwidth (signal Processing)
Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to '' passband bandwidth'' or ''baseband bandwidth''. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel. A key characteristic of bandwidth is that any band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum. For exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonances
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, orbital resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Predictive Coding
Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model. LPC is the most widely used method in speech coding and speech synthesis. It is a powerful speech analysis technique, and a useful method for encoding good quality speech at a low bit rate. Overview LPC starts with the assumption that a speech signal is produced by a buzzer at the end of a tube (for voiced sounds), with occasional added hissing and popping sounds (for voiceless sounds such as sibilants and plosives). Although apparently crude, this Source–filter model is actually a close approximation of the reality of speech production. The glottis (the space between the vocal folds) produces the buzz, which is characterized by its intensity (loudness) and frequency (pitch). The vocal tract (the throat and mouth) forms the tub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pole (complex Analysis)
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. In some sense, it is the simplest type of singularity. Technically, a point is a pole of a function if it is a zero of the function and is holomorphic in some neighbourhood of (that is, complex differentiable in a neighbourhood of ). A function is meromorphic in an open set if for every point of there is a neighborhood of in which either or is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicities of its poles equals the sum of the multiplicities of its zeros. Definitions A function of a complex variable is holomorphic in an open ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Filter
In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized digital signal processor (DSP) with specific paralleled architecture for expediting operations such as filter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Prediction
Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis, a subfield of mathematics, linear prediction can be viewed as a part of mathematical modelling or optimization. The prediction model The most common representation is :\widehat(n) = \sum_^p a_i x(n-i)\, where \widehat(n) is the predicted signal value, x(n-i) the previous observed values, with p \leq n , and a_i the predictor coefficients. The error generated by this estimate is :e(n) = x(n) - \widehat(n)\, where x(n) is the true signal value. These equations are valid for all types of (one-dimensional) linear prediction. The differences are found in the way the predictor coefficients a_i are chosen. For multi-dimensional signals the error metric is often defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CELP
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in 1985. At the time, it provided significantly better quality than existing low bit-rate algorithms, such as residual-excited linear prediction (RELP) and linear predictive coding (LPC) vocoders (e.g., FS-1015). Along with its variants, such as algebraic CELP, relaxed CELP, low-delay CELP and vector sum excited linear prediction, it is currently the most widely used speech coding algorithm. It is also used in MPEG-4 Audio speech coding. CELP is commonly used as a generic term for a class of algorithms and not for a particular codec. Background The CELP algorithm is based on four main ideas: * Using the source-filter model of speech production through linear prediction (LP) (see the textbook "speech coding algorithm"); * Using an adaptive and a fixed codebook as the input (excitation) of the LP model; * Performing a search in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighting Filter
A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes. Audio applications In each field of audio measurement, special units are used to indicate a weighted measurement as opposed to a basic physical measurement of energy level. For sound, the unit is the phon (1 kHz equivalent level). Sound Sound has three basic components, the wavelength, frequency, and speed. In sound measurement, we measure the loudness of the sound in decibels (dB). Decibels are logarithmic with 0 dB as the reference. There are also a range of frequencies that sounds can have. Frequency is the number of times a sine wave repeats itself in a second. Normal auditory systems can usually hear between 20 and 20,000 Hz. When we measure sound, the measurement instrument takes the incoming auditory signal and analyzes it for these different features. Weighting filters in these instruments then filter out certain fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lag Windowing
Lag windowing is a technique that consists of windowing the autocorrelation coefficients prior to estimating linear prediction coefficients (LPC). The windowing in the autocorrelation domain has the same effect as a convolution (smoothing) in the power spectral domain and helps in stabilizing the result of the Levinson-Durbin algorithm. The window function is typically a Gaussian function. External links PLP and RASTA (and MFCC, and inversion) in Matlab{{Webarchive, url=https://web.archive.org/web/20161122094213/http://labrosa.ee.columbia.edu/matlab/rastamat/ , date=2016-11-22 See also * Linear predictive coding * Bandwidth expansion Bandwidth expansion is a technique for widening the bandwidth or the resonances in an LPC filter. This is done by moving all the poles towards the origin by a constant factor \gamma. The bandwidth-expanded filter A'(z) can be easily derived from ... Autocorrelation Statistical signal processing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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