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Linear Phase
In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay. Consequently, there is no phase distortion due to the time delay of frequencies relative to one another. For discrete-time signals, perfect linear phase is easily achieved with a finite impulse response (FIR) filter by having coefficients which are symmetric or anti-symmetric. Approximations can be achieved with infinite impulse response (IIR) designs, which are more computationally efficient. Several techniques are: * a Bessel transfer function which has a maximally flat group delay approximation function * a phase equalizer Definition A filter is called a linear phase filter if the phase component of the frequency response is a linear f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to 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 publis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impulse Response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system). In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects. Since the impulse function contains all frequencies (see the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function has), the impulse response defines the response of a linear time-invariant system for all frequencies. Mathematical considerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Plots
Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematical space in which each possible state of a physical system is represented by a point also referred to as a "microscopic state" ** Phase space formulation, a formulation of quantum mechanics in phase space *Phase (waves), the position of a point in time (an instant) on a waveform cycle **Instantaneous phase, generalization for both cyclic and non-cyclic phenomena *AC phase, the phase offset between alternating current electric power in multiple conducting wires **Single-phase electric power, distribution of AC electric power in a system where the voltages of the supply vary in unison **Three-phase electric power, a common method of AC electric power generation, transmission, and distribution *Phase problem, the loss of information (the phase) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalized Frequency (digital Signal Processing)
In digital signal processing (DSP), a normalized frequency is a ratio of a variable frequency (f) and a constant frequency associated with a system (such as a '' sampling rate'', f_s). Some software applications require normalized inputs and produce normalized outputs, which can be re-scaled to physical units when necessary. Mathematical derivations are usually done in normalized units, relevant to a wide range of applications. Examples of normalization A typical choice of characteristic frequency is the '' sampling rate'' (f_s) that is used to create the digital signal from a continuous one. The normalized quantity, f' = \tfrac, has the unit ''cycle per sample'' regardless of whether the original signal is a function of time or distance. For example, when f is expressed in Hz (''cycles per second''), f_s is expressed in ''samples per second''. Some programs (such as MATLAB toolboxes) that design filters with real-valued coefficients prefer the Nyquist frequency (f_s/2) as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist Frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a Sampling (signal processing), sampler, which converts a continuous function or signal into a discrete sequence. For a given Sampling (signal processing), sampling rate (''samples per second''), the Nyquist frequency ''(cycles per second'') is the frequency whose cycle-length (or period) is twice the interval between samples, thus ''0.5 cycle/sample''. For example, audio compact disc, CDs have a sampling rate of 44100 ''samples/second''. At ''0.5 cycle/sample'', the corresponding Nyquist frequency is 22050 ''cycles/second'' (hertz, Hz). Conversely, the Nyquist rate for sampling a 22050 Hz signal is 44100 ''samples/second''. When the highest frequency (Bandwidth (signal processing), bandwidth) of a signal is less than the Nyquist frequency of the sampler, the resulting discrete-time sequence is said to be free of the distortion known as aliasing, and the corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Value
In mathematics, specifically complex analysis, the principal values of a multivalued function are the values along one chosen branch (mathematical analysis), branch of that Function (mathematics), function, so that it is Single-valued function, single-valued. A simple case arises in taking the square root of a positive real number. For example, 4 has two square roots: 2 and −2; of these the positive root, 2, is considered the principal root and is denoted as \sqrt. Motivation Consider the complex logarithm function . It is defined as the complex number such that :e^w = z. Now, for example, say we wish to find . This means we want to solve :e^w = i for w. The value i\pi/2 is a solution. However, there are other solutions, which is evidenced by considering the position of in the complex plane and in particular its argument (complex analysis), argument \arg i. We can rotate counterclockwise \pi/2 radians from 1 to reach initially, but if we rotate further another 2\pi we rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bode Plots
In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments. Overview Among his several important contributions to circuit theory and control theory, engineer Hendrik Wade Bode, while working at Bell Labs in the 1930s, devised a simple but accurate method for graphing gain and phase-shift plots. These bear his name, ''Bode gain plot'' and ''Bode phase plot''. "Bode" is often pronounced in English as , whereas in Dutch it is usually , closer to English , which is preferred by his family, but less common among researchers.Van Valkenburg, M. E. University of Illinois at Urbana-Champaign, "In m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Passband
A passband is the range of frequency, frequencies or wavelengths that can pass through a Filter (signal processing), filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenna. The passband of a receiver is the range of frequencies it can receive when it is tuned into the desired frequency as in a radio station or television channel. A band-pass filter, bandpass-filtered signal (that is, a signal with energy only in a passband), is known as a bandpass signal, in contrast to a baseband signal. The bandpass filter usually has two stopband, band-stop filters. Filters In telecommunications, optics, and acoustics, a passband (a band-pass filtered signal) is the portion of the frequency spectrum that is transmitted (with minimum relative loss or maximum relative Gain (electronics), gain) by some filtering device. In other words, it is a ''band'' of frequencies which ''pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete-time Fourier Transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function. In simpler terms, when you take the DTFT of regularly-spaced samples of a continuous signal, you get repeating (and possibly overlapping) copies of the signal's frequency spectrum, spaced at intervals corresponding to the sampling frequency. Under certain theoretical conditions, described by the sampling theorem, the original continuous function can be recovered perfectly from the DTFT and thus from the original discrete samples. The DTFT itself is a continuous functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always Convergent series, converge. Well-behaved functions, for example Smoothness, smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete-time Fourier Transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function. In simpler terms, when you take the DTFT of regularly-spaced samples of a continuous signal, you get repeating (and possibly overlapping) copies of the signal's frequency spectrum, spaced at intervals corresponding to the sampling frequency. Under certain theoretical conditions, described by the sampling theorem, the original continuous function can be recovered perfectly from the DTFT and thus from the original discrete samples. The DTFT itself is a continuous functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
