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Root-raised-cosine Filter
In signal processing, a root-raised-cosine filter (RRC), sometimes known as square-root-raised-cosine filter (SRRC), is frequently used as the transmit and receive filter in a digital communication system to perform matched filtering. This helps in minimizing intersymbol interference (ISI). The combined response of two such filters is that of the raised-cosine filter. It obtains its name from the fact that its frequency response, H_(f), is the square root of the frequency response of the raised-cosine filter, H_(f): :H_(f) = H_(f)\cdot H_(f) or: :, H_(f), = \sqrt Why it is required To have minimum ISI (Intersymbol interference), the overall response of transmit filter, channel response and receive filter has to satisfy Nyquist ISI criterion. The raised-cosine filter is the most popular filter response satisfying this criterion. Half of this filtering is done on the transmit side and half is done on the receive side. On the receive side, the channel response, if it can be acc ... [...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, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Communication
Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or point-to-multipoint communication channel. Examples of such channels are copper wires, optical fibers, wireless communication using radio spectrum, storage media and computer buses. The data are represented as an electromagnetic signal, such as an electrical voltage, radiowave, microwave, or infrared signal. Analog transmission is a method of conveying voice, data, image, signal or video information using a continuous signal which varies in amplitude, phase, or some other property in proportion to that of a variable. The messages are either represented by a sequence of pulses by means of a line code (''baseband transmission''), or by a limited set of continuously varying waveforms (''passband transmission''), using a digital modulation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matched Filter
In signal processing, a matched filter is obtained by correlating a known delayed signal, or ''template'', with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise. Matched filters are commonly used in radar, in which a known signal is sent out, and the reflected signal is examined for common elements of the out-going signal. Pulse compression is an example of matched filtering. It is so called because the impulse response is matched to input pulse signals. Two-dimensional matched filters are commonly used in image processing, e.g., to improve the SNR of X-ray observations. Matched filtering is a demodulation technique with LTI (linear time invariant) filters to maximize SNR. It was originally also known a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersymbol Interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making the communication less reliable. The spreading of the pulse beyond its allotted time interval causes it to interfere with neighboring pulses. ISI is usually caused by multipath propagation or the inherent linear or non-linear frequency response of a communication channel causing successive symbols to blur together. The presence of ISI in the system introduces errors in the decision device at the receiver output. Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI, and thereby deliver the digital data to its destination with the smallest error rate possible. Ways to alleviate intersymbol interference include adaptive equalization and error correcting codes. Causes Multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raised-cosine Filter
The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form (\beta = 1) is a cosine function, 'raised' up to sit above the f (horizontal) axis. Mathematical description The raised-cosine filter is an implementation of a low-pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry about \frac, where T is the symbol-period of the communications system. Its frequency-domain description is a piecewise-defined function, given by: :H(f) = \begin 1, & , f, \leq \frac \\ \frac\left _-_\frac\rightright)\right _______&_\frac_f.html" ;"title="html" ;"title=" + \cos\left(\frac\left f">_-_\frac\rightright)\right _______&_\frac_f.html" ;"title=">f"> - \frac\rightright)\right & \frac f"> \leq \frac \\ 0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersymbol Interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making the communication less reliable. The spreading of the pulse beyond its allotted time interval causes it to interfere with neighboring pulses. ISI is usually caused by multipath propagation or the inherent linear or non-linear frequency response of a communication channel causing successive symbols to blur together. The presence of ISI in the system introduces errors in the decision device at the receiver output. Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI, and thereby deliver the digital data to its destination with the smallest error rate possible. Ways to alleviate intersymbol interference include adaptive equalization and error correcting codes. Causes Multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist ISI Criterion
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference. When consecutive symbols are transmitted over a channel by a linear modulation (such as Amplitude-shift keying, ASK, Quadrature amplitude modulation, QAM, etc.), the impulse response (or equivalently the frequency response) of the channel causes a transmitted symbol to be spread in the time domain. This causes intersymbol interference because the previously transmitted symbols affect the currently received symbol, thus reducing tolerance for noise. The Nyquist theorem relates this time-domain condition to an equivalent frequency-domain condition. The Nyquist criterion is closely related to the Nyquist–Shannon sampling theorem, with only a differing poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roll-off
Roll-off is the steepness of a Transfer function, transfer function with frequency, particularly in network analysis (electrical circuits), electrical network analysis, and most especially in connection with filter (signal processing), filter circuits in the transition between a passband and a stopband. It is most typically applied to the insertion loss of the network, but can, in principle, be applied to any relevant function of frequency, and any technology, not just electronics. It is usual to measure roll-off as a function of logarithmic scale, logarithmic frequency; consequently, the units of roll-off are either decibels per decade (log scale), decade (dB/decade), where a decade is a tenfold increase in frequency, or decibels per octave (electronics), octave (dB/8ve), where an octave is a twofold increase in frequency. The concept of roll-off stems from the fact that in many networks roll-off tends towards a constant gradient at frequencies well away from the cut-off freque ... [...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 Dirac delta function, 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 (mathematics), 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 Dirac delta function#Fourier transform, the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function has), the impulse response defines the response ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Filters
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components (resistors, capacitors, inductors, and linear amplifiers) will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies (their frequency response), they are so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
