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Encyclopedia > Digital filter
An FIR filter

In electronics,nirali a digital filter is any electronic filter that works by performing digital mathematical operations on an intermediate form of a signal. This is in contrast to older analog filters which work entirely in the analog realm and must rely on physical networks of electronic components (such as resistors, capacitors, transistors, etc.) to achieve the desired filtering effect. A Finite Impulse Response EQ, by iluvcapra File links The following pages link to this file: Digital filter Electronic filter Categories: GFDL images ... A Finite Impulse Response EQ, by iluvcapra File links The following pages link to this file: Digital filter Electronic filter Categories: GFDL images ... A finite impulse response (FIR) filter is a type of a digital filter. ... The field of electronics comprises the study and use of systems that operate by controlling the flow of electrons (or other charge carriers) in devices such as thermionic valves (vacuum tubes) and semiconductors. ... Television signal splitter consisting of a hi-pass and a low-pass filter. ... An analog filter handles analog stimuli (e. ...

Digital filters can achieve virtually any filtering effect that can be expressed as a mathematical function or algorithm. The two primary limitations of digital filters are their speed (the filter can't operate any faster than the computer at the heart of the filter), and their cost. However as the cost of integrated circuits has continued to drop over time, digital filters have become increasingly commonplace and are now an essential element of many everyday objects such as radios, cellphones, and stereo receivers. In mathematics, computing, linguistics, and related disciplines, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. ... Integrated circuit showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window showing the integrated circuit inside. ... Cellular redirects here. ... Label for 2. ...

## Contents

Digital filters can easily realize performance characteristics far beyond what are implementable with analog filters. It is not particularly difficult, for example, to create a 1000 Hz low-pass filter which can achieve near-perfect transmission of a 999 Hz input while entirely blocking a 1001 Hz signal. Analog filters cannot discriminate between such closely spaced signals. A low-pass filter is a filter that passes low frequencies well, but attenuates (or reduces) frequencies higher than the cutoff frequency. ...

Also, for complex multi-stage filtering operations, digital filters have the potential to attain much better signal to noise ratios than analog filters. This is because whereas at each intermediate stage the analog filter adds more noise to the signal, the digital filter performs noiseless mathematical operations at each intermediate step in the transform. The primary source of noise in a digital filter is to be found in the initial ADC - analog to digital conversion step, where in addition to any circuit noise introduced, the signal is subject to an unavoidable quantization error which is due to the finite resolution of the digital representation of the signal. The phrase signal-to-noise ratio, often abbreviated SNR or S/N, is an engineering term for the ratio between the magnitude of a signal (meaningful information) and the magnitude of background noise. ... This article or section should include material from AD converters In electronics, an analog-to-digital converter (abbreviated ADC, A/D, or A to D) is a device that converts continuous signals to discrete digital numbers. ... It has been suggested that this article or section be merged with quantization noise. ...

Note also that frequency components exceeding half the sampling rate of the filter (cf. Nyquist sampling theorem) will be confounded (or aliased) by the filter. Thus a small anti-aliasing filter is always placed ahead of the analog to digital conversion circuitry to prevent these high-frequency components from aliasing. A sample refers to a value or set of values at a point in time and/or space. ... The Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. ... In digital signal processing, anti-aliasing is the technique of minimizing aliasing (jagged or blocky patterns) when representing a high-resolution signal at a lower resolution. ... This article or section should include material from AD converters In electronics, an analog-to-digital converter (abbreviated ADC, A/D, or A to D) is a device that converts continuous signals to discrete digital numbers. ...

## Types of digital filters

Many digital filters are based on the Fast Fourier transform, a mathematical algorithm that quickly extracts the frequency spectrum of a signal, allowing the spectrum to be manipulated (such as to create pass-band filters) before converting the modified spectrum back into a time-series signal. A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. ... Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. ...

Another form of a typical linear digital filter, expressed as a transform in the Z-domain, is In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ...

$H(z) = frac{B(z)}{A(z)} = frac{{b_{0}+b_{1}z^{-1}+b_{2}z^{-2} + cdots + b_{N}z^{-N}}}{{1+a_{1}z^{-1}+a_{2}z^{-2} + cdots +a_{M}z^{-M}}}$

where M is the order of the filter. See Z-transform's LCCD equation for further discussion of this transfer function. In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ...

This form is for an infinite impulse response filter, but if the denominator is unity then this is the form for a finite impulse response filter. IIR (infinite impulse response) is a property of signal processing systems. ... In algebra, a vulgar fraction consists of one integer divided by a non-zero integer. ... Look up one in Wiktionary, the free dictionary. ... A finite impulse response (FIR) filter is a type of a digital filter. ...

Another form of a digital filter is that of a state space model. A well used state-space filter is the Kalman filter published by Rudolf Kalman in 1960. In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. ... The Kalman filter is an efficient recursive filter which estimates the state of a dynamic system from a series of incomplete and noisy measurements. ... Rudolf Emil Kalman (May 19, 1930 -) is a mathematical system theorist, who is an electrical engineer by training. ... 1960 (MCMLX) was a leap year starting on Friday (the link is to a full 1960 calendar). ...

## References

• A. Antoniou, Digital Filters: Analysis, Design, and Applications, New York, NY: McGraw-Hill, 1993.
• S.K. Mitra, Digital Signal Processing: A Computer-Based Approach, New York, NY: McGraw-Hill, 1998.
• A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999.
• J.F. Kaiser, Nonrecursive Digital Filter Design Using the Io-sinh Window Function, Proc. 1974 IEEE Int. Symp. Circuit Theory, pp. 20-23, 1974.
• S.W.A. Bergen and A. Antoniou, Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function, EURASIP Journal on Applied Signal Processing, vol. 2005, no. 12, pp. 1910-1922, 2005.
• T.W. Parks and J.H. McClellan, Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase, IEEE Trans. Circuit Theory, vol. CT-19, pp. 189-194, Mar. 1972.
• L. R. Rabiner, J.H. McClellan, and T.W. Parks, FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation, Proc. IEEE, vol. 63, pp. 595-610, Apr. 1975.
• A.G. Deczky, Synthesis of Recursive Digital Filters Using the Minimum p-Error Criterion, IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 257-263, Oct. 1972.

Lawrence R. Rabiner (born 28 September 1943 in Brooklyn, New York) is an electrical engineer working in the fields of digital signal processing and speech processing; in particular in digital signal processing for automatic speech recognition. ...

An analog filter handles analog stimuli (e. ... In electronics and signal processing, a Bessel filter is a variety of linear filter with a maximally flat group delay (linear phase response). ... The Butterworth filter is one type of electronic filter design. ... This article may be too technical for most readers to understand. ... Magnitude plot of 2nd and 4th order Linkwitz-Riley filters A Linkwitz-Riley (L-R) filter is an infinite impulse response filter used in Linkwitz-Riley audio crossovers, named after its inventors Siegfried Linkwitz and Russ Riley, which was originally described in Passive Crossover Networks for Noncoincident Drivers in JAES... The frequency response of a fourth-order type I Chebyshev low-pass filter Chebyshev filters, are analog or digital filters having a steeper roll-off and more passband ripple than Butterworth filters. ... Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. ... A sample refers to a value or set of values at a point in time and/or space. ... Television signal splitter consisting of a hi-pass and a low-pass filter. ... Filter design is the process of working out a filter (in the sense in which the term is used in signal processing, statistics, and applied mathematics), often a linear shift-invariant filter, which satisfies a set of requirements, some of which are contradicting. ... A high-pass filter is a filter that passes high frequencies well, but attenuates (or reduces) frequencies lower than the cutoff frequency. ... A low-pass filter is a filter that passes low frequencies well, but attenuates (or reduces) frequencies higher than the cutoff frequency. ... IIR (infinite impulse response) is a property of signal processing systems. ... A finite impulse response (FIR) filter is a type of a digital filter. ... In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ...

Results from FactBites:

 Digital Filter Design (DSP Blockset) (563 words) The block applies the specified filter to each channel of a discrete-time input signal, and outputs the result. The outputs of the block numerically match the outputs of the Digital Filter block, the The sampling frequency, Fs, you specify in the FDATool GUI should be identical to the sampling frequency of the Digital Filter Design block's input block.
 Digital Filter (550 words) A digital filter is any digital-computing means that accepts as its input a set of one or more digital signals from which it generates as its output a second set of digital signals. By controlling the accuracy of the calculations within the filter (that is, the arithmetic word length), it is possible to produce filters whose performance comes arbitrarily close to the performance expected of the perfect models. These filters are called adaptive because they adapt their parameters in response to changes in the operating environment.
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