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Butterworth Filter
The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled "On the Theory of Filter Amplifiers". Original paper Butterworth had a reputation for solving "impossible" mathematical problems. At the time, filter design required a considerable amount of designer experience due to limitations of the theory then in use. The filter was not in common use for over 30 years after its publication. Butterworth stated that: Such an ideal filter cannot be achieved, but Butterworth showed that successively closer approximations were obtained with increasing numbers of filter elements of the right values. At the time, filters generated substantial ripple in the passband, and the choice of component values was highly interactive. Butter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Band-pass Filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-port circuit or device which removes frequency components of a signal (an alternating voltage or current). A band-pass filter allows through components in a specified band of frequencies, called its ''passband'' but blocks components with frequencies above or below this band. This contrasts with a high-pass filter, which allows through components with frequencies above a specific frequency, and a low-pass filter, which allows through components with frequencies below a specific frequency. In digital signal processing, in which signals represented by digital numbers are processed by computer programs, a band-pass filter is a computer algorithm that performs the same function. The term band-pass filter is also used for optical filters, she ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer Function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used in electronics and control systems. In some simple cases, this function is a two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory. The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (). Its symbol is usually , and it may be represented by writing its magnitude and phase in the polar form . However, Cartesian complex number representation is often more powerful for circuit analysis purposes. The notion of impedance is useful fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roll-off
Roll-off is the steepness of a transfer function with frequency, particularly in electrical network analysis, and most especially in connection with 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 frequency; consequently, the units of roll-off are either decibels per decade (dB/decade), where a decade is a tenfold increase in frequency, or decibels per 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 point of the frequency curve. Roll-off enables the cut-off performance of such a filter network to be reduced to a single number. Note that roll-off ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in gain between the passband and the stopband, for the given values of ripple (whether the ripple is equalized or not). Alternatively, one may give up the ability to adjust independently the passband and stopband ripple, and instead design a filter which is maximally insensitive to component variations. As the ripple in the stopband approaches zero, the filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as both ripple values approach zero, the filter becomes a Butterworth filter. The gain of a lowpass elliptic filter as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chebyshev Filter
Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband ripple (type II). Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter (See references eg. aniels utovac, but with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Because of the passband ripple inherent in Chebyshev filters, filters with a smoother response in the passband but a more irregular response in the stopband are preferred for certain applications. Type I Chebyshev filters (Chebyshev filters) Type I Chebyshev filters are the most common types of Chebyshev filters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decade (log Scale)
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers. Example: Scientific notation When a real number like .007 is denoted alternatively by 7. × 10—3 then it is said that the number is represented in scientific notation. More generally, to write a number in the form ''a'' × 10''b'', where 1 < ''a'' < 10 and ''b'' is an , is to express it in , and ''a'' is called the ''significand'' or the ''mantissa'', and ''b'' is its |
Octave (electronics)
In electronics, an octave (symbol: oct) is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency. For example, the frequency one octave above 40 Hz is 80 Hz. The term is derived from the Western musical scale where an octave is a doubling in frequency. Specification in terms of octaves is therefore common in audio electronics. Along with the decade, it is a unit used to describe frequency bands or frequency ratios.Perdikaris, G. (1991). ''Computer Controlled Systems: Theory and Applications'', p. 117. . Ratios and slopes A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio: : \text = \log_2\left(\frac\right) An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stopband
A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on application, the required attenuation within the stopband may typically be a value between 20 and 120 dB higher than the nominal passband attenuation, which often is 0 dB. The lower and upper ''limiting frequencies'', also denoted lower and upper stopband corner frequencies, are the frequencies where the stopband and the transition bands meet in a filter specification. The stopband of a low-pass filter is the frequencies from the stopband corner frequency (which is slightly higher than the passband 3 dB cut-off frequency) up to the infinite frequency. The stopband of a high-pass filter consists of the frequencies from 0 hertz to a stopband corner frequency (slightly lower than the passband cut-off frequency). A band-stop filter has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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