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Topic: Butterworth filter

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	A BUTTERWORTH-FILTER COOKBOOK
		The appropriate bandpass filter is one whose time decay can be chosen to be reasonable (in combination with a reasonable necessary compromise on the shape of the rectangle).
		Figure 14 Spectra of Butterworth filters of various-order n.
		Conceptually, the easiest form of Butterworth filtering is to take data to the frequency domain and multiply by equation (21), where you have selected some value of n to compromise between the demands of the frequency domain (sharp cutoff) and the time domain (rapid decay).
	sepwww.stanford.edu /sep/prof/pvi/spec/paper_html/node14.html (450 words)

	[No title]
		These filters are applied in the frequency domain; the advantages or disadvantages of this technique as opposed to the filtering in the spatial domain that is done with 2D Filter or the 2D convolution applications are 1) For a filter which has a large spatial extent, the frequency domain techniques will be generally faster.
		Two variants of Butterworth filters are provided, a smoothing filter which passes low frequencies and attenuates the high frequency components of the input and a sharpening filter which attenuates the low frequency components.
		The inverse filter is computed as a simplified Wiener filter: H(k) / (H(k) H(k) + C) where H(k) is the frequency response of the filter to be inverted, H*(k) is complex conjugate of H(k), and C is a non-negative constant.
	www.msg.ucsf.edu /IVE/HELP/FFilter2D.hlp (2706 words)

	Butterworth filter - Wikipedia, the free encyclopedia
		Butterworth filters have a monotonically decreasing magnitude function with ω.
		The Butterworth is the only filter that maintains this same shape for higher orders (but with a steeper decline in the stopband) whereas other varieties of filters (Bessel, Chebyshev, elliptic) have different shapes at higher orders.
		The group delay is defined as the derivative of the phase with respect to angular frequency and is a measure of the distortion in the signal introduced by phase differences for different frequencies.
	en.wikipedia.org /wiki/Butterworth_filter (1177 words)

	Digital Signal Processing Filter Terminology
		Filter attenuation is the ratio, at a given frequency, of the signal amplitude at the output of the filter over the signal amplitude at the input of the filter, defined as
		For an FIR filter, the filter coefficients are, by definition, the impulse response of the filter.
		With a constant group delay of 0.04 seconds, the 1 Hz input sinewave is delayed at the filter output by 0.25 radians, the 3 Hz sinewave is delayed by 0.75 radians, the 5 Hz sinewave by 1.25 radians, and the 7 Hz sinewave by 1.75 radians.
	www.dspguru.com /info/terms/filtterm/index2.htm (2987 words)

	Analog Filter Design (DSP Blockset)
		The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall.
		The magnitude response of a Chebyshev type I filter is equiripple in the passband and monotonic in the stopband.
		The magnitude response of an elliptic filter is equiripple in both the passband and the stopband.
	www.weizmann.ac.il /matlab/toolbox/dspblks/analogfilterdesign.html (503 words)

	Priism Help: 3D Filter (Frequency domain)
		These filters are applied in the frequency domain; the advantages or disadvanteges of this technique as opposed to the filtering in the spatial domain that is done with 3D Filter are
		Also of practical note is that the types of filters offered by this application and by the applications that filter in the spatial domain are quite different, and the availability of the filter you want will frequently limit your choice to one or the other.
		Two variants of Butterworth filters are provided, a smoothing filter which passes low frequencies and attenuates the high frequency components of the input and a sharpening filter which attenuates the low frequency components.
	util.ucsf.edu /IVE/IVE3.3_HTML/FFilter3D.html (1562 words)

	kyma•tweaky: Learn FilterTypeDefinition
		Generally, when speaking of filters, we speak of the characteristics of a prototypical lowpass filter (for example, a Butterworth filter), transformed into the frequency response of interest (Butterworth bandpass filter).
		Butterworth (Kyma IIR HP/LP filters): maximally flat amplitude response, no consideration of phase linearity or group delay variations.
		Finite Impulse Response Filter (Kyma FIR): FIR filters are stable, and have linear phase responses if the coefficients of the filter are symmetric about their center point (for example, 0.5, 1, 0.5).
	www.symbolicsound.com /cgi-bin/bin/view/Learn/FilterTypeDefinition (718 words)

	Elliptic filter - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-09-20)
		As the ripple in the in the pass band 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 poles of the gain of an elliptic filter may be derived in a manner very similar to the derivation of the poles of the gain of a type I Chebyshev filter.
		Elliptic filters are generally specified by requiring a particular value for the pass band ripple, stop band ripple and the sharpness of the cutoff.
	en.wikipedia.org /wiki/Elliptic_filter (1168 words)

	Filter Design Guide
		In a classic, passive filter made of inductors, capacitors, and resistores, the filter's frequency response is the result of the impedance of inductors and capacitors changing with respect to one another, and with respect to the resistors in the filter.
		The poles of a two-pole filter are at ±45°.
		The blue graph is a two-stage (four-pole) active low-pass filter, the pink is a single-stage (two-pole) active filter, and the yellow is a one-and-a-half stage (three-pole) filter.
	alignment.hep.brandeis.edu /Electronics/A2037/Filter.html (5610 words)

	Butterworth Filters
		The Butterworth filter is a filter that can be constructed out of passive R, L, C circuits.
		The important aspects of figure 1 are that it does not ripple in the passband or stopband as other filters tend to, and that the larger n, the sharper the cutoff (the smaller the transition band).
		Design a Butterworth filter with a passband gain between 1 and 0.891 (-1 dB gain) for 0andlt;ωandlt;10 and a stopband not to exceed 0.0316 (-30 dB gain) for ω≥20.
	cnx.org /content/m10127/latest (569 words)

	butter :: Functions (Signal Processing Toolbox)
		Butterworth filters are characterized by a magnitude response that is maximally flat in the passband and monotonic overall.
		Butterworth filters sacrifice rolloff steepness for monotonicity in the pass- and stopbands.
		It transforms the lowpass filter into a bandpass, highpass, or bandstop filter with desired cutoff frequencies, using a state-space transformation.
	www.mathworks.com /access/helpdesk/help/toolbox/signal/butter.html (463 words)

	XO Wave: Using EQ
		Unfortunately, no filter is perfect -- all filters produce some sort of distortion, or they pass or reduce frequencies they shouldn't -- and Butterworth filters are no exception.
		The reason Butterworth filters have been selected for XO Wave (and most other digital audio software) is that they are computationally efficient, and they provide a relatively flat response in the "passband".
		While you can change the exact filter types and center frequencies later, it is a good idea to start with the filter as close to what you need as possible.
	www.xowave.com /doc/effect/eq (2262 words)

	Microstrip - Type of Filter Responses
		The butterworth filter is also know as maximally flat because it has a flat passband response as shown in the figure below and it does not contains any ripple.
		The butterworth type filter response is most ideal for filters with slow cutoff smooth attenuation in the passband region.
		Compare with a butterworth filter of a similar order, the chebyshev filter exhibit a bad linear response because there are ripple exist in the passband and steeper initial descent into the stopband region.
	www.eng.newcastle.edu.au /~c3033046/filters.html (282 words)

	Normalized Butterworth Filter Polynomials
		Computes the numerator and denominator polynomials for a normalized Butterworth filter with n poles, where n is an integer greater than 0.
		The output value of numout is set to the double-precision column vector corresponding to the numerator polynomial of the Butterworth filter (numout is equal to the scalar 1 because normalized Butterworth filters have no zeros).
		The output value of denout is set to the double-precision column vector corresponding to the denominator polynomial of the Butterworth filter.
	www.omatrix.com /manual/fnbut.htm (99 words)

	A Filter Primer - Maxim/Dallas
		A type of filter that is common to many applications requires a response that is flat in the passband but cuts off as sharply as possible afterwards.
		Butterworth and Chebychev filters with sharp cutoffs carry a penalty that is evident from the positions of their poles in the s plane.
		Note that all the filters described have the same number of zeros as poles (this must be the case, or the transfer function would not be a dimensionless expression).
	www.maxim-ic.com /appnotes.cfm/appnote_number/733 (3812 words)

	Analog Filter Design Demystified - Maxim/Dallas
		Butterworth ensures a flat response in the passband and an adequate rate of rolloff.
		Note, however, that a 4th-order Butterworth filter is not obtained simply by calculating the components for a 2nd-order filter and then cascading two such stages.
		To ensure conformance with the generic filter described by equation 4, and to ensure that the last term equals unity, the first two quadratics have been multiplied by a constant.
	www.maxim-ic.com /appnotes.cfm/appnote_number/1795 (2295 words)

	PROJECT 3
		The butterworth filter can be made to behave like a box or like a Gaussian by changing its parameters.
		This can be obtained by subtracting the area between the ideal filter and the filter under interest till the cutoff of the filter (region of interest) (This can be done on paper or by numerical integration).
		It is the extent of filter that is being truncated as the filter is being applied to the finite extent of the fourier transform.
	www.cs.utah.edu /~lavanyat/ip/report3/report.htm (804 words)

	Verilog HDL: Butterworth IIR Filter (Site not responding. Last check: 2007-09-20)
		Butterworth filters are also known as "maximally flat" filters because they have no passband ripple.
		The complexity of calculating the result of the Butterworth filter can be greatly reduced if the filter is broken down into several second order systems known as biquads.
		The input is a 12-bit signed integer, the filter coefficients are scaled to 10 bits, and the output is 21 bits wide.
	www.altera.com /support/examples/verilog/ver_butterworth.html (411 words)

	Filters (Site not responding. Last check: 2007-09-20)
		Note the open area under the lower right of the figure which represents the filter response and which illustrates the conventional frequency attenuation curve as the animation progresses.
		Extended tables of Butterworth polynomials, poles, and circuit elements are provided in a separate paper, for filter orders up to 10.
		This is a screen shot of a DOS executable which displays a complete summary of the time and frequency domain behavior of any filter, given its representation as a ratio of polynomials in the complex variable 's'.
	www.crbond.com /filters.htm (396 words)

	Digital Filter Design, Writing Difference Equations For Digital Filters, a Tutorial
		The above low pass filter (not the notch or RES_COMP filters) equations are mapped to the appropriate filter type using the following mappings.
		Where, for any filters obtained using the normalized low-pass butterworth filter as the basis for the digital filter, n = d = order of the filter.
		For low-pass to low-pass and low-pass to high-pass mapping the order of the digital filter is the same as the order of the starting normalized butterworth filter.
	www.apicsllc.com /apics/Sr_3/Sr_3.htm (477 words)

	How to choose a filter? (Butterworth, Chebyshev, Inverse Chebyshev, Bessel or Thomson) (Site not responding. Last check: 2007-09-20)
		This filter response has the steeper initial rate of attenuation beyond the cutoff frequency than Butterworth.This advantage comes at the penalty of amplitude variation(ripple) in the pass-band.
		Unlike Butterworth and Bessel response, which have 3dB attenuation at the cutoff frequency,Cebyshev cutoff frequency is defined as the frequency at which the response falls below the ripple band.
		The difference is that the ripple of the Inverse Chebyshev filter is confined to the stop-band.
	www.etc.tuiasi.ro /cin/Downloads/Filters/Filters.htm (310 words)

	Butterworth Low-Pass Filter
		Filters are classified according to the functions that they are to perform, in terms of ranges of frequencies.
		We will be dealing with the low-pass filter, which has the property that low-frequency excitation signal components down to and including direct current, are transmitted, while high-frequency components, up to and including infinite ones are blocked.
		The ideal low-pass filter response can be approximated by a rational function approximation scheme such as the Butterworth response.
	www.ece.uic.edu /~jmorisak/blpf.html (458 words)

	FDI Online Design Guide
		To convert a normalized amplitude response curve to a curve representing a filter whose corner frequency is not at one Hertz, multiplying any number on the frequency axis by the intended corner or ripple frequency scales the frequency axis.
		For active filters, the THD is usually specified in dBc (dB relative to the amplitude of the fundamental frequency component) and at a specific frequency and amplitude (ex.
		Since a switched-capacitor filter is a sampling device, it experiences aliasing errors, frequency components near the sampling frequency that must be eliminated to ensure accuracy.
	www.freqdev.com /guide/fullguide.html (8801 words)

	The MathWorks - Filter Design HDL Coder - HDL Butterworth Filter Demo
		The cutoff-frequency for this filter is very low relative to the sample rate, leading to a filter that is difficult to make practical.
		Also, small input (8-bit) and output (9-bit) word sizes cause the quantized filter to require scaling to be realizable.
		Since the passband of this filter is so low relative to the sampling rate, a custom input stimulus is a better way to test the filter implementation.
	www.mathworks.com /products/filterhdl/demos.html?file=/products/demos/shipping/hdlfilter/hdlbutter.html (861 words)

	Improve group delay response in the anti-aliasing filter
		Anti-aliasing filters are necessary in most video-acquisition circuits to prevent signals at frequencies greater than 1/2 the sampling rate from contaminating desired signals during the sampling process.
		A 5-pole filter with a Butterworthlike amplitude response and reduced phase lag near the 4-MHz cutoff is shown in Figure 1.
		Note that the stopband slope of the modified filter is not as steep as that of the Butterworth filter, but the phase delay near cutoff is significantly reduced.
	www.elecdesign.com /Articles/ArticleID/6299/6299.html (866 words)

	Sound and Music - Analog Filter Designs (Site not responding. Last check: 2007-09-20)
		The Butterworth and Chebyshev filters are special kinds of elliptic filters (also known as Cauer filters).
		Bessel filters have maximally linear phase response at low frequencies, though their frequency response is not as good as the other three lowpass filters described here.
		Once a lowpass filter is obtained, it may be transformed into other kinds of filters by a simple variable substitution.
	rooster.stanford.edu /~ben/sound/analog.html (643 words)

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