In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat group delay (i.e., maximally linear phase response), which preserves the wave shape of filtered signals in the passband.[1] Bessel filters are often used in audio crossover systems.
The filter's name is a reference to German mathematician Friedrich Bessel (1784–1846), who developed the mathematical theory on which the filter is based. The filters are also called Bessel–Thomson filters in recognition of W. E. Thomson, who worked out how to apply Bessel functions to filter design in 1949.[2]
The Bessel filter is very similar to the Gaussian filter, and tends towards the same shape as filter order increases.[3][4] While the time-domain step response of the Gaussian filter has zero overshoot,[5] the Bessel filter has a small amount of overshoot,[6][7] but still much less than other common frequency-domain filters, such as Butterworth filters. It has been noted that the impulse response of Bessel–Thomson filters tends towards a Gaussian as the order of the filter is increased.[3]
Compared to finite-order approximations of the Gaussian filter, the Bessel filter has better shaping factor, flatter phase delay, and flatter group delay than a Gaussian of the same order, although the Gaussian has lower time delay and zero overshoot.[8]
^Cite error: The named reference BesselFilterTI was invoked but never defined (see the help page).
^Cite error: The named reference Thomson1949 was invoked but never defined (see the help page).
^ abCite error: The named reference RobertsTRT was invoked but never defined (see the help page).
^Cite error: The named reference compdsp was invoked but never defined (see the help page).
^Cite error: The named reference nuhertz was invoked but never defined (see the help page).
^Cite error: The named reference tuiasi was invoked but never defined (see the help page).
^Cite error: The named reference kecktaylor was invoked but never defined (see the help page).
^Cite error: The named reference Paarmann2001 was invoked but never defined (see the help page).
In electronics and signal processing, a Besselfilter is a type of analog linear filter with a maximally flat group delay (i.e., maximally linear phase...
statistics. Besselfilter, a linear filter often used in audio crossover systems Bessel Fjord, NE Greenland Bessel Fjord, NW Greenland Bessel (crater),...
than the Chebyshev filter or the Elliptic filter, but without ripple. Besselfilter Chebyshev filter Comb filter Elliptic filterFilter design Butterworth...
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's...
Butterworth filter; they are not as sharp as the elliptic one, but they show fewer ripples over the bandwidth. Besselfilter Butterworth filter Chebyshev...
signal processing, mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation...
response with frequency. The Besselfilter is named after Friedrich Bessel and the transfer function is based on Bessel polynomials. The driving point...
Butterworth filter has the poorest transition but has a more even response, avoiding ripples in either the passband or stopband. A Besselfilter (not shown)...
Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic...
met using IIR filters and then only as an approximation (for instance with the Besselfilter). Another issue regarding digital IIR filters is the potential...
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...
The Kaiser window, also known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions...
band-pass filter, band-stop filter, low-pass filter or high-pass filter. The tuning application, for instance, is an example of band-pass filtering. The RLC...
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by...
any other fifth-order Besselfilter, but it cannot be transformed into a third-order Besselfilter or a fifth-order Chebyshev filter. A passive lumped low-pass...
Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio...
A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or...
filter of the same order Chebyshev filter (Type II) – maximally flat in passband, sharper cutoff than a Butterworth filter of the same order Bessel filter –...
bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners...
The reverse Bessel polynomial is used in the design of Bessel electronic filters. The Bessel polynomial may also be defined using Bessel functions from...