Bessel filter

Bessel filters are often used in audio crossover systems.

Bessel filter, has a maximally flat phase delay.

A Bessel filter (not shown) has an even poorer transition in the frequency domain, but maintains the best phase fidelity of a waveform.

A Bessel filter (i.e., continuous-time filter with flattest group delay) has an underdamped .

The Bessel filter is very similar to the Gaussian filter, and tends towards the same shape as filter order increases.

Analog Bessel filters are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.

Bessel functions also appear in other problems, such as signal processing (e.g., see FM synthesis, Kaiser window, or Bessel filter).

In electronics and signal processing, a Bessel filter is a type of linear filter with a maximally flat group delay (maximally linear phase response).

The Bessel filter is named after Friedrich Bessel and the transfer function is based on Bessel polynomials.

The various types of filters (Butterworth filter, Chebyshev filter, Bessel filter, etc.) all have different-looking "knee curves".

The transfer function of the Bessel filter is a rational function whose denominator is a reverse Bessel polynomial, such as the following:

The Bessel filter has better shaping factor, flatter phase delay, and flatter group delay than a Gaussian of the same order, though the Gaussian has lower time delay.

Currents were sampled at 0.5-5 kHz low-pass filtered at 5 kHz using the 4-pole Bessel filter in the patch clamp amplifier, digitized, and stored on the computer for later analysis.

Also FIR filters can be easily made to be linear phase (constant group delay vs frequency), a property that is not easily met using IIR filters and then only as an approximation (for instance with the Bessel filter).

The Bessel filter has minimal distortion in the time domain due to the phase response with frequency as opposed to the Butterworth filter which has minimal distortion in the frequency domain due to the attenuation response with frequency.

For instance, a fifth order Bessel filter prototype can be converted into any other fifth order Bessel filter, but it cannot be transformed into a third order Bessel filter or a fifth order Tchebyscheff filter.