Bessel analog filter design
Compute the transfer function coefficients of an analog Bessel filter.
besself(n, w, type = c("low", "high", "stop", "pass"))
n: filter order.w: critical frequencies of the filter. w must be a scalar for low-pass and high-pass filters, and w must be a two-element vector c(low, high) specifying the lower and upper bands in radians/second.type: filter type, one of "low" (default), "high", "stop", or "pass".List of class 'Zpg' containing poles and gain of the filter.
Bessel filters are characterized by an almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.
Lowpass Bessel filters have a monotonically decreasing magnitude response, as do lowpass Butterworth filters. Compared to the Butterworth, Chebyshev, and elliptic filters, the Bessel filter has the slowest rolloff and requires the highest order to meet an attenuation specification.
As the important characteristic of a Bessel filter is its maximally-flat group delay, and not the amplitude response, it is inappropriate to use the bilinear transform to convert the analog Bessel filter into a digital form (since this preserves the amplitude response but not the group delay) [1].
w <- seq(0, 4, length.out = 128) ## 5th order Bessel low-pass analog filter zp <- besself(5, 1.0) freqs(zp, w) ## 5th order Bessel high-pass analog filter zp <- besself(5, 1.0, 'high') freqs(zp, w) ## 5th order Bessel band-pass analog filter zp <- besself(5, c(1, 2), 'pass') freqs(zp, w) ## 5th order Bessel band-stop analog filter zp <- besself(5, c(1, 2), 'stop') freqs(zp, w)
[1] https://en.wikipedia.org/wiki/Bessel_filter
Paul Kienzle, pkienzle@users.sf.net ,
Doug Stewart, dastew@sympatico.ca ,
Thomas Sailer, t.sailer@alumni.ethz.ch .
Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .