Bessel analog low-pass filter prototype
Return the poles and gain of a Bessel analog low-pass filter prototype.
besselap(n)
n |
order of the filter; must be < 25. |
The transfer function is
k
H(s) = -----------------------------
(s-p(1))(s-p(2))...(s-p(n))besselap normalizes the poles and gain so that at low frequency and
high frequency the Bessel prototype is asymptotically equivalent to the
Butterworth prototype of the same order. The magnitude of the filter is less
than 1/√{2} at the unity cutoff frequency Ω_c = 1.
Analog Bessel filters are characterized by a group delay that is maximally flat at zero frequency and almost constant throughout the passband. The group delay at zero frequency is
/ (2n!) \ 2 | ------ | \ 2^n n! /
List of class Zpg containing poles and gain of the
filter
Thomas Sailer, emailt.sailer@alumni.ethz.ch.
Conversion to R by
Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
## 6th order Bessel low-pass analog filter zp <- besselap(6) w <- seq(0, 4, length.out = 128) freqs(zp, w)
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