ellip function

Elliptic filter design

Compute the transfer function coefficients of an elliptic filter.

ellip(n, ...)

## S3 method for class 'FilterSpecs'
ellip(n, Rp = n$Rp, Rs = n$Rs, w = n$Wc, type = n$type, plane = n$plane, ...)

## Default S3 method:
ellip(
  n,
  Rp,
  Rs,
  w,
  type = c("low", "high", "stop", "pass"),
  plane = c("z", "s"),
  output = c("Arma", "Zpg", "Sos"),
  ...
)

Arguments

• n: filter order.

• ...: additional arguments passed to ellip, overriding those given by n of class FilterSpecs.

• Rp: dB of passband ripple.

• Rs: dB of stopband ripple.

• 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. For digital filters, w must be between 0 and 1 where 1 is the Nyquist frequency.

• type: filter type, one of "low", "high", "stop", or "pass".

• plane: "z" for a digital filter or "s" for an analog filter.

• output: Type of output, one of:

  • "Arma": Autoregressive-Moving average (aka numerator/denominator, aka b/a)
  • "Zpg": Zero-pole-gain format
  • "Sos": Second-order sections

  Default is "Arma" for compatibility with the 'signal' package and the 'Matlab' and 'Octave' equivalents, but "Sos" should be preferred for general-purpose filtering because of numeric stability.

Returns

Depending on the value of the output parameter, a list of class Arma, Zpg, or Sos

containing the filter coefficients

Details

An elliptic filter is a filter with equalized ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in gain between the passband and the stopband, for the given values of ripple.

As the ripple in the stopband approaches zero, the filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as both ripple values approach zero, the filter becomes a Butterworth filter.

Because ellip is generic, it can be extended to accept other inputs, using ellipord to generate filter criteria for example.

Examples

## compare the frequency responses of 5th-order Butterworth
## and elliptic filters.
bf <- butter(5, 0.1)
ef <- ellip(5, 3, 40, 0.1)
bfr <- freqz(bf)
efr <- freqz(ef)
plot(bfr$w, 20 * log10(abs(bfr$h)), type = "l", ylim = c(-80, 0),
     xlab = "Frequency (Rad)", ylab = c("dB"), lwd = 2,
     main = paste("Elliptic versus Butterworth filter",
     "low-pass -3 dB cutoff at 0.1 rad", sep = "\n"))
lines(efr$w, 20 * log10(abs(efr$h)), col = "red", lwd = 2)
legend ("topright", legend = c("Butterworh", "Elliptic"),
        lty = 1, lwd = 2, col = 1:2)

References

https://en.wikipedia.org/wiki/Elliptic_filter

See Also

Arma, filter, butter, cheby1, ellipord

Author(s)

Paulo Neis, p_neis@yahoo.com.br ,

adapted by Doug Stewart, dastew@sympatico.ca .

Conversion to R Tom Short,

adapted by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .