cheby1 {gsignal}

Chebyshev Type I filter design

Description

Compute the transfer function coefficients of a Chebyshev Type I filter.

Usage

cheby1(n, ...)

## S3 method for class 'FilterSpecs'
cheby1(n, ...)

## Default S3 method:
cheby1(
  n,
  Rp,
  w,
  type = c("low", "high", "stop", "pass"),
  plane = c("z", "s"),
  output = c("Arma", "Zpg", "Sos"),
  ...
)

Arguments

n

filter order.

...

additional arguments passed to cheby1, overriding those given by n of class FilterSpecs.

Rp

dB of passband 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.

Details

Chebyshev filters are analog or digital filters having a steeper roll-off than Butterworth filters, and have passband ripple (type I) or stopband ripple (type II).

Because cheby1 is generic, it can be extended to accept other inputs, using cheb1ord to generate filter criteria for example.

Value

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

Author(s)

Paul Kienzle, [e-mail],
Doug Stewart, [e-mail].
Conversion to R Tom Short,
adapted by Geert van Boxtel, [e-mail].

References

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

See Also

Arma, filter, butter, ellip, cheb1ord, FilterSpecs

Examples

## compare the frequency responses of 5th-order
## Butterworth and Chebyshev filters.
bf <- butter(5, 0.1)
cf <- cheby1(5, 3, 0.1)
bfr <- freqz(bf)
cfr <- freqz(cf)
plot(bfr$w / pi, 20 * log10(abs(bfr$h)), type = "l", ylim = c(-40, 0),
  xlim = c(0, .5), xlab = "Frequency", ylab = c("dB"))
lines(cfr$w / pi, 20 * log10(abs(cfr$h)), col = "red")

# compare type I and type II Chebyshev filters.
c1fr <- freqz(cheby1(5, .5, 0.5))
c2fr <- freqz(cheby2(5, 20, 0.5))
plot(c1fr$w / pi, abs(c1fr$h), type = "l", ylim = c(0, 1),
  xlab = "Frequency", ylab = c("Magnitude"))
  lines(c2fr$w / pi, abs(c2fr$h), col = "red")