remez() R function from [gsignal]

Parks-McClellan optimal FIR filter design

Parks-McClellan optimal FIR filter design using the Remez exchange algorithm.


remez(
  n,
  f,
  a,
  w = rep(1, length(f)/2),
  ftype = c("bandpass", "differentiator", "hilbert"),
  density = 16
)

Arguments

n: filter order (1 less than the length of the filter).
f: normalized frequency points, strictly increasing vector in the range [0, 1], where 1 is the Nyquist frequency. The number of elements in the vector is always a multiple of 2.
a: vector of desired amplitudes at the points specified in f. f and a must be the same length. The length must be an even number.
w: vector of weights used to adjust the fit in each frequency band. The length of w is half the length of f and a, so there is exactly one weight per band. Default: 1.
ftype: filter type, matched to one of "bandpass" (default), "differentiatior", or "hilbert".
density: determines how accurately the filter will be constructed. The minimum value is 16 (default), but higher numbers are slower to compute.

Returns

The FIR filter coefficients, a vector of length n + 1, of class Ma

Examples


## low pass filter
f1 <- remez(15, c(0, 0.3, 0.4, 1), c(1, 1, 0, 0))
freqz(f1)

## band pass
f <- c(0, 0.3, 0.4, 0.6, 0.7, 1)
a <- c(0, 0, 1, 1, 0, 0)
b <- remez(17, f, a)
hw <- freqz(b, 512)
plot(f, a, type = "l", xlab = "Radian Frequency (w / pi)",
     ylab = "Magnitude")
lines(hw$w/pi, abs(hw$h), col = "red")
legend("topright", legend = c("Ideal", "Remez"), lty = 1,
       col = c("black", "red"))

References

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

Rabiner, L.R., McClellan, J.H., and Parks, T.W. (1975). FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximations, IEEE Proceedings, vol. 63, pp. 595 - 610.

https://en.wikipedia.org/wiki/Parks-McClellan_filter_design_algorithm