Butterworth, Elliptic, and Chebyshev I/II Filter Order Estimation (#453)

* Adding filter order routines.

* Adding test cases for `cheb1ord` and `ellipord`

* Adding `cheb2ord` test cases.

* Adding `cheb2ord` docstrings

* Adding order estimation routines to the docs.

* Adding argument error and `brent` test cases.

docs/src/filters.md

@@ -84,7 +84,9 @@ or [`Bandstop`](@ref) and includes the edges of the bands.
 The design method is [`Butterworth`](@ref), [`Chebyshev1`](@ref), [`Chebyshev2`](@ref), 
 [`Elliptic`](@ref), or [`FIRWindow`](@ref), and includes any
 necessary parameters for the method that affect the shape of the response,
-such as filter order, ripple, and attenuation.
+such as filter order, ripple, and attenuation. [Filter order estimation methods](@ref order-est-methods) 
+are available in [`buttord`](@ref), [`cheb1ord`](@ref), [`cheb2ord`](@ref), 
+and [`ellipord`](@ref) if the corner frequencies for different IIR filter types are known.
 
 ```@docs
 analogfilter
@@ -119,6 +121,15 @@ Chebyshev2
 Elliptic
 ```
 
+### [IIR filter order estimation methods](@id order-est-methods)
+
+```@docs
+buttord
+cheb1ord
+cheb2ord
+ellipord
+```
+
 #### FIR filter design methods
 
 ```@docs
@@ -180,3 +191,11 @@ responsetype = Lowpass(5; fs=50)
 designmethod = FIRWindow(hanning(64))
 filt(digitalfilter(responsetype, designmethod), x)
 ```
+
+Estimate a Lowpass Elliptic filter order with a normalized
+passband cutoff frequency of 0.2, a stopband cutoff frequency of 0.4,
+3 dB of passband ripple, and 40 dB attenuation in the stopband:
+
+```julia
+(N, ωn) = ellipord(0.2, 0.4, 3, 40)
+```

src/Filters/Filters.jl

@@ -6,6 +6,7 @@ using Polynomials: LaurentPolynomial, Polynomial, coeffs, derivative, fromroots,
 import Base: *
 using LinearAlgebra: I, mul!, rmul!
 using Statistics: middle
+using SpecialFunctions: ellipk
 import ..DSP: filt, filt!, optimalfftfiltlength, os_fft_complexity, SMALL_FILT_CUTOFF
 import Compat
 using FFTW
@@ -44,6 +45,13 @@ export  FilterType,
         FIRWindow,
         resample_filter
 
+include("filt_order.jl")
+export  buttord,
+        ellipord,
+        cheb1ord,
+        cheb2ord
+
+
 include("response.jl")
 export  freqresp,
         phaseresp,