Change term arg-type for nuttall and blackmanharris

To preserve the conventional kwargs structure of all windows, the `term`
argument for blackmanharris and nuttall are change into normal
positional arguments. This implies some updates for the tests and the
make_matrix function, but it works quite well. Now it is even possible
to create a two-dimensional nuttall window, where the first dimension
consists of a 4-term nuttall window of arbitrary length while the second
dimension consists of a 3-term nuttall window of a different length.

Author: daniel-s-w

src/windows.jl

@@ -462,8 +462,9 @@ end
 """
 $blackmanharris_winplot
 
-    blackmanharris(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
-    blackmanharris(dims; term::Integer=4, padding=0, zerophase=false)
+    blackmanharris(n::Integer, term::Integer=4; padding::Integer=0, zerophase::Bool=false)
+    blackmanharris(dims, term::Integer; padding=0, zerophase=false)
+    blackmanharris(dims, Tuple{term::Integer, term::Integer}; padding=0, zerophase=false)
 
 Blackman-Harris window of length `n` with `padding` zeros. The Blackman-Harris
 window is a linear combination of three or four trigonometric terms, optimized
@@ -475,7 +476,6 @@ optimized ones in [Nuttall, A. H. (1981). Some windows with very good sidelobe
 behavior. IEEE Transactions on Acoustics, Speech, Signal Processing, 29,
 84-91](https://ieeexplore.ieee.org/document/1163506).
 
-
 The 3-term window `w3(x)` and the 4-term window `w4(x)` are defined by sampling
 the following continuous functions in the range `[-0.5, 0.5]`:
 
@@ -499,7 +499,7 @@ $(twoD_docs())
 
 $zerophase_docs
 """
-function blackmanharris(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
+function blackmanharris(n::Integer, term::Integer=4; padding::Integer=0, zerophase::Bool=false)
     if term == 4
         a0, a1, a2, a3 = 0.35875, 0.48829, 0.14128, 0.01168
         makewindow(n, padding, zerophase) do x
@@ -518,8 +518,9 @@ end
 """
 $nuttall_winplot
 
-    nuttall(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
-    nuttall(dims; term::Integer=4, padding=0, zerophase=false)
+    nuttall(n::Integer, term::Integer=4; padding::Integer=0, zerophase::Bool=false)
+    nuttall(dims, term::Integer; padding=0, zerophase=false)
+    nuttall(dims, Tuple{term_x::Integer, term_y::Integer}; padding=0, zerophase=false)
 
 Nuttall window of length `n` with `padding` zeros. These windows can be seen as
 the improved version of the Blackman-Harris windows with regard to maximum
@@ -550,7 +551,7 @@ $(twoD_docs())
 
 $zerophase_docs
 """
-function nuttall(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
+function nuttall(n::Integer, term::Integer=4; padding::Integer=0, zerophase::Bool=false)
     if term == 4
         a0, a1, a2, a3 = 0.3635819, 0.4891775, 0.1365995, 0.0106411
         makewindow(n, padding, zerophase) do x
@@ -781,7 +782,7 @@ const IntegerOr2 = Union{Tuple{Integer, Integer}, Integer}
 const RealOr2 = Union{Tuple{Real, Real}, Real}
 const BoolOr2 = Union{Tuple{Bool, Bool}, Bool}
 
-function matrix_window(func::F, dims::Tuple{Integer,Integer}, arg::Union{RealOr2,Nothing}=nothing;
+function matrix_window(func::F, dims::Tuple{Integer,Integer}, arg::Union{RealOr2,IntegerOr2,Nothing}=nothing;
         padding::IntegerOr2=0, zerophase::BoolOr2=false) where {F}
     paddings = argdup(padding)
     zerophases = argdup(zerophase)
@@ -797,7 +798,7 @@ function matrix_window(func::F, dims::Tuple{Integer,Integer}, arg::Union{RealOr2
 end
 
 for func in (:rect, :hanning, :hamming, :cosine, :lanczos,
-    :triang, :bartlett, :bartlett_hann, :blackman, :blackmanharris, :nuttall, :flattop)
+    :triang, :bartlett, :bartlett_hann, :blackman, :flattop)
     @eval function $func(dims::Tuple{Integer,Integer}; padding::IntegerOr2=0, zerophase::BoolOr2=false)
         return matrix_window($func, dims; padding, zerophase)
     end
@@ -809,4 +810,10 @@ for func in (:tukey, :gaussian, :kaiser)
     end
 end
 
+for func in (:blackmanharris, :nuttall)
+    @eval function $func(dims::Tuple{Integer,Integer}, arg::IntegerOr2; padding::IntegerOr2=0, zerophase::BoolOr2=false)
+        return matrix_window($func, dims, arg; padding, zerophase)
+    end
+end
+
 end # end module definition

test/windows.jl

@@ -83,15 +83,15 @@ end
     @test blackman_jl ≈ blackman_ml
     @test minimum(blackman_jl) == 0.0
 
-    blackmanharris_3term_jl = blackmanharris(128;term=3)
+    blackmanharris_3term_jl = blackmanharris(128, 3)
     blackmanharris_3term_ref = read_reference_data("blackmanharris_3term_128.txt")
     @test blackmanharris_3term_jl ≈ blackmanharris_3term_ref
 
     blackmanharris_4term_jl = blackmanharris(128)
     blackmanharris_4term_ml = read_reference_data("blackmanharris_4term_128.txt")
     @test blackmanharris_4term_jl ≈ blackmanharris_4term_ml
 
-    nuttall_3term_jl = nuttall(128;term=3)
+    nuttall_3term_jl = nuttall(128, 3)
     nuttall_3term_ref = read_reference_data("nuttall_3term_128.txt")
     @test nuttall_3term_jl ≈ nuttall_3term_ref
 
@@ -125,14 +125,14 @@ end
     cosine_ref = read_reference_data("cosine128.txt")
     @test cosine_jl ≈ cosine_ref
 
-    @test_throws ArgumentError blackmanharris(128;term=2)
-    @test_throws ArgumentError nuttall(128;term=2)
+    @test_throws ArgumentError blackmanharris(128, 2)
+    @test_throws ArgumentError nuttall(128, 2)
 end
 
 zeroarg_wins = [rect, hanning, hamming, cosine, lanczos,
-    bartlett, bartlett_hann, blackman, blackmanharris,
-    nuttall, triang, flattop]
+    bartlett, bartlett_hann, blackman, triang, flattop]
 onearg_wins = [gaussian, kaiser, tukey]
+termarg_wins = [blackmanharris, nuttall]
 @testset "zero-phase windows" begin
     for winf in zeroarg_wins
         if winf == triang
@@ -156,6 +156,16 @@ onearg_wins = [gaussian, kaiser, tukey]
         @test winf(9, 0.5, zerophase=true) == ifftshift(winf(19, 0.5)[2:2:end])
     end
 
+    # Test the window functions that have the term arg (number of ceofficients)
+    for winf in termarg_wins
+        @test winf(8, 4, zerophase=true) == ifftshift(winf(9, 4)[1:8])
+        @test winf(9, 4, zerophase=true) == ifftshift(winf(19, 4)[2:2:end])
+    end
+    # 3-term blackmanharris and nuttall are a spocial case because of their odd
+    # number of coefficients
+    @test blackmanharris(6, 3, zerophase=true) ≈ [1.0, 0.632395, 0.134845, 0.0049, 0.134845, 0.632395]
+    @test nuttall(6, 3, zerophase=true) ≈ [1.0, 0.63391075, 0.13657015, 0.0053188, 0.13657015, 0.63391075]
+
     @test dpss(8, 2, 1, zerophase=true)[:] == ifftshift(dpss(9, 2, 1)[1:8])
     # odd-length zerophase dpss windows not currently supported
     @test_throws ArgumentError dpss(9, 2, 1, zerophase=true)
@@ -173,6 +183,10 @@ end
     @test Array{ft,1} == typeof(gaussian(n, 0.4)) && length(gaussian(n, 0.4)) == n
     @test Array{ft,1} == typeof(kaiser(n, 0.4)) && length(kaiser(n, 0.4)) == n
     @test Array{ft,2} == typeof(dpss(n, 1.5)) && size(dpss(n, 1.5),1) == n  # size(,2) depends on the parameters
+    @test Array{ft,1} == typeof(blackmanharris(n, 4)) && length(blackmanharris(n, 4)) == n
+    @test Array{ft,1} == typeof(blackmanharris(n, 3)) && length(blackmanharris(n, 3)) == n
+    @test Array{ft,1} == typeof(nuttall(n, 4)) && length(nuttall(n, 4)) == n
+    @test Array{ft,1} == typeof(nuttall(n, 3)) && length(nuttall(n, 3)) == n
 end
 
 @testset "tensor product windows" begin
@@ -212,4 +226,24 @@ end
             @test w3 ≈ w1 * w2'
         end
     end
+
+    for winf in termarg_wins,
+        arg in (3, 4)
+        for padding in (nothing, 4, (4,5)),
+          zerophase in (nothing, true, (true,false))
+            w1_expr = :($winf(15))
+            w2_expr = :($winf(20))
+            w3_expr = :($winf((15,20)))
+            w_all = (w1_expr, w2_expr, w3_expr)
+
+            push_args!(w_all, arg, Integer, identity)
+            push_args!(w_all, padding, Integer, s -> Expr(:kw, :padding, s))
+            push_args!(w_all, zerophase, Bool, s -> Expr(:kw, :zerophase, s))
+
+            w1 = eval(w1_expr)
+            w2 = eval(w2_expr)
+            w3 = eval(w3_expr)
+            @test w3 ≈ w1 * w2'
+        end
+    end
 end