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Add Nuttall window (3-term and 4-term)
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Lines changed: 348 additions & 8 deletions

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‎docs/src/windows.md‎

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@@ -13,6 +13,7 @@ gaussian
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bartlett_hann
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blackman
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blackmanharris
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nuttall
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kaiser
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flattop
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dpss

‎gen/gen_winplots.jl‎

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@@ -25,6 +25,7 @@ open(joinpath(@__DIR__, "..", "src", "winplots.jl"), "w") do io
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(bartlett_hann, ()),
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(blackman, ()),
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(blackmanharris, ()),
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(nuttall, ()),
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(kaiser, (3)),
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(flattop, ()),
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(dpss, (2, 1)),

‎src/windows.jl‎

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@@ -17,6 +17,7 @@ export rect,
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bartlett_hann,
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blackman,
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blackmanharris,
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nuttall,
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kaiser,
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flattop,
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dpss,
@@ -514,6 +515,57 @@ function blackmanharris(n::Integer; term::Integer=4, padding::Integer=0, zeropha
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end
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end
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"""
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$nuttall_winplot
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nuttall(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
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nuttall(dims; term::Integer=4, padding=0, zerophase=false)
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Nuttall window of length `n` with `padding` zeros. These windows can be seen as
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the improved version of the Blackman-Harris windows with regard to maximum
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sidelobe level. The number of terms can be selected with `term` ∈ [3,4]. For
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`term = 3`, the maximum sidelobe level is about -71.48 dB, while for `term = 4`
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(the default), it improves to -98.17 dB.
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The 3-term window `w3(x)` and the 4-term window `w4(x)` are defined by sampling
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the following continuous functions in the range `[-0.5, 0.5]`:
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w3(x) = 0.4243801 + 0.4973406*cos(2π*x) + 0.0782793*cos(4π*x)
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w4(x) = 0.3635819 + 0.4891775*cos(2π*x) + 0.1365995*cos(4π*x) + 0.0106411*cos(6π*x)
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For more details see [Nuttall, A. H. (1981). Some windows with very good
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sidelobe behavior. IEEE Transactions on Acoustics, Speech, Signal Processing,
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29, 84-91](https://ieeexplore.ieee.org/document/1163506)
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The `nuttall` windows do not generally satisfy the Constant Overlap-Add
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(COLA) property. Nevertheless, when using `zerophase = true` and implementing the
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following boundary conditions they approximately do:
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- For the 3-term window the overlap should be 66% and the window length should
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be a multiple of 3.
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- For the 4-term window the overlap should be 75% and the window length should
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be a multiple of 4.
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$(twoD_docs())
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$zerophase_docs
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"""
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function nuttall(n::Integer; term::Integer=4, padding::Integer=0, zerophase::Bool=false)
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if term == 4
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a0, a1, a2, a3 = 0.3635819, 0.4891775, 0.1365995, 0.0106411
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makewindow(n, padding, zerophase) do x
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muladd(a1, cospi(2x), muladd(a2, cospi(4x), muladd(a3, cospi(6x), a0)))
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end
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elseif term == 3
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a0, a1, a2 = 0.4243801, 0.4973406, 0.0782793
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makewindow(n, padding, zerophase) do x
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muladd(a1, cospi(2x), muladd(a2, cospi(4x), a0))
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end
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else
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throw(ArgumentError("`term` must be either 3 or 4"))
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end
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end
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"""
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$kaiser_winplot
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@@ -745,7 +797,7 @@ function matrix_window(func::F, dims::Tuple{Integer,Integer}, arg::Union{RealOr2
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end
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for func in (:rect, :hanning, :hamming, :cosine, :lanczos,
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:triang, :bartlett, :bartlett_hann, :blackman, :blackmanharris, :flattop)
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:triang, :bartlett, :bartlett_hann, :blackman, :blackmanharris, :nuttall, :flattop)
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@eval function $func(dims::Tuple{Integer,Integer}; padding::IntegerOr2=0, zerophase::BoolOr2=false)
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return matrix_window($func, dims; padding, zerophase)
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end

‎src/winplots.jl‎

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@@ -243,6 +243,26 @@ const blackmanharris_winplot = padplot("""
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└──────────────────────────────────────────────────────────────────────┘
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1 69 """)
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const nuttall_winplot = padplot("""
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┌──────────────────────────────────────────────────────────────────────┐
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1 │ ▄▀▀▀▀▀▀▄ │
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│ ▗▀ ▀▖ │
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│ ▞▘ ▝▚ │
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│ ▞ ▚ │
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│ ▗▀ ▀▖ │
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│ ▗▘ ▝▖ │
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│ ▗▘ ▝▖ │
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│ ▗▘ ▝▖ │
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│ ▄▘ ▝▄ │
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│ ▞ ▚ │
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│ ▗▞ ▚▖ │
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│ ▗▄▘ ▝▄▖ │
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│ ▗▞▘ ▝▚▖ │
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│ ▄▞▘ ▝▚▄ │
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0 │▄▄▄▄▄▄▄▄▄▞▀▀ ▀▀▚▄▄▄▄▄▄▄▄▄│
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└──────────────────────────────────────────────────────────────────────┘
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1 69 """)
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const kaiser_winplot = padplot("""
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┌──────────────────────────────────────────────────────────────────────┐
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1 │ ▗▄▀▀▀▀▀▀▄▖ │

‎test/data/nuttall_3term_128.txt‎

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‎test/data/nuttall_4term_128.txt‎

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