Apodization

TransferFunctions.Apodization — Module

TransferFunctions.Apodization

Module defining apodization functions.

Apodization types Blackman, ExactBlackman, Connes, Cosine, Gaussian, Hamming, Welch, BlackmanNuttall, PowerCosine, Triangular, Nuttall, SineSum, BlackmanHarris, FlatTop and Hann

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TransferFunctions.Apodization.ApodizationFunction — Type

ApodizationFunction{T}

Abstract type for apodization functions with return values of type T.

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using TransferFunctions: Apodization as Apo

Apodization functions

TransferFunctions.Apodization.Blackman — Type

Blackman{T,α} == SineSum{T,((1 - α) / 2, 1 / 2, α / 2)} <: ApodizationFunction{T}

Blackman apodization function with the coefficient α (Defaults to α = 0.16).

See SineSum See also ExactBlackman

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TransferFunctions.Apodization.ExactBlackman — Type

ExactBlackman{T} == Blackman{T,683 // 4652}

See Blackman

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TransferFunctions.Apodization.BlackmanHarris — Type

BlackmanHarris{T} == SineSum{T,(0.35875, 0.48829, 0.14128, 0.01168)} <: ApodizationFunction{T}

See SineSum

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TransferFunctions.Apodization.BlackmanNuttall — Type

BlackmanNuttall{T} = SineSum{T,(0.3635819, 0.4891775, 0.1365995, 0.0106411)} <: ApodizationFunction{T}

See SineSum

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blackman = Apo.Blackman()
exact_blackman = Apo.ExactBlackman()
blackman_harris = Apo.BlackmanHarris()
blackman_nuttall = Apo.BlackmanNuttall()

TransferFunctions.Apodization.Connes — Type

Connes{T} <: ApodizationFunction{T}

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connes = Apo.Connes{Float64}()

TransferFunctions.Apodization.Cosine — Type

Cosine{T} == PowerCosine{T, 1} <: ApodizationFunction{T}

zero-phase function – $w₀(r) = \cos(πr/2)$
instrument function – $I(k) = 4\cos(2k)/(π(1 - 16k²))$

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cosine = Apo.Cosine{Float64}()

TransferFunctions.Apodization.Gaussian — Type

Gaussian{T} <: ApodizationFunction{T}

Gaussian apodization function with a given standard deviation σ.

zero-phase function – $w₀(r) = e^{-r²/2σ²}$

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gaussian = Apo.Gaussian(0.2)

TransferFunctions.Apodization.Hamming — Type

Hamming{T} == SineSum{T,(25//46, 21//46)} <: ApodizationFunction{T}

See SineSum

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hamming = Apo.Hamming{Float64}()

TransferFunctions.Apodization.Welch — Type

Welch{T} <: ApodizationFunction{T}

zero-phase function – $w₀(r) = 1 - r²$

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welch = Apo.Welch{Float64}()

TransferFunctions.Apodization.PowerCosine — Type

PowerCosine{T} <: ApodizationFunction{T}

zero-phase function – $w₀(r) = \cos(πr/2)^α$

Instances: Cosine and Hann

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TransferFunctions.Apodization.Triangular — Type

Triangular{T} <: ApodizationFunction{T}

Formulas: zero-phase function –$w₀(r) = 1-|r|$ \ instrument function – $I(k) = \mathrm{sinc}²(π k)$

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triangular = Apo.Triangular{Float64}()

TransferFunctions.Apodization.Nuttall — Type

Nuttall{T} == SineSum{T,(0.355768, 0.487396, 0.144232, 0.012604)} <: ApodizationFunction{T}

See SineSum

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nuttall = Apo.Nuttall{Float64}()

TransferFunctions.Apodization.SineSum — Type

SineSum{T,Cs} <: ApodizationFunction{T}

Sum of sines with coefficients Cs with output type of T

zero-phase function – $w₀(r) = ∑ᴺₖ₌₀ (-1)ᵏ Cs[k] \cos(πk(r + 1))$

Instances: Hamming, Nuttall, BlackmanNuttall, BlackmanHarris, FlatTop, Blackman and ExactBlackman

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TransferFunctions.Apodization.FlatTop — Type

FlatTop{T} = SineSum{T,(0.21557895, 0.41663158, 0.277263158, 0.083578947, 0.006947365)} <: ApodizationFunction{T}

MATLAB variant of the flat-top filter

See SineSum

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flat_top = Apo.FlatTop{Float64}()

TransferFunctions.Apodization.Hann — Type

Hann{T} == PowerCosine{T,2} <: ApodizationFunction{T}

Formulas: zero-phase function – $w₀(r) = \cos²(πr/2)$

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hann = Apo.Hann{Float64}()