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An implementation of the Savitzky-Golay filter using generated functions. Accompanies https://medium.com/@acidflask/smoothing-data-with-julia-s-generated-functions-c80e240e05f3
"""
Savitzky-Golay filter of window half-width M and degree N
M is the number of points before and after to interpolate, i.e. the full width
of the window is 2M+1
"""
immutable SavitzkyGolayFilter{M,N} end
@generated function Base.call{M,N,T}(::Type{SavitzkyGolayFilter{M,N}},
data::AbstractVector{T})
#Create Jacobian matrix
J = zeros(2M+1, N+1)
for i=1:2M+1, j=1:N+1
J[i, j] = (i-M-1)^(j-1)
end
e₁ = zeros(N+1)
e₁[1] = 1.0
#Compute filter coefficients
C = J' \ e₁
#Evaluate filter on data matrix
To = typeof(C[1] * one(T)) #Calculate type of output
expr = quote
n = size(data, 1)
smoothed = zeros($To, n)
@inbounds for i in eachindex(smoothed)
smoothed[i] += $(C[M+1])*data[i]
end
smoothed
end
for j=1:M
insert!(expr.args[6].args[2].args[2].args, 1,
:(if i - $j 1
smoothed[i] += $(C[M+1-j])*data[i-$j]
end)
)
push!(expr.args[6].args[2].args[2].args,
:(if i + $j n
smoothed[i] += $(C[M+1+j])*data[i+$j]
end)
)
end
return expr
end
#Two sample invocations
@show SavitzkyGolayFilter{2,3}([1:11;])
@show SavitzkyGolayFilter{1,1}([1:11;])
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