An implementation of the Savitzky-Golay filter using generated functions. Accompanies https://medium.com/@acidflask/smoothing-data-with-julia-s-generated-functions-c80e240e05f3

savitzkygolay.jl

"""
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;])

I have added a line for derivatives computations

struct SavitzkyGolayFilter{M,N,deriv} end
@generated function (::SavitzkyGolayFilter{M,N,deriv})(data::AbstractVector{T}) where {M, N, deriv, 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)/factorial(j-1)
            end
            e₁ = zeros(N+1)
            e₁[deriv+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[3].args[2].args, 1,
                    :(if i - $j ≥ 1
                        smoothed[i] += $(C[M+1-j])*data[i-$j]
                      end)
                )
                push!(expr.args[6].args[3].args[2].args,
                    :(if i + $j ≤ n
                        smoothed[i] += $(C[M+1+j])*data[i+$j]
                      end)
                )
            end

            return expr
end