Implementation of Savitzky Golay in Julia - julia

Question

I have come across an implementation of SG-filter in Julia at this link. When I execute the function apply_filter, an error is returned -
UndefVarError: apply_filter not defined
I think this is an implementation for a previous version of Julia (?). I am executing this in Julia 1.0 as of now. Couldn't find documentation about the defined types, which is where my guess is concerning the error

Answer 1

I would like to forewarn the user about using the function savitzkyGolay in Julia. There is a mismatch with the result from Scipy implementation (which must have undergone several iterations of checking by the community)
#pyimport scipy.signal as ss
x=[1,2,3,4,5,6,7,8,9,10]
savitzkyGolay(x,5,1)
10-element Array{Float64,1}:
1.6000000000000003
2.200000000000001
3.0
4.0
5.000000000000001
6.000000000000001
7.0
8.0
8.8
9.400000000000002
#Python's scipy implementation
ss.savgol_filter(x,5,1)
10-element Array{Float64,1}:
1.0000000000000007
2.0000000000000004
2.9999999999999996
3.999999999999999
4.999999999999999
5.999999999999999
6.999999999999998
7.999999999999998
8.999999999999996
9.999999999999995

Answer 2

If it can help, I have simplified the code.
using Pkg, LinearAlgebra, DSP, Plots
function vandermonde(halfWindow, polyDeg)
x=[1.0*i for i in -halfWindow:halfWindow]
n = polyDeg+1
m = length(x)
V = zeros(m, n)
for i = 1:m
V[i,1] = 1.0
end
for j = 2:n
for i = 1:m
V[i,j] = x[i] * V[i,j-1]
end
end
return V
end
function SG(halfWindow, polyDeg)
V = vandermonde(halfWindow,polyDeg)
Q,R=qr(V)
n = polyDeg+1
m = 2*halfWindow+1
R1 = vcat(R, zeros(m-n,n))
sg = R1\Q'
for i in 1:(polyDeg+1)
sg[i,:] = sg[i,:]*factorial(i-1)
end
return sg'
end
function apply_filter(filter,signal)
halfWindow = round(Int,(length(filter)-1)/2)
padded_signal = [signal[1]*ones(halfWindow);signal;signal[end]*ones(halfWindow)]
filter_cross_signal = conv(filter[end:-1:1], padded_signal)
return filter_cross_signal[2*halfWindow+1:end-2*halfWindow]
end
Here is how I use it :
mean_speed_unfiltered = readdlm("mean_speeds_raw_-2.txt")
sg = SG(500,2); # halt-window, polynomal degree
t = 10*10^(-3)#s #time of the simulation
dt = 0.1/γ; #time step
Nt = convert(Int, round(t/dt)); #number of iteration
#Smooth the mean speed curve:
mean_speeds_smoothed = apply_filter(sg[:,1],mean_speed_unfiltered)
png(plot([j*dt for j=0:Nt] , mean_speeds_smoothed, title = "Smoothed mean speed over
time", xlabel = "t (s)"), "Mean_speed_filtered_SG")
derivative_mean_speeds_smoothed = apply_filter(sg[:,2],mean_speed_unfiltered)
plt1 = plot(mean_speeds_smoothed,derivative_mean_speeds_smoothed, title = "derivative mean speed over speed", xlabel = "<v>(t) (s)", ylabel = "d<v(t)>/dt")
png(plt1, "Force_SG_1D2Lasers")
However it seems to me that the code presented in https://gist.github.com/lnacquaroli/c97fbc9a15488607e236b3472bcdf097#file-savitzkygolay-jl-L34 is faster.