Implementation of the Saviztky-Golay filter in julia version 1.0 or later. Adapted from: https://github.com/BBN-Q/Qlab.jl/blob/master/src/SavitskyGolay.jl

savitzkyGolay.jl

"""

Polynomial smoothing with the Savitzky Golay filters. Adapted for julia >= 1.0.

Sources: https://github.com/BBN-Q/Qlab.jl/blob/master/src/SavitskyGolay.jl

Requires LinearAlgebra and DSP modules loaded.

"""

function savitzkyGolay(x::Vector, windowSize::Int, polyOrder::Int; deriv::Int=0)
  
  isodd(windowSize) || throw("Window size must be an odd integer.")
  polyOrder < windowSize || throw("Polynomial order must me less than window size.")
  
  halfWindow = Int( ceil((windowSize-1)/2) )
  
  # Setup the S matrix of basis vectors
  S = zeros.(windowSize, polyOrder+1)
  for ct = 0:polyOrder
    S[:,ct+1] = (-halfWindow:halfWindow).^(ct)
  end
  
  ## Compute the filter coefficients for all orders
  
  # From the scipy code it seems pinv(S) and taking rows should be enough
  G = S * pinv(S' * S)
  
  # Slice out the derivative order we want
  filterCoeffs = G[:, deriv+1] * factorial(deriv)
  
  # Pad the signal with the endpoints and convolve with filter
  paddedX = [x[1]*ones(halfWindow); x; x[end]*ones(halfWindow)]
  y = conv(filterCoeffs[end:-1:1], paddedX)
  
  # Return the valid midsection
  return y[2*halfWindow+1:end-2*halfWindow]
  
end

The result from this function is not entirely correct. As someone else posted on StackOverflow, e.g

x=[1,2,3,4,5,6,7,8,9,10]
savitzkyGolay(x,5,1)

The expected values are exactly x, but the Julia results are not.

Can you provide the SO link please. Also, could you submit an issue here. Thanks for reporting.

You could also check this implementation to check.

Note that the values at the edges are actually not handled correctly.

Note that the values at the edges are actually not handled correctly.

Yes, exactly. I will submit an issue.

There is a standalone package for the Savitzky-Golay filter: check SavitzkyGolay.jl

Thank you for making this small package!