                  DCT-II, IDCT-II/DCT-III minimal notes.
                  --------------------------------------

  As is mentioned elsewhere in this archive these two Python scripts are the
  absolute bare minimum that conforms to scipy's DEFAULT "type=2";
  "norm=None" or "norm='backward'".
  It is easy to change the 'DFT_Multiplier' scaling to say 'ortho' by adding
  two 'if' statements to the script like this in the DCT-II, (IDCT-II)
  minimal scripts, shown is the DCT-II, IDCT-II is similar:-

def DCT_II(data):
	N=len(data)
	DCT_II_Results=[0.0]*N

	for data_position in range(0, N, 1):
		SUM=0.0
		for element in range(0, N, 1):
			SUM=SUM+float((data[element])*math.cos((math.pi*float(data_position)*(2.0*float(element)+1.0))/(2.0*float(N))))
		if data_position==0: DFT_Multiplier=2.0
		if data_position>=1: DFT_Multiplier=2.0
		DCT_II_Results[data_position]=(DFT_Multiplier*SUM)
	return(DCT_II_Results)

  Also if you intend to always 'start' at 0, then 'start=0.' can be removed
  and the for loops hard coded to zero, 0, as shown.
  Because there are a few differing methods of the minimal scripts scaling
  in use the demo shown above is left as scipy's DEFAULT.
  Note that the intialising of 'DFT_Multiplier=2.0' has been removed also
  but now you can change the scaling to suit your needs...

  A useful piece of reference is here:-

 https://docs.scipy.org/doc/scipy/reference/generated/scipy.fftpack.dct.html

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