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I don't understand the use of scale factors, why do we need them? Can we not use them or are they essential?

The wikipedia page on DCT II shows this: https://en.wikipedia.org/wiki/Discrete_cosine_transform

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  • $\begingroup$ Could you add some references? I don't know to which uses are you referring to. $\endgroup$
    – Tendero
    Commented Jan 7, 2017 at 17:03

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Scale factors ensure the normality of each DCT vector. Since the vectors are already orthogonal, factors are needed whenever the orthonormality of the DCT is needed (often compression, denoising). For visualization, comparison, feature extraction, scaling factors may be less important.

For operation efficiency, especially when integer arithmetic is used, the scaling factor can be incorporated afterward, in the quantization stage when used in compression.

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    $\begingroup$ But what if it was for a simple 1 dimension dct? When I don't use the factors my cosine sums are shifted up by a factor, what is going on? $\endgroup$
    – Nicolas du Roy
    Commented Jan 12, 2017 at 10:22

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