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Is DCT differentiable? I.e. is d(DCT(x))/dx$$\frac{\mathrm{d}\mathrm{DCT}(x)}{\mathrm{d} x}$$ defined? I've

I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is positive, but I'm still missing a mathematical proof.

Is DCT differentiable? I.e. is d(DCT(x))/dx defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is positive, but I'm still missing a mathematical proof.

Is DCT differentiable? I.e. is $$\frac{\mathrm{d}\mathrm{DCT}(x)}{\mathrm{d} x}$$ defined?

I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is positive, but I'm still missing a mathematical proof.

Notice added Draw attention by Elliot Gorokhovsky
Bounty Started worth 50 reputation by Elliot Gorokhovsky
1

Is discrete cosine transform differentiable?

Is DCT differentiable? I.e. is d(DCT(x))/dx defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is positive, but I'm still missing a mathematical proof.