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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.

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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.