Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The DFT shift theorem implies that any circular shift in the input space is equivalent to a phase change in the frequency domain, while the absolute values are preserved.

$$ \mathcal{F}(\{x_{n-m}\})_k=\mathcal{F}(\{x_n\})_k\cdot e^{-\frac{2\pi i}{N}k m} $$

A circular shift can be represented as a multiplication by a particular orthogonal matrix, and DFT is a special kind of unitary transformation.

I wonder if there are generalizations of the shift theorem to wider classes of input transformations than circular shifts and DFT, such that the original transformation always looks like a phase change in the new representation?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.