# Tag Info

### Under what conditions does DFT(f(x)) = f(DFT(x)) hold?

The fft is an efficient computation of the DFT. So your question is about the DFT, not the fft. The DFT of a signal can be ...
Accepted

Accepted

### Decomposing Sobel Filter

The decomposition of a separable filter is not unique, since $u v' = (u a) (v a^{-1})'$ The solution you are expecting is found by using a $-\sqrt{2}$ factor, namely ...

### Proof of complex conjugate symmetry property of DFT

Remember that $e^z$ has a very different meaning than $e^x$ (taking $z\in\mathbb{C}$ and $x\in\mathbb{R}$). If the exponent was real, then, as you state in your question: $$e^x = 1 \iff x=0$$ ...

### Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

The main advantage of OMP is that the residual is orthogonal to the current solution. Let's say you select all $k$ columns from $A$ (also called atoms) at once and let us also presume that $A$ is an ...

### Under what conditions does DFT(f(x)) = f(DFT(x)) hold?

One (almost trivial) function is the ifft. So fft(ifft(x))=ifft(fft(x)).

### Accessing Maximum Value from a Singular Value Decomposed Matrix

[EDIT: some code made available] A common framework for (multivariate) image processing is to suppose that its useful features (edges, textures, spectral correlation) contain redundancy, while the ...

### Sequential Form of the Least Squares Estimator for Linear Least Squares Model

There are really great answers. I will try to give the Sequential Least Squares approach which generalizes to any Linear Model. Sequential Least Squares Model We're after solving the Linear Least ...