All Questions
Tagged with fourier-transform signal-analysis
9 questions with no upvoted or accepted answers
4
votes
0
answers
171
views
Convergence of integral formula for Fourier inversion (and Hilbert transform) for integrable piecewise-smooth functions
I asked the question below on Math Stack Exchange, https://math.stackexchange.com/questions/2592555/convergence-of-integral-formula-for-fourier-inversion-and-hilbert-transform-fo, but [despite it ...
- 708
3
votes
0
answers
106
views
A new arranging of discrete sine transform
Let $n$ be even and consider the discrete sine transform of type 5 which is the matrix
$$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$
Let us denote by $s_{-,l}$ the $l^{\text{...
- 4,058
2
votes
0
answers
127
views
eigenvectors of a graph Laplacian VS Fourier basis
Could you please illustrate the following statement:
the eigenvectors of a
graph Laplacian behave similarly to a Fourier basis, motivating
the development of graph-based Fourier analysis theory.
- 4,058
1
vote
0
answers
69
views
Is there an generalisation of convolution theorem to integral transforms
Basic convolutions can be computed efficiently by taking fourier transforms and applying the convolution theorem. Is there something analogous for a more general transform, where we have a varying ...
1
vote
0
answers
57
views
The meaning of the frequency in continuous signals
Suppose that for a given signal $x:\mathbb{R}\to \mathbb{C}$ both of the following Fourier identities hold.
$$ \hat{x}(\omega)=\int_\mathbb{R} x(t)e^{-it\omega} dt~~~,~~~x(t)=\frac{1}{2\pi} \int_\...
- 4,058
1
vote
0
answers
40
views
Fitting an inverse DFT within predefined bounds
My problems starts out with a variable length of samples. Usually, it is 1024 or higher powers of 2. The DFT of this "signal" is taken and only the amplitude spectrum is retained and the phase ...
- 111
1
vote
0
answers
138
views
Proof that two vectors can not have the same power spectrum when one is a permutation (excluding rotations) of the other?
The power spectrum being the absolute value of the DFT of the vector.
Has it been proven that two vectors can not have the same power spectrum if one is a permutation of the other? Where, in this ...
1
vote
0
answers
41
views
Multidimensional Filters
Say you want to design a LP FIR filter with low pass cutoff $fc$, transition band $fc$ to $fs$ and ripple factor $dp$ at passband and $ds$ at stop band. If one divides the frequencies by $\pi$, then $...
- 13.9k
0
votes
0
answers
113
views
Is this formula for 2D Fourier integral of diffraction kernel correct?
Well I have a function parametrized by $z$
$$g_z(x,y) = \frac{z}{i \lambda r^2} e^{i k r}, \quad r = \sqrt{x^2+y^2+z^2},$$
where $\lambda > 0$ is real constant and $k = \frac{2\pi}{\lambda}$. This ...
- 151