Linked Questions
22 questions linked to/from What is "filter periodization"?
4
votes
4
answers
2k
views
Why to pad zeros at the middle of sequence instead at the end of the sequence?
One of the implementation of Bluestein algorithm as show in the below link
Bluestein's Algorithm
[conj(W), zeros(1, L-2*N+1), conj(W(N:-1:2)) ]
padding the zeros ...
- 669
4
votes
2
answers
675
views
Fourier transform of modulus of sum of sines
$$
x(t) = |\cos(\omega_0 t) + \cos(\omega_1 t)|
$$
with $\omega_0, \omega_1 > 0$.
Is there a known result for $\mathcal{F}\{x(t)\}$? Derivation not needed but is welcome. Of main interest is the ...
- 9,232
4
votes
3
answers
466
views
Spectrum Width vs Data Carrying Capacity
Newbie struggling to understand why a larger chunk of signal bandwidth is needed to carry more information. For example, why do you need more bandwidth to carry video as opposed to voice or CW? ...
- 41
7
votes
2
answers
940
views
Equivalence between "windowed Fourier transform" and STFT as convolutions/filtering
I've heard, that "windowed Fourier transform" is but one perspective on STFT, and that STFT is fundamentally convolutions of windowed complex sinusoids with the input, i.e. bandpass ...
- 9,232
1
vote
1
answer
958
views
Why does the bandwidth of a signal need to be half of the sampling rate? [duplicate]
Suppose I perform a DFT on some function with sampling rate of $\frac{1}{\Delta t}$. According to this page, the bandwidth, which is the maximum frequency that can be analyzed when performed the DFT, ...
- 119
-3
votes
2
answers
549
views
DFT modulus property?
We know fft(cos), and abs(cos) is just positive cos with halved period, so seems there ...
- 9,232
1
vote
1
answer
1k
views
Power/Energy from Continuous Wavelet Transform
How can power or energy be computed from Continuous Wavelet Transform? Is it just $\sum |\text{CWT}(x)|^2$, or are there other considerations, particularly if interested in a subset of frequencies?
Do ...
- 9,232
1
vote
1
answer
592
views
Subsampling in frequency domain? Effect of sampling rate on spectrum?
Given a sequence
$$
x[n] = [0, 1, 2, 3, 4, 5, 6, 7]
$$
and its subsampling (by e.g. factor of 2)
$$
x_\text{sub}[n] = [0, 2, 4, 6]
$$
are $x_\text{sub}$ and $x$ related in spectrum? That is, given $X =...
- 9,232
0
votes
1
answer
572
views
Why are there copies of a signal in the frequency domain? [closed]
I only know about this from images and some videos and articles I've read, but I haven't managed to find an explanation. It only says they exist.
This is what I mean:
Blue is the frequency domain of ...
- 73
0
votes
1
answer
601
views
Is online Continuous Wavelet Transform possible?
I have recently created a real-time STFT with 50% overlap.
I wanted to know if this window-based is possible for scalogram, especially continuous wavelet transform. I haven't found anyone ...
- 157
3
votes
1
answer
384
views
Sparse signal FFT
Say I had a time domain signal $x[k]$ wich is sparse: $\log(N)^2$ nonzero samples and the fourier transform has only a very (very!) small number of high frequency components. Are there any techniques ...
- 33
0
votes
1
answer
367
views
How to achieve a periodized Mexican hat wavelet with period L by using Python?
Now I have a scaled Mexican hat wavelet, i.e.
$$
\psi(a,x)=\frac{1}{\sqrt{a}}…\left(1-\frac{x^2}{a^2}\right)e^{-x^2/(2a^2)},
$$
which decays quickly along the x-axis. Here I want to define a ...
- 124
1
vote
1
answer
240
views
Having Nyquist bin = aliasing?
Here I motivate the question by deriving FFT upsampling for $N \rightarrow 2N$ with even $N$.
One might naively try xup = 2*ifft([xf[:N//2], zeros(N), xf[-N//2:]]), ...
- 9,232
3
votes
1
answer
360
views
Why are wavelet transforms implemented in Python/Matlab often called Continuous wavelet transform when they take discrete-time input?
The implementations of Synchrosqueezing wavelet transform in Python (ssqueezepy) and MATLAB both write in their documentation that they implement the synchrosqueezing algorithm on the Continuous ...
- 31
1
vote
2
answers
206
views
Multiplication term $ \frac{ 1}{T_s} $ in sampling theorem
\begin{equation}
X(\Omega) = \frac{ 1}{T_s} \sum ^{\infty}_{k=-\infty} X_a\left \lbrace \frac{\Omega /( 2 \pi) - k}{T_s}\right \rbrace
\end{equation}
What is the purpose of multiplying sampled ...
- 460