Questions tagged [derivative]
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11
questions
8
votes
2answers
636 views
Bounds of the derivative of a bounded band-limited function
Let $f(t)$ be a function with properties:
$$\begin{array}{ll}
t\in\mathbf{R}&t\text{ is in reals}\\
f(t)\in\mathbf{R}\text{ for all } t&f(t)\text{ is in reals}\\
|f(t)|<A\text{ for all }t&...
4
votes
5answers
7k views
Derivative of noisy signal
My input signal is phase vector. I want to differentiate it to get frequency vector. My input signal is somewhat noisy. Here is the input signal.
This is the derivative of the input signal as ...
3
votes
2answers
561 views
Differentiation of sine in Fourier domain
The derivative of $\sin(\omega_o t)$ is $\cos(\omega_o t)$.
The Fourier transform of $\sin(\omega_o t)$ is $\frac{\pi}{j}[\delta(\omega-\omega_o) - \delta(\omega+\omega_o)]$.
Differentiation in the ...
0
votes
2answers
3k views
Compute the time derivative of a noisy digital signal?
The issue is that my signal is very noisy. I need extract its time derivative as accurate as possible. P.S. I do not have any prior knowledge on the signal (black box).
On forums some suggested ...
4
votes
2answers
3k views
derivative filter transfer function
In many of the papers it is said that the derivative filter transfer function is given by: $$H(z) = \dfrac{1}{8T}\left(-z^{-2} - 2z^{-1} + 2z + z^{2}\right)$$ But no one gave the detailed information ...
0
votes
2answers
4k views
Derivative filter in Python
In Alaa Kharbouch, Ali Shoeb, John Guttag, Sydney S. Cash,
An algorithm for seizure onset detection using intracranial EEG,
Epilepsy & Behavior,
Volume 22, Supplement 1,
2011 (section 2.1, 3rd ...
4
votes
1answer
2k views
What exactly is Savitzky-Golay differentiation filter?
I could understand Savitzky-Golay filter as being smoothing filter, but then there also seems to be Savitzky-Golay differentiation filter, though for some reason, details do not seem to be clear.
So ...
2
votes
4answers
248 views
Causal Noise Free 1st Order Derivative in Discrete Domain
I need to have causal noise free first order derivation (Derivative).
Now I am using a simple finite differences formula:
$$ \frac{ x \left( n \right) - x \left( n - 1 \right) }{ {T}_{s} } $$
The ...
1
vote
1answer
74 views
Frequency response of FM modulation/demodulation chain with phase derivative demodulation
Frequency modulating a carrier by white noise and then demodulating the complex signal using discrete derivative of phase it appears that the discriminator is acting as a low-pass filter.
How do I ...
0
votes
2answers
228 views
What are the implications of resampling the derivative of a signal with a higher frequency than the original signal?
Suppose I have a digital signal measured with sampling time, $T_s=1$ sec. If I take it's derivative, it will, naturally have $T_s=1$ sec. But what are the implications if I re-sample this derivative ...
0
votes
2answers
172 views
MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)
This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv
If $v \sim CN(0,2\sigma^2_v)$ ...
