Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/
Questions tagged [signal-processing]
2068 questions
11
votes
3 answers
The definition of NMSE (normalized mean square error)
Many papers use the NMSE function without ever explicitly defining it. I have always assumed that
$$MSE(x,y)=\frac 1N \sum_i (x_i-y_i)^2$$
and
$$ NMSE(x,y)=MSE(x,y)/MSE(x,0) = \frac{\| x-y\|_2^2}{\| x\|_2^2}$$
where $y$ is the approximation to $x$.…
Gummi F
- 309
11
votes
2 answers
Speech processing pre-emphasis: how does it work?
In speech processing, the original signal usually has too much lower frequency energy, and processing the signal to emphasize higher frequency energy is necessary. To perform pre-emphasis, we choose some value α between .9 and 1. Then each value in…
Nate Glenn
- 323
6
votes
4 answers
why use complex numbers when representing periodic signals?
a large class of periodic signals can be defined with sinusoidals. but many texts introduce these and then use a representation of periodic signals that has sinusoidals with real and imaginary parts - like here:…
user9576
- 355
6
votes
3 answers
How can I interpret "energy" in signals?
I am learning about various signal processing methods in my university course, and I can't seem to grasp what 'energy' in signals represent. I mean, I know that it is the integral of the absolute value of energy squared (side question: why is…
thomas1234
- 335
6
votes
3 answers
Bases in compressed sensing (signal reconstruction)
I have been posting this kind of question in Cross Validated, but since this one deals almost entirely with mathematics, I will post it here.
In signal reconstruction using compressed sensing, we want to sample a signal $f$ in order to obtain a…
r_31415
- 2,934
6
votes
2 answers
What is the convolution of 2 dirac functions?
I ran into a problem, which wants to find the convolution $\delta (3-t) * \delta (t-2)$ and I am stuck. How can I approach it?
Mitsos
- 61
5
votes
2 answers
Spatially invariant systems
I was watching this video on spatially invariant systems:
And I found the definition a bit confusing, or seems vacuous, because isn't $T[x(n_1 - k_1, n_2 - k_2)] = y(n_1 - k_1, n_2 - k_2)$ always true by definition?
qed
- 1,083
4
votes
4 answers
What is the sum of a sinc function series sampled periodically
What is the sum of the following sinc series?
$$f(k,y)=\sum_{n=-\infty}^{\infty} \frac{\text{sin} \pi(kn-y)}{\pi(kn-y)}$$
where $k$ is an integer greater then zero
This question is a generalisation of What is the sum over a shifted sinc function?…
Daniel
- 99
- 5
4
votes
1 answer
$y(n) = x(-n)$ , causal or not , memory or memoryless?
$y(n) = x(-n)$ , causal or not , memory or memory-less ?
it's a question in digital signal processing course .
My guess it's memory less , causal because $x(-n)$ is only the inverse of the function ?
Memoryless System
A system is memoryless if…
xsari3x
- 187
3
votes
0 answers
Signal filtering and moving averages
Background
Given a signal $x_n$ for $n=1,2,\dots$ we can consider its filtered values:
$$y_n = \frac{b(L)}{a(L)}x_n$$
where $a(L)=a_0 + a_1L + a_2L^2 + \cdots + a_nL^n$ (similarly for $b$) and $L$ is the lag operator,
$$L^k x_n = x_{n-k}$$
and the…
Chris Taylor
- 28,955
3
votes
0 answers
Difference between Signal Processing and Filtering Theory
Here's a question.
I have been reading the entries on wikipedia on signal processing and the filtering problem. It seems as both theories are conserned with the processing or estimation of some "true" or underlying signal/parameter.
How is the…
fundamentals
- 31
3
votes
1 answer
Power of signal $x(t) = 2\operatorname{rect}(\sin(2\pi t))$
Assuming that $\operatorname{rect}(x)$ is the rectangular function:
$$ \operatorname{rect}(t) = \Pi(t) = \begin{cases} 0 &|t| >\frac{1}{2} \\ \frac{1}{2} & |t| = \frac{1}{2} \\ 1 & |t|< \frac{1}{2} \end{cases} $$
Find the power of the signal $x(t)…
3
votes
1 answer
What is boxcar averaging?
This is an application in signal processing but what I don't understand is how it's done algorithmically. I've seen some stuff online but most of it is just pictures. I would like an example on some type of sample data such as [0 1 2 3 4 5 6 7 8 9…
ranzy
- 31
3
votes
1 answer
Find the expression and the system impulse response
I've started to learn signal fundamentals and I have to do one exercise and I can't understand something.
It is said that $$x[n]=1.5\cos(0.025 \Pi n)(u[n+40]-u[n-40]))$$ and that the signal $u[n-m]$ is a unit step with the value $0$ for $n
Favolas
- 803
- 1
- 8
- 15
3
votes
1 answer
LULU Smoother, how is L and U combined?
https://en.wikipedia.org/wiki/Lulu_smoothing
I'm interested in using this approach to remove signal spikes from an analog sensor connected to a microcontroller. I understand the L and U operations, however the Wikipedia page fails to indicate how…
Cody Smith
- 231