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
2
votes
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$μ$-law: What operation is being performed in the $μ|x|$ portion of the algorithm?
According to wikipedia $\mu$-law is:
$$F(x) = \operatorname{sgn}(x)\frac{\ln(1+\mu|x|)}{\ln(1+\mu)} \qquad -1\le x \le 1$$
where $μ = 255$ ($8$ bits) in the North American and Japanese standards (This is a signal processing algorithm).
What…
Chris Tarn
- 121
2
votes
1 answer
Frequency Swept sine wave -- chirp
I am experiencing what I think is really simple confusion.
Take $y(t) = \sin(2 \cdot \pi \cdot t \cdot\omega(t))$
and $\omega(t) = a \cdot t+b$ for $t \in [0,p)$ and let $\omega(t)$ have a periodic extension with period $p$. The values $a,b,p$ are…
Gus
- 1,491
2
votes
1 answer
Specific question about downsampling in frequency domain
I'm confused about why Equation 4.74 can be expressed as Equation 4.76 after the summation index is expressed as in Equation 4.75. Could somebody please explain? Thanks!
Downsampling DTFT
Mega Corsair
- 23
- 2
2
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0 answers
Extracting a Cosine Function from a Linear Combination of Cosines
I have a frequency modulated signal which must contain only $ g(t)=B.\cos(\omega(t).t+\phi)$, but it gets the form as below
$$ f(t)=B.\cos(\omega(t).t+\phi)+A_1.\cos(\omega(t-t_1).t+\phi_1)+A_2.\cos(\omega(t-t_2).t+\phi_2)+...$$
where $$A_k<
Kami A
- 21
2
votes
0 answers
ICA obsession with gaussianity
There are two reasons to focus on "gaussianity". (1) Orthogonal transformations of gaussian distributions are again gaussian. (2) Mixing of signals tends to a gaussian distribution via Central Limit Theorem. The latter is very good reason, but I…
user3391229
- 151
2
votes
2 answers
wave separation
Say there is a wave of sines and cosines. (<- one can think of Fourier theory.)
A) There is a wave that has the same frequency all the time. However, amplitude (- shape) of each period differs. Is it possible to separate this wave into combinations…
user27515
- 895
2
votes
1 answer
Nyquist–Shannon sampling theorem shannon's proof
In Wikipedia, there is Shannon's proof on Nyquist-Shannon sampling theorem. ( http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#Shannon.27s_original_proof )
The original proof presented by Shannon is elegant and quite brief, but…
user27515
- 895
2
votes
2 answers
How to derive FWHM of sinc function
So this is probably a simple question, but I am unable to get my head around it. If we have $\operatorname{sinc}(2 \pi v L)$, what is the width of that $\operatorname{sinc}$ in terms of $v$ at half the maximum point.
Normally I'd just say that the…
user209848
2
votes
1 answer
Is this solution correct? [Discrete-time signals and systems]
Consider this question taken from Oppenheim - Discrete-time Signal and Systems:
Now consider its solution (from the Solutions manual)
My question is: is the solution for itens (a) and (b) valid? It considers a sequence with only one sample in both…
Frias
- 95
- 3
2
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Detection theory - Sensitivity, Specificity - in Multi-Detection scenario
I am working in computer vision and have this scenario:
For each frame of a video sequence I have the following:
Image with a resolution of width * height discrete pixel locations.
List of "detections" (e.g. from HaarCascadeClassifier)…
Micka
- 131
2
votes
1 answer
Show that for a real impulse response function the response to a sine input is ...
Working on this problem on linear invariant systems in signal processing, but unsure if I've got the right answer:
Show that for a real impulse response function of $H(\omega)$, the response to a sine input of $\sin(\omega_0 t)$ is the imaginary…
George93
- 41
1
vote
0 answers
Cross-talk filter with known source
Hello fellow Stackers,
This question was also posted on StackOverflow, but perhaps this is a more suitable location for this question. I currently work in an experimental rock mechanics lab, and when I conduct an experiment, I record the output…
MPA
- 165
1
vote
2 answers
I want to know whether the following is periodic or not periodic
I have a question about system properties of the following function whether it is periodic or aperiodic.
With an insight, I'd determine the function is aperiodic since the unit-step term looks implying that jump discontinuities occur at odd number…
MathEW
- 13
1
vote
1 answer
Hilbert transform pair
We know the Hilbert transform is defined as:
$$
y(t)=\mathcal{H}(x(t))=\operatorname{P.V.}\ \left\{x(t)*\frac{1}{\pi t}\right\}
$$
In the frequency domain this is equivalent to:
$$
Y(f)=X(f)\times (-j\operatorname{sgn}(f))
$$
Using this twice, we…
Robert Fan
- 759
1
vote
0 answers
use wavelet transform to analyze signal
let us suppose that we have following signal
function [ x ] = generate1(N,m,A3)
f1 = 100;
f2 = 200;
T = 1./f1;
t = (0:(N*T/m):(N*T))'; %'
wn = randn(length(t),1); %zero mean variance 1
x = 20.*sin(2.*pi.*f1.*t) + 30.*cos(2.*pi.*f2.*t) +…
dato datuashvili
- 9,194