Questions tagged [math]
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101
questions
0
votes
1answer
35 views
Absolute value based AM envelope detection viewed in the frequency domain
In my understanding when a passband AM signal is demodulated with an envelope detector taking the absolute value restores the original baseband version of the signal and the low-pass filter removes ...
0
votes
0answers
8 views
active contour without edges
i am new to image segmentation.i am studying chanvese ACWE paper1.This is level set equation of chan vese paper ACWE.
Above, μ,ν,λ1,λ2 are real parameters, c1,c2 are constants determined for ...
0
votes
0answers
12 views
Spread out flux in 2D gaussian
I want to generate a 2D Gaussian model with flux spread out for a given radius. From theory, I found out that the total integrated flux of a Gaussian model. Now I want to image it such that total flux ...
0
votes
1answer
125 views
Separation of signals without loss of information about the signals themselves
There is a signal that contains:
Rectangular pulses on frequency of 1 kHz
Rectangular pulses on frequency of 1.4 kHz
Other noises.
Required:
Separate 1kHz pulses from everything else and measure ...
1
vote
1answer
42 views
Dummy DSP student request for IDTFT Calculation and Integration Process
We have one DSP course in biomedical engineering, so i have been for 10 years away from mathematical calculation and working in this years by programing by c and ..., so one of our exercise is to ...
0
votes
0answers
42 views
Solving equation with convolution
I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$:
$$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$
where $\ast$ is the convolution.
I know $A(f)$, $B(f)$,...
2
votes
0answers
528 views
Derivation of ZOH Discretization
I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps.
I think I understand the first part, this is just the ...
0
votes
1answer
21 views
Why is the anisotropic diffusion equivalent to the heat equation when using a constant diffusion coefficient?
The anisotropic diffusion is defined as
$$\frac{\partial I}{\partial t} = \mathrm{div} \left( c(x,y,t) \nabla I \right)= \nabla c \cdot \nabla I + c(x,y,t) \Delta I$$
where $\operatorname{div}$ is ...
0
votes
2answers
194 views
Resolution of Discrete Fourier Transform is 1/T - Mathematical proof?
In many articles I see that the frequency resolution of the Discrete Fourier Transform (DFT) equals Fs/N where Fs is the sampling rate and N is the total number of samples. Fs/N is equivalent to 1/T ...
0
votes
0answers
88 views
Power, energy and amplitude spectrum from fft in MATLAB - scaling
I've looked at previous answers and none of the answers seem to agree (perhaps I'm missing something obvious):
I would like to know what the correct scaling to use is for
amplitude,
energy and
power ...
0
votes
0answers
54 views
How to find the filter coefficient of matched filter to detect the pulse of a signal?
I would to understand how to find the coefficient of a matched filter.
Let's consider we have a signal and the signal is buried in the following noise. we want to find the coefficient of a matched ...
0
votes
0answers
20 views
How to match resolution of two or more signals
I have received the following 4 time-series signals and wanted to do some data analytics using these. Although the sampling is the same for all of these signals, 2 samples per second, problem is that ...
0
votes
0answers
38 views
On $H_\infty$ norm for transfer function
For a given scenario in the context of control system, I'm trying to investigate how the $H_\infty$ norm can be calculated for a transfer function as follows:
$$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
0
votes
2answers
280 views
Differential Equations applications in Signal Processing [closed]
Does differential and partial differential equations subject has applications in Signal Processing? I have basic DSP background and know Matrix algebra and Fourier transforms very well, but I am not ...
0
votes
1answer
111 views
How to find the impulse response of filter that outputs the autocorrelation of the input?
I am trying to solve question 9.61 in the attached image.
I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
1
vote
2answers
107 views
Check whether a given equation is linear
$ a = (x, y) \in \mathbb{Z}^2 $ is given as a pixel. My equation in which $g$ is image(matrix) is defined as,
$f(x, y) = 56g(x,y)+93g(x−1,y)+92g(x+1, y)−57g(x, y−1)+555g(x, y+1) $
How can we know ...
0
votes
1answer
47 views
how to set Equalizer's coefficient using generalized eigenvector.
In that paper https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2012-72 .. Equation 3,
$J(w) = w^HBw/w^HCw$ ..
$B$ and $C$ are matrices, $w$ the filter coefficients vector ...
0
votes
2answers
587 views
What does it mean for a function to have frequencies?
In a lecture, my professor mentioned that $\cos$ has two frequencies. I see that using the inverse Euler's formula we can express $\cos$ as a some linear combination of complex exponentials, each with ...
1
vote
1answer
57 views
Intuitive understanding of frequency
I know that $f = \frac{\text{cycles}}{\text{unit of time}}$ and I know that period $T = \text{time it takes to complete one cycle}$.
So if we take the definition
$f = \frac{1}{T} = \frac{\text{1 ...
1
vote
2answers
43 views
Rearranging exp terms
I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but I‘m not able to spot my mistake.
I know the solution (since i looked it up with wolfram alpha) ...
0
votes
1answer
28 views
Equation Derivation: Help with intermediate steps
As per the attached image above, I don't know how the equation in the first line transformed to the form in second line.
I tried solving it by multiplication but the result was different.
1
vote
1answer
398 views
Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation
While I was reading SIFT paper(Lowe, 2004), I came across the method that he apply "heat diffusion equation" to Gaussian function to derive that
$$ \frac{∂G}{∂σ}
= σ∇^2G
$$
I searched Wikipedia and ...
0
votes
1answer
75 views
How to measure the distance between two circle-like-lines over 360 degree
I am looking for a slim and with that quickly programmable image processing strategy to measure the distance between two circles over 360°. It is important to notice that the circles are not perfect, ...
1
vote
1answer
61 views
How to prove Line Spectral Pair coefficient properties?
I am trying to understand the definition of LSP coefficients from http://www.dspcsp.com/pdf/lsp.pdf.
We take the polynomial $a(x)$ of degree $M$ from the denominator of the LPC system function, and ...
0
votes
1answer
60 views
Explicit a succession using z inverse transform
Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?:
$ y(0) = 1 \\ y(n+1) = 2y(n) + 3 $
I can't write ...
0
votes
0answers
39 views
Relationships between $f(t)$ signal and $f(t) \times \sin(\omega t)$ signal
Let's assume that there is a signal $f(t)$, $0\le t \le T$. Then, is there any special meaning of the signal $g(t) =f(t) \times \sin(\omega t)$? Like AM transmission. What is shown/heard when we play ...
1
vote
0answers
217 views
NMSE of complex numbers
Actually I am doing an RF measurement and this includes phase and power. i generate a list of powers ranging for example from (-50 to 40) dBm, while the phase rotate to make it for example spiral ...
0
votes
2answers
155 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 $v \sim CN(0,2\sigma^2_v)$ ...
0
votes
2answers
68 views
MLE formulation — confusion regarding the terms in the equation (Part1)
If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model
$$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
0
votes
0answers
67 views
What kind of math is introduced in this answer related to DSP?
What kind of math is introduced in this answer:
https://dsp.stackexchange.com/a/40225/30897
It smells like standard linear algebra course (which I haven't studied, yet), but is it only that?
Thanks!
0
votes
1answer
93 views
How does the assumption that symbols are equi-probable hold
If I draw a number uniformly between zero and one, what is the probability that they are equal? Mathematically, it should be zero but I don't recall why? Can somebody please help in explaining why the ...
1
vote
2answers
491 views
Autocorrelation of a Shifted Sequence
Suppose I have a sequence $x[k]$ with $\mathcal{Z}$-transform
$$ X(z) = x_{0} + x_{1}z^{-1} + x_{2}z^{-2} + \ldots + x_{N-1}z^{N-1}$$
I know that for real-valued $x[k]$ the $\mathcal{Z}$-transform ...
-1
votes
1answer
112 views
BIBO Stability of a piecewise function
I have a function $y$ defined as
$$
y(t) =
\left\{\begin{array}
~t~ \mbox{ where} |t| \le 3\\
0~ \mbox{ otherwise}
\end{array}
\right .
$$
With a system defined as
$$G(t) = ty(t), $$
is it BIBO ...
1
vote
1answer
239 views
Drawing the modulus from a Transfer function
As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks
In this exercise from an exam i was given that transfer function with poles and ...
0
votes
1answer
70 views
How is this was derived? DTFT for symmetric pulse
do not understand how the middle expression was derived from above expression,
after all summation\multiplication i get:
$$\frac{e^{-jwN} + e^{jwN} - e^{-jw(N+1)} + e^{jw(N+1)}}{2 - e^{-jw} - e^{jw}...
3
votes
2answers
350 views
Mathematical relationship between highpass and lowpass filtering
Let $g, h_{HP}, h_{LP}: \mathbb{R} \rightarrow \mathbb{R}$ and $G, H_{HP}, H_{LP}$ denote their continuous Fourier transforms under the Fourier operator $\mathcal{F}$. Let $*$ denote the continuous ...
1
vote
1answer
57 views
Should zero element be considered to calculate mean when smoothing spectrogram by window?
My (mass spectrometry) spectrogram does not measure the intensity constantly. I obtain the spectrogram, for example,
...
0
votes
1answer
222 views
What is stochastic differential equation and its need?
A white noise process can be simulated using the Matlab command randn(). The numbers will be drawn from a Normal distribution of zero mean and variance 1.
Is the ...
1
vote
2answers
454 views
Closed form expression for $\sum_{k=0}^{n} \alpha^{-k}$?
I have seen this sum a couple of times now in the textbook and in the problems book but I don't know how to solve it. I know this might be more suited for math.stackexchange but since this is a fairly ...
3
votes
3answers
876 views
What is the meaning of this notation?
I have seen this notation in the book Schaums-Outline a couple of times now and I can't quite understand it. I'd very much appreciate if someone explained what it means. I am thinking that it means ...
1
vote
0answers
141 views
What is the difference between entropy and entropy rate and which one is important in information theory? [duplicate]
By entropy I understand the uncertainty or randomness. But if the uncertainty is high then what is its implication and advantage in transmitting information or as an information source or is high ...
0
votes
1answer
982 views
Z-transform of an impulse signal in discrete time
am trying to compute the Z-transform of the following signal
\begin{equation*}
x\left[n\right]\:=\:\sum_{k=-\infty \:}^{\infty \:}\:\delta \:\left[n-k\right]
\end{equation*}
so I thought it would be
\...
-1
votes
1answer
33 views
Why GCD(1+D, 1+D^2) = 1+D?
I'm reading Digital Communications, Proakis, and in order to classify an encoder as catastrophic or noncatastrophic I need the GCD of the elements in the generator G(D).
I don't really know what kind ...
8
votes
3answers
2k views
Replacing “e” in Euler's formula with another number
Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$.
I tried this idea in ...
1
vote
1answer
54 views
Proving Convergence of a limit related to Cross-Spectrum Estimation
Proving asymptotic covariance of Cross-Spectrum Estimation I came across this mathematical problem:
Consider two constants $M,L$ such that $M\to \infty, L \to \infty \hbox{ and } \frac{L}{M} \to 0$, ...
2
votes
0answers
160 views
Career Question: As a person who likes math is signal processing a career that's worth it?
I like high level math and I love deep theory based math.
In industry will I use high level math and theory to implement my own algorithms?
I love high level math but I do not love probability (...
-1
votes
1answer
78 views
Is it mathematically possible to compute Fourier transform without comparing the signal?
If I'm correct, Fourier transform lets me know the magnitude and phase of any given frequency in a signal.
I have a sampled signal and I want to compute its Fourier transform (any frequency) without ...
0
votes
1answer
35 views
Help with Determinants [closed]
Okay so i understand the first det, which is why i got the correct solution. However for the second det, im not sure how to solve it since because of the different coefficents (0,2,4) and i tried of ...
1
vote
2answers
90 views
What is this theorem in this formula?
I just read a paper yesterday and there is confusion:
I want to know what is reconstruction fidelity term and the theorem of changing the formula from upper to lower one. Is this theorm from ...
-2
votes
0answers
42 views
Directional derivative [closed]
I know that D ⃗ v f = ∇ f ⋅ ⃗ v Dv→f=∇f⋅v→ is the directional derivative. My question is why must the vector ⃗ v v→ be a unit vector? I am sure there is an obvious answer, but my book doesn't really ...
