Questions tagged [math]
The math tag has no usage guidance.
121
questions
0
votes
0answers
13 views
Is it important to learn to find de period of the sum fo two DT signals?
The fundamental period (N) of the sum of two DT signals could be the LCM of the fundamental periods. However, this is not always the case. I would like to know wether, during engineering design or ...
0
votes
0answers
18 views
When is Markov a Martingale
I have two questions and I am very confused about the concepts
Can a Markov process of order one also be a a Martingale?
Is any Markov process of order one also a Martingale?
For 1. I would say yes, ...
1
vote
2answers
215 views
Problems computing the DFT of finite length sequence
I am having trouble finding the same answer as the solution manual for this sequence.
The problem asks to compute the DFT of
$$
x[n] = \begin{cases}
1 & \text{for even } n \in \{0\...
0
votes
1answer
76 views
Linear correlation of two vectors?
We had a lecture on digital watermark detection using linear correlation. Here it was explained that the linear correlation of two vectors is equal to their scalar product divided by the dimension. So,...
0
votes
1answer
30 views
Relation between the matrix trace and the amplitude of each element
Assume a diagonal matrix $\mathbf X$ whose size $N\times N$ and its diagonal elements are $0.5 + 0.5i$, and the vector $\mathbf p$ of size $N\times 1$ whose elements have similar amplitude.
I have ...
2
votes
2answers
213 views
DFT of pure sinusoidal wave
I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to ...
1
vote
1answer
65 views
SNR for the magnitude of a complex signal
The SNR for a complex valued signal is presented by Dilip Sarwate in: https://dsp.stackexchange.com/a/42359
Following the same steps I would like to estimate the SNR for the magnitude of a complex ...
0
votes
1answer
29 views
I don't understand how the zeros are found of this 2nd order feed-forward filter
I realized someone asked a question about the exact same section of a book, which can be found here: Question about zeroes of simple 2nd order FIR filter.
While the answer to this question looks ...
2
votes
2answers
110 views
Coordinate system in digital image processing
I am trying to understand image coordinate system where I read that it is reversed.
So if $f(x,y)$ is actually $f(y,x)$ where $f(\cdot, \cdot)$ is the image. I am a bit confused and would appreciate ...
1
vote
1answer
50 views
Summations in Z-Transform
I'm currently working on a problem that involves a Z-Transform. Basically, the essence of the problem is that if:
\begin{equation}
H\left(z\right) = \sum_{n=0}^{N-1}h\left(n\right)z^{-n}
\end{equation}...
0
votes
1answer
41 views
Adding attenuations in dB
I am writing a synthesizer. One part of the synthesizer specification says that different sources can specify an attenuation to be applied to a signal, and that these attenuations should be summed.
...
1
vote
0answers
75 views
Fourier Transform of an Exponential Sine Sweep
The Exponential Sine Sweep (ESS), according to Farina [1], can be described by the following formula:
$$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$
where,
$t$ - ...
1
vote
0answers
73 views
Problem with natural logarithmic function in fixed point notation
I am facing a problem with natural logarithmic function in fixed-point notation.
Let's say
$$x = 0.54, \qquad\text{then}\qquad \ln(x) = -0.616186, \qquad\text{a negative number} \tag{1}$$
Then in ...
1
vote
1answer
70 views
FFT algorithm gives wrong signs on my output numbers
I was told from another stack exchange (stackoverflow and computer science stack exchange) to post here - so hopefully now i can get some help from people who understand the algorithm, but if this is ...
5
votes
1answer
103 views
Why Cramér spectral representation and not DTFT for stochastic process
In a lot of time-series analysis references I find (written by mathematicians or statisticians rather than engineers), I find the following signal decomposition for a stochastic process, termed the &...
5
votes
6answers
3k views
What is the first derivative of Dirac delta function?
Could you please help me in a simple way, what is the first derivative of a Dirac delta function?
I found this answer:
The informal answer is a positive Delta function immediately followed by a ...
0
votes
0answers
38 views
Setting some values in a vector to have specific values after multiplying with such matrix
Assume I have a known matrix $X$ of size, for example, $(16$ x $16)$, and a vector $z$ of size $(1$ x $16)$ where only some equispaced values are known, for example $1:4:16$ or values in locations $(...
0
votes
1answer
46 views
Solve equations with conjugates multiplications
If I have a two variables $x_1$, $x_2$ and two equations. In the first equation the first variable $x_1$ is multiplied with the conjugate of same number which is multiplied with $x_2$, and in the ...
1
vote
1answer
57 views
Finding the system output by convolution
pretty new to this concept, so do bear with me.
A linear dynamic system is described by the following differential equation:
Transfer function H(s) is calculated to be =
I've already found the ...
0
votes
4answers
64 views
On the simplification using trigonometric functions
Assume I have a matrix $D$ whose its entries are as below :
Where $A$ and $B$ can be written using using the trigonometric functions for (1) as:
My question, Is it possible to simplify (1)
more? ...
0
votes
1answer
98 views
Calculate autocorrelation of a sinus
I am a beginer in signal processing.
I am currently studying a signal $s(t) = \cos(h(t))$, and I have to calculate its autocorellation.
Since $h(t)$ is periodic of period $T_s$, I calculated the value ...
0
votes
2answers
66 views
Q format doubts
Is my understanding correct w.r.t Q format.
signed Q15.1 format means, 15 bits for fractional and 1 for integer bits
SO max range is - 2^15 / 2^15 to + (2 ^ 15 - 1) / 2^15
signed Q7.0 means, 7 bits ...
0
votes
2answers
31 views
Understanding Communication Theory Jargon for Statistical Linear Models
Coming from a statistical background, I understand the following formula:
\begin{equation}
y = X\beta + \epsilon
\end{equation}
as a linear regression model, with data input-output pair: $(X,y)$, ...
1
vote
3answers
1k views
Convolution of two rectangular pulses intuition
From what I understand the convolution of the impulse response of a system with the input to that system gives the output.
Now if the impulse response is a rectangular function and the input is also ...
0
votes
1answer
111 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 ...
1
vote
1answer
151 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
61 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
43 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)$$
where $\ast$ is the convolution.
I know $A(f)$, $B(f)$,...
2
votes
0answers
553 views
Derivation of ZOH Discretization
I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps.
I think I understand the first part, this is just the ...
0
votes
1answer
35 views
Why is the anisotropic diffusion equivalent to the heat equation when using a constant diffusion coefficient?
The anisotropic diffusion is defined as
$$\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$$
where $\operatorname{div}$ is ...
0
votes
3answers
662 views
Resolution of Discrete Fourier Transform is 1/T - Mathematical proof?
In many articles I see that the frequency resolution of the Discrete Fourier Transform (DFT) equals Fs/N where Fs is the sampling rate and N is the total number of samples. Fs/N is equivalent to 1/T ...
0
votes
0answers
141 views
Power, energy and amplitude spectrum from fft in MATLAB - scaling
I've looked at previous answers and none of the answers seem to agree (perhaps I'm missing something obvious):
I would like to know what the correct scaling to use is for
amplitude,
energy and
power ...
0
votes
0answers
39 views
On $H_\infty$ norm for transfer function
For a given scenario in the context of control system, I'm trying to investigate how the $H_\infty$ norm can be calculated for a transfer function as follows:
$$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
0
votes
2answers
576 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
166 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 : $$ h (t)...
1
vote
2answers
125 views
Check whether a given equation is linear
$ a = (x, y) \in \mathbb{Z}^2 $ is given as a pixel. My equation in which $g$ is image(matrix) is defined as,
$f(x, y) = 56g(x,y)+93g(xā1,y)+92g(x+1, y)ā57g(x, yā1)+555g(x, y+1) $
How can we know ...
0
votes
1answer
48 views
how to set Equalizer's coefficient using generalized eigenvector.
In that paper https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2012-72 .. Equation 3,
$J(w) = w^HBw/w^HCw$ ..
$B$ and $C$ are matrices, $w$ the filter coefficients vector ...
0
votes
2answers
593 views
What does it mean for a function to have frequencies?
In a lecture, my professor mentioned that $\cos$ has two frequencies. I see that using the inverse Euler's formula we can express $\cos$ as a some linear combination of complex exponentials, each with ...
1
vote
1answer
81 views
Intuitive understanding of frequency
I know that $f = \frac{\text{cycles}}{\text{unit of time}}$ and I know that period $T = \text{time it takes to complete one cycle}$.
So if we take the definition
$f = \frac{1}{T} = \frac{\text{1 ...
1
vote
2answers
51 views
Rearranging exp terms
I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but Iām not able to spot my mistake.
I know the solution (since i looked it up with wolfram alpha) ...
0
votes
1answer
29 views
Equation Derivation: Help with intermediate steps
As per the attached image above, I don't know how the equation in the first line transformed to the form in second line.
I tried solving it by multiplication but the result was different.
3
votes
1answer
534 views
Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation
While I was reading SIFT paper(Lowe, 2004), I came across the method that he apply "heat diffusion equation" to Gaussian function to derive that
$$ \frac{āG}{āĻ}
= Ļā^2G
$$
I searched Wikipedia and ...
1
vote
1answer
94 views
How to measure the distance between two circle-like-lines over 360 degree
I am looking for a slim and with that quickly programmable image processing strategy to measure the distance between two circles over 360Ā°. It is important to notice that the circles are not perfect, ...
1
vote
1answer
165 views
How to prove Line Spectral Pair coefficient properties?
I am trying to understand the definition of LSP coefficients from http://www.dspcsp.com/pdf/lsp.pdf.
We take the polynomial $a(x)$ of degree $M$ from the denominator of the LPC system function, and ...
0
votes
1answer
70 views
Explicit a succession using z inverse transform
Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?:
$ y(0) = 1 \\ y(n+1) = 2y(n) + 3 $
I can't write ...
0
votes
0answers
39 views
Relationships between $f(t)$ signal and $f(t) \times \sin(\omega t)$ signal
Let's assume that there is a signal $f(t)$, $0\le t \le T$. Then, is there any special meaning of the signal $g(t) =f(t) \times \sin(\omega t)$? Like AM transmission. What is shown/heard when we play ...
1
vote
0answers
298 views
NMSE of complex numbers
Actually I am doing an RF measurement and this includes phase and power. i generate a list of powers ranging for example from (-50 to 40) dBm, while the phase rotate to make it for example spiral ...
0
votes
2answers
191 views
MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)
This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv
If $v \sim CN(0,2\sigma^2_v)$ ...
0
votes
2answers
73 views
MLE formulation — confusion regarding the terms in the equation (Part1)
If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model
$$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
0
votes
0answers
70 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!
