Questions tagged [math]
The math tag has no usage guidance.
136
questions
0
votes
1answer
60 views
I'm having problems simplifying this discrete-time fourier tranform
I have this problem, and I can't get to the solution.
$$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty} {(0.6)^{|n|}[u(n + 10) − u(n − 11)]}e^{-j\omega n}$$
The solution is
$$X(e^{j\omega}) = \frac{0.64 − ...
0
votes
1answer
15 views
How do I carry out SRT Radix-4 fixed-point division with more than a few bits?
I've managed to get a hand on how SRT division works, but I haven't been able to construct a working example. My current sticking point is that e.g. the Pentium floating-point division bug came about ...
-2
votes
1answer
25 views
what are the application of fourier transform in finding frequency response? [duplicate]
i need the application of Fourier transform in finding frequency response in mathematical terms
3
votes
1answer
77 views
Is it possible to compute the PSD of s(t)^2 given the PSD of s(t)?
Given a well-behaved signal $s(t)$ given by,
$s(t) = \sum_{i}^{N} \cos( \omega_it + \phi_i) $
with a large $N$ and a well-known power spectral density (PSD), $\tilde{S_1}(\omega)$. Is it possible to ...
0
votes
1answer
57 views
False positive rate with CRC
What is the technique to calculate the false positive rate for an N-bit CRC?
Example: Communication system sends M-bit packets with a N-bit CRC (M >> N) appended to each packet. What is the ...
0
votes
0answers
43 views
Problem with the output self implemented “ Iterative FFT DIT Radix2 ” algorithm matlab
I´m trying to implement my own FFT with the iterative Radix2 algorithm (I even thought about using the recursive one but it seems Simulink doesn´t allow me to). I tried all of the possible variations ...
1
vote
2answers
46 views
Parseval's Theorem for Time Domain Data with DC
I have read several times that the variance for time domain data with a zero mean is equal to the integral of the power spectral density divided by N.
From wikipedia, the discrete form of Parseval's ...
0
votes
1answer
43 views
Different mathematical signal models for different applications
I am looking for some interesting and physically meaningful applications of different signal models. I am currently working with complex analytic signal model given below, but I couldn't come up with ...
1
vote
0answers
19 views
Backpropagation in a Network [closed]
Hi does anyone know how to solve this. Im really struggling to figuring this one out.
I am unclear of how the backpropagation part would work in this network and how to calculate it for each weight. ...
1
vote
1answer
56 views
Calculating Haar features
I am confused on how to solve this problem, does anyone have any ideas?
https://www.merl.com/publications/docs/TR2004-043.pdf
For a Haar filter $H \in \mathbb{R}^{3 \times 5}$ defined as below:
What ...
2
votes
1answer
95 views
Digital integrator
I have been implementing a control software where I need to calculate a magnetic flux based on the measurement of the phase voltages of a three phase grid (basically three sinewaves) according to the ...
1
vote
2answers
104 views
Question about delayed sampled sinusoid math expression
I have been studying the digital audio processing by using the book <Designing Audio Effect Plugins in C++>.
For analog Sinusoid:
Complex Sinusoid = $e^{jωt}$
Delayed Sinusoid = $e^{jω(t−n)} = e^...
5
votes
1answer
84 views
Why Does the Median Filter Minimize the Absolute Value Error $L_1$ Cost Function?
I can easily prove that the mean filter minimizes the square error $L_2$ cost function using simple calculus.
However, how do you prove that the median filter is optimal with respect the absolute ...
0
votes
1answer
43 views
mathematical expression to detect modulated data within a vector
Assume I have such modulated data which is, for example, $x=0.7+0.7i$. That modulated data is encapsulated in a vector as below:
OR
where $c$ is any constant number, let’s say, for example: $c=0.7$ ...
1
vote
1answer
41 views
Effectively extracting “real” data from a noisy dataset
This question was originally posed to Math SE. It was suggested that DSP SE would be more suitable.
Background & Motivation:
I have three lists of timestamps (UNIX timestamps, plus a subsecond ...
0
votes
0answers
19 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
24 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
321 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\...
1
vote
1answer
121 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
63 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
681 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
131 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
466 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
75 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
47 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
167 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
117 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
123 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 &...
12
votes
6answers
20k 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
1answer
48 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
155 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
69 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
160 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
212 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
49 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
6k 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 ...
1
vote
1answer
229 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
165 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
91 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
45 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
585 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
3answers
1k 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 ...
1
vote
0answers
259 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
41 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:
$$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
0
votes
2answers
896 views
Differential Equations applications in Signal Processing [closed]
Does differential and partial differential equations subject has applications in Signal Processing? I have basic DSP background and know Matrix algebra and Fourier transforms very well, but I am not ...
0
votes
1answer
211 views
How to find the impulse response of filter that outputs the autocorrelation of the input?
I am trying to solve question 9.61 in the attached image.
I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
1
vote
2answers
157 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
52 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 ...