Questions tagged [math]
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144
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Fourier transform why can I convert one of the axes into an imaginary number?
Contextualizing
This question is inspired by the following video:
https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown
I own a sign, a drawing of a square with 200 points ...
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3
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456
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Why Hilbert Transform is terrible choice for amplitude demodulation of broadband signals?
A reference answer empirically demonstrates that Hilbert envelope does not work well for the (amplitude) demodulation of a broadband signal. I am looking for the math which explains why...
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2
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37
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Get IMU acceleration of a direction when tilted
I have an IMU that is placed on the body. My goal is to calculate the position data of the vertical upward movement. Since the sensor is never perfectly aligned and will always have a little tilt, I ...
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Confusion Understanding the mathematical expression of duality property of dft?
Duality Property for DFT
Above dsp.se question provides good understanding about dft duality property but i am having difficulty understanding its mathematical expression because on Google when i try ...
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2
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122
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What *is* pitch-shift?
As I understand it, pitch-shifting (without changing speed) and time-scaling (without changing pitch) are two sides of the same coin, because if we can do one we can get the other through resampling ...
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How to Get Started On Demodulating Signals Such As Amplitude Modulation and Pulse Width Modulation
I'm looking to understand how signal modulation/demodulation works.
My goal is to be able to demodulate a 315 MHz key fob and be able to tell what buttons are being pressed so I can have a Python ...
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0
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51
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How to find the kernel of the convolution?
I'm trying to solve the following exercise:
Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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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 − ...
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1
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118
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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 ...
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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
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100
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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 ...
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1
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179
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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 ...
- 359
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60
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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 ...
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93
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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 ...
- 196
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45
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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 ...
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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. ...
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120
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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 ...
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1
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288
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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 ...
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3
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148
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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^...
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125
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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 ...
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46
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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$ ...
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1
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51
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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 ...
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23
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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 ...
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37
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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, ...
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2
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417
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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\...
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1
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208
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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,...
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1
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82
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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 ...
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2
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1k
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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 ...
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190
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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 ...
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1
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39
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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 ...
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2
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1k
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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 ...
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130
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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}...
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1
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77
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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.
...
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247
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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,
$t$ - ...
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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 ...
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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 ...
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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 &...
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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 ...
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1
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51
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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 ...
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1
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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 ...
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4
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76
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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? ...
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182
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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 ...
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352
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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 ...
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2
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56
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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: $(X,y)$, ...
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3
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10k
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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 ...
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1
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307
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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 ...
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193
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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 ...
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108
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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 ...
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48
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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 $A(f)$, $B(f)$,...
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634
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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 ...
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