Questions tagged [discrete-signals]
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
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How to compute the 2D coordinate in the s-domain?
I am not sure if my question is a right question to ask or not since I am still learning about Laplace Transform and S-Domain.
If we have 2D coordinates (x,y) in the spatial domain (i.e., Euclidean ...
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Is the magnitude spectrum of the Discrete Time Fourier Series of a Discrete Time periodic Signal , an even Function?
We know that the magnitude spectrum of a continuous time fourier series representation of a real periodic signal is an even function (i.e. symmetric about y axis). Does this hold true for discrete ...
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Proof that the order of a linear prediction model cannot be reduced by analysing non-adjacent points
I have a signal, for which a linear prediction model of order $M$ can be constructed. This means, that a system of the shape
$$
\begin{bmatrix}
s_0 & s_1 & \cdots & s_M \\
s_1 & s_2 &...
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Real-world examples of unweighted directed graphs
Social Networks, Internet Traffic, Citation Networks, Transportation Networks, and Biological Networks exemplify real-world instances of unweighted directed graphs. Within these domains, the Graph ...
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Related to SNR in wireless communication
I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SNR (which is a ratio of Signal variance in numerator to Noise variance ...
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Looking for an online course
I work for a company with expertise in electromagnetics physics, specifically dealing with time domain-based simulation software. We routinely need to transform our results into frequency domain, ...
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Smoothing sensor signal with discontinuities on DSP for obtaining signal derivative
I am trying to implement PID control on a sensor signal that has many discontinuities in it. Due to these discontinuities, the differentiated signal does not provide a meaningful or useful signal I ...
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Why are MFCCs of different signals equal?
What I am trying to do:
I am trying to extract features based on the difference between a reference signal (white noise in my case, let's call it ref) and different processed versions of it (let's ...
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If the input of the system depends on the future outputs then is the system non-causal?
While I'm aware of the fact that causality implies that the present output is only dependent on present and past inputs, something that is bugging me is what if the input is dependent on future ...
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Signal level from its FFT
Suppose I have the FFT of an arbitrary real audio signal z samples long. Is there a way to discover the signal level (intended as the largest absolute value of its samples) from the FFT without ...
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Laplace Transform and Inverse laplace Transform for 2D images python code available?
I am wondering if there is any implementation of Laplace Transform and Inverse Laplace Transform available for 2D data (i.e., images). For example, a batch of N ...
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Lowpass Filter to Average sinusoid signal
How to get an average of a sinusoidal signal? The frequency of a signal is 50 Hz and could have harmonics, i.e. high THD.
I tried to use exponential moving average with low cut-off frequency (about 1....
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Fusing multiple IMUs in EKF framework
What is the approach to fuse multiple IMUs in EKF framework?
Normally you take the IMU as the motion model and the sense step to consist of other sensors but when have multiple IMUs operating, what is ...
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Show that the similarity between a signal at an analysis frequency with a phase offset with a reference signal is $\frac{N}{2}\text{cos}(\phi)$
I'm reading Brian McFee's excellent book Digital Signals Theory.
He presents the DFT as a measure of similarity $S$ between a digital signal $x[n]$ with $N$ samples and a set of reference signals $y_m[...
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Filter coefficients hamming window for low-complexity Welch PSD computation
I am trying to implement the proposed method from this paper 1, to eventually have a more efficient PSD computation for feature extraction on a microcontroller.
The method is suitable since I am using ...
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Correlation between two signals
I am having an input signal x[n]=[1 2 3 4 5 6] and another signal y[n]=[2 3 4].
In order to check whether y[n] is present in the signal x[n],I did cross correlation and the result obtained was [ 0 0 0 ...
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insights into making AR Burg extrapolate finite periodic signals
Following a past question, I'd like to extrapolate a periodic signal using AR Burg, but when doing so, it seems that I need to sample "enough" for that to work. For example, if I use the ...
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Influence of phase discontinuity on power spectrum density
I was wondering about the influence of phase discontinuities on a power spectrum density calculated with f.e. Welch's method. I know you shouldn't have any phase discontinuities in your signal, but I'...
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Is there something wrong with MATLAB's pwelch function?
The normalized factor for windowing, is it $(\sum w[n])^2$ or $\sum w^2[n]$?
I try to reproduce the pwelch function, if I set the normalized factor to $(\sum w[n])^2$, I get the same result as MATLAB ...
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How can I denoise this signal?
I have data captured by a wireless sensor that is noisy. It randomly jumps in value frequently, and I want to know what this signal will look like without these jumps. I am looking for an elegant ...
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What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)
I'm looking at two different books written by Oppenheim. In Discrete-Time Signal Processing (source 1) he defines the DFS to be:
where, $W_N=e^{-j(2\pi/N)kn}$ , while in Signals and Systems (source 2)...
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FFT analysis of signals that were combined
I have a dataset with ECG artefacts, noise and EMG activations. Now I want to analyse the EMG activation using Welch's and Burg's method. The EMG realizations are approximately 0.25 s long, resulting ...
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The Discrete Fourier Transform (DFT) decomposes any signal into four orthogonal signal components
Let $F=\frac{1}{\sqrt{n}}(w^{kl})_{k,l=0}^{n-1}$ be the discrete Fourier matrix of size $n$ where $w=\exp^{-\frac{2\pi i}{n}}$.
It is a well-known that $F_n^4 = I_n$ where $I_n$ represents the ...
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Quasi-static-detector operation principle
Im currently working on a project to get navigation information of a robot from Data-Fusion through different IMUs.
First step is to make a calibration and I picked a method where I need to detect ...
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I need help finding the PSF and characterizations of the following
My professor explained this to me in a super convoluted way, so hopefully someone can explain this to me better.
I'm trying to find the PSF of the following signals. I also need to check if it's FIR ...
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Discrete time serie online derivative
I'm looking for an algorithm to compute the numeric derivative $\dot x_i$ of a discrete time serie $(x_i, t_i)$.
It should runs as the data is generated, hence $\dot x_i$ can only depend on $x_{j<=...
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Understanding Fresnel reflection coefficient formula
In textbook "Wireless Communications Principles and Practice" by Theodore S. Rappaport, the expression of Fresnel reflection coefficient ($\Gamma$) for parallel polarization is given as
$\...
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Relation between DTFT and DFT
Let $X \left( e^{j \omega} \right)$ be the DTFT of a discrete-time signal $x \left[ n \right]$ given as
$$ x \left[ n \right] = \left( \frac{1}{3} \right)^{n} u \left[ n \right] \tag{1} $$
Determine a ...
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physical energy definition for acoustic signals
Recently I am reading Books "Signals and Systems" from Oppenheim and "Ultrasonic testing of materials" from Krautkrämer. In those books there are some definitions about wave energy:...
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second order cross correlation
I have two signal sequences $u$ and $y$, where the former is the input to a system and the latter is the output of the same system. I would like to find second-order correlation between the two ...
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Calculation of a position from the angles of arrival
For locating a target by TDOA (Time Difference Of Arrival) with $3$ stations we have the Chan method which gives an exact solution of the position.
I keep the $3$ stations but instead of measuring the ...
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$i^{\text{th}}$-dimensional autocorrelation function
I am referring to the work of Stephen A. Billings on "Identification of a class of nonlinear systems using correlation analysis" from the year 1978, where it is mentioned that the $i^{\text{...
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Finding inverse $Z$ Transformation of a LTI system and switching of input output signal regarding to difference equation
I have 2 stuffs that are bothering me:
I have the equation:
$y[n]=8x[n]-2x[n-2]-x[n-4]$
When $x[n]$ input and $y[n]$ output.
Now, the system is swapped, $x[n]$ output and $y[n]$ input
The difference ...
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Accumulative Value Difference in Adjacent Intervals
im trying to implement eq. 14 of this study, but im not sure how to set an interval in python. The equation is $sumAD[k]=sumA[k] - sumA[k+1]$, where $sumA[k]=\sum_{i=1}^{N} a[i]$. N is the total ...
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Confused on the ROC of Z-transform
I'm given a specific function to find its inverse Z-transform. Specifically:
$$X(z) = z^3 + \frac{1}{z - 2i} + \frac{1}{z+2i}, |z| > 2 $$
Notice the $|z| >2$. Now what concerns me is the term $z^...
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Window function with no sidelobes
I found the Hann–Poisson window on Wikipedia. It has no sidelobe for $\alpha \ge 2$.
I am interested to know more examples of such window function with no sidelobes and what they are useful for.
I ...
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error on angle of arrival
I have $2$ sensors allowing me to measure angles of arrival. These sensors are a distance $d$ ($d \simeq 10$ m) apart and the target to be located is at a distance $R$ with $d<<R$. In the ...
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How To Calculate Length Of Sequences And A Suitable N?
I have been struggling to understand how to calculate the length of a sequence and also the minimal N to choose in order to avoid aliasing.
Most sources tell me to take the (last non-zero value - ...
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Ergodicity clarification
On page 201 of https://stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf,
it is mentioned that
This observation suggests that the capacity result (5.89) holds for a ...
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How to prove the mutual infomation expression in paper "Optimized Degree Distributions for Binary and Non-Binary LDPC Codes in Flash Memory"
Recently I met a question when I read the paper Optimized Degree Distributions for Binary and Non-Binary LDPC Codes in Flash Memory and Soft Information for LDPC Decoding in Flash: Mutual-Information ...
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Compare Discrete Fourier Transform for multiple signals
I have heart rate data from a wearable sensor (no ECG). I want to perform Discrete Fourier Transform to see if some patterns are present. I have over 200 signals, as each individual has heart rate ...
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Derive PSD of an MA(1) process
Suppose there is a moving average process of order 1 that also includes a zeroth term thus:
\begin{equation}
Y_t=\theta\left(B\right)X_t = \left(\theta_0+\theta_1B\right)X_t
\end{equation}
where $X_t$ ...
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Moving average of a signal
Problem is to find 1 second moving average of a signal having sample time as Ts.
To solve this, it is suggested to pass the signal through a Butterworth low pass filter having the following ...
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Decomposing a signal so that the magnitude spectrum of the decomposed signals lie in some specific amplitude range
Suppose I have the following signal:
I can compute its power magnitude spectrum:
PSD = np.abs(np.fft.rfft(signal))
Now I would like to pick a specific amplitude ...
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How to design an optimal LLR Quantization of LLR for LDPC Decoding under AWGN channel using BPSK(Known quantization boundaries)?
Recently I met an optimazition problem, i.e., finding an optimal quantizer which maps floating point LLRs to integers of range $-11,\ldots +11$, where the quantizer boundaries have been calculated out....
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Discrete Frequency representation for central frequency/ discretize up-converted signal in time and frequency
I want to analyze a signal after up-conversion in discrete time and frequency, for example:
Let's assume a continuous up-converted signal is:
$$e^{j2\pi ft} \cdot e^{j2\pi f_c t} = e^{j 2 \pi (f+fc) t}...
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Z-Transform of $ x(n+2)u(n) $
I don't know where I went wrong, this might be a dumb question. I am solving for the z-transform of $$ y(n) = x(n+2)u(n) $$.
To solve, I used the z-transform equation,
$$ Y(z) = \sum_{n=-\infty}^\...
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How to impose power constraint on an encoder's output while training a deep NN?
A deep encoder which takes in a 4 bit input gives out an 8-dimensional vector. If I want the power of this 8-D vector constrained to be 1, then I should multiply all the elements by A/B? Where A is ...
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Discrete Fourier Transform of the Gaussian
Cross-posted from here
I encountered the following question in a Digital Image Processing examination:
Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ ...
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Finding zero input response with only one initial condition
I have to find the Zero input response of the following system if $y[-2]= 0.5$
$$x[n] - 3y[n-1] - 4y[n-2] = 0$$
I am not sure if this is the correct way since every other example I have done had two ...
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