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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What is the definition of a "Symbol"
I’m looking for the simplest, precise definition of a Symbol
e.g.
The symbols found within a signal
The signal has a N symbols per second
I'm following this tutorial. The fellow defines the term ...
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Digital filter coefficients from low-pass to high-pass
Given I have coefficients a0, a1, a2, b1, and b2, defining the difference equation for a digital filter as:
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How can output sequence be equal to the sum of copies of the impulse response, scaled and time-shifted signals?
I am sorry, this is a very basic question. But i am having hard time understanding is how it is possible.
I know impulse response is the output of the system when impulse sequence is given as input ...
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Intuition behind commutativity of convolution in LTI systems
Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system?
If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
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Scalogram (and related nomenclatures) for DWT?
My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
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Zero Phase Filter: Determining Initial Conditions for Forward Backward Filtering
Is anybody familiar with Gustafson's algorithm for minimizing transients in forward backward filtering [1]? I'm trying to implement it and my first guess was to check Matlab's filtfilt.m, since they ...
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Clear understanding of compressed sensing
I am trying to get a clear understanding of how compressed sensing works.
A continuous signal $x(t)$ is under-sampled (less samples are collected than the numbers required by the Nyquist theorem). The ...
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What should be the correct scaling for PSD calculation using $\tt fft$
I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow :
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Discrete Time Signal Property
Property:
The frequency of oscillation of discrete time sinusoids sequence increases as $\omega$ increases from $0$ to $\pi$. If $\omega$ is increased from $\pi$ to $2\pi$ then frequency of ...
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Mathematically Inclined Signal and Systems / Signal Processing Book Recommendations
I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
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Does it make sense to have complex numbers representing real-world audio signals?
In this course (Coursera: Audio Signal Processing for Music Applications) the professor uses an example of obtaining the DFT of a complex sinusoid:
\begin{align}
x_2[n]&=e^{\jmath\left(2\pi f_0 n+...
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Is the system $y(n)=x(n^2)$ time invariant?
According to my solution,
$$y(n) = x(n^2) \tag{1}$$
for $y(n,k)$ i.e output for delayed input $x(n-k)$
$$x_2(n) = x(n-k)$$
so $$y_2(n) = x_2(n) = x\big((n-k)^2\big)$$
and for delayed output ...
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How to compute Laplace Transform in Python?
I am trying to do practicals for signal processing where I need to Laplace Transform a function. Used 'fft' of numpy before. Nothing of Laplace is found in the documentation. Do we have any other ...
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Using Total Variation Denoising to Clean Accelerometer Data
I know this is maybe a very basic question but I am doing this as a hobby and I can't find a solution to this problem.
Basically I am trying to remove some noise from data I am reading from an ...
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Audio normalization
I have a recording in pcm format and I want to do some simple analysis.
I have some questions about what is normalization.
As far I understand it is to get all the amplitudes between a range i.e. [-1,...
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determine two signals with a scale factor
Suppose I have 2 signals from function $f_1(x)$ and $f_2(x)$, respectively, and assume the sampling rate is above Nyquist frequency, so we can restore the underlying functions $f_1(x)$ and $f_2(x)$. ...
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What are high frequencies and low frequencies in a signal?
I'm new to signal processing. I'm plotting a signal in the time-domain in matlab. I don't understand which parts of the signal are high frequencies and low frequencies, can someone explain what a high ...
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Solving Inverse Problem of Multiple Pulses Over Multiple Channels with Convolution Kernel and Cross Channel Mix
Before I start, let me note that I have 0 experience with signal processing, so please bear with me:
My System
My system can be represented as an $m \times n$ matrix $X$ (input) where each
column ...
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How to Reduce Phase Lag Caused by Kalman Filter
Background
I have been developing a system using a moving robot with a distance sensor against another robot. I want to control these robots by estimating relative velocity and acceleration derived ...
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Questions about discrete signal energy calculation
I'm looking at the definition of signal energy (e.g. Wikipedia, cnx.org). For discrete signals, it's defined like the following, where $x(n)$ holds the signal:
$
Energy = \sum_{n=-\infty}^{\infty} |...
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What are some methods for detecting a sinusoid in noise?
I'm looking for a broad classification on the kinds of techniques available. Something I can use to begin a literature survey.
Some details:
should be feasible for real-time implementation.
Binary ...
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Open access signal processing journal?
Signal processing is Elsevier, so it's not open access, and IEEE Transactions on Signal Processing is also not open access. I was wondering if there's any decent journal on par with those that's open ...
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Apply wavelet transform to analyse EEG signal
I would like to apply The Morlet wavelet transform to analyse my EEG signals. I have many short signals each is only 1 min long. and they all recorded in 30Hz.
I have Two questions:
In the Morlet ...
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Continuous Time Signal and Discrete Time Signal - Connection Between Periodicity and Discretness
I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time?
Also, can all periodic signals be ...
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Applying DFT twice does not actually reverse an array. Instead, the first element stays in place while the rest of the array is reversed. Why?
I've heard a million times that applying DFT twice will result in a reversed array, but that is not what actually happens. Instead, the first element remains where it was, and the rest of the elements ...
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If the convolution of two signals is a unit impulse, what does this tell us?
I have two discrete-time LTI systems whose transfer functions satisfy $h_1[n] * h_2[n]= \delta[n]$. We also know that system 1 is causal and stable. Does $h_1[n] * h_2[n]= \delta[n]$ tell us anything ...
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Why integrate over $2\pi$ in inverse DTFT?
In DTFT of a signal, the spectrum of a sequence is periodic with period $2\pi$ and all the information needed for derivation of the original signal from its spectrum is contained in $\pi <\omega &...
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Choosing the length of a signal when calculating the FFT
I'm trying to transforming an already know signal from time domain to frequency domain using fft function in MATLAB. And I got different values of amplitude when I ...
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Demonstrating the effect of aliasing
How does the signal look when we don't use the Nyquist rate to remove aliasing from a signal during sampling?
Let's suppose the signal is sinusoidal, with a frequency of 500 Hz and an amplitude ...
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Difference between RMS and a moving RMS
I don't quite get the difference between RMS and a moving RMS.
When one calculates RMS, one integrates (or sums in case of a discrete signal) over a period of time(number of samples).
When it comes ...
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As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?
There are several types of discrete nonlinear time-invariant systems with memory ("NTIM") which are considered "easy" to model and identify. Any such system can be represented using a Volterra series, ...
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can't find out the period of my signal
I've a noisy signal, which is the sound of motor with a constant speed, so the sound "should" be periodic, I know that there is a way to use the autocorrelation function to get the period,I did it, ...
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Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?
I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
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Determining the mean of of a sampled signal (improvements to time averaging method)
I am sampling a signal at 1kHz, which is essentially a single-frequency sinusoid with a DC offset (and a small amount of noise). I don't know the precise frequency of the sinusoid (it is at most 10Hz),...
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eigen values and eigen vectors of signal
What does the Eigen values and Eigen vector of a signal or function represent? What is its physical significance? I know about basis vectors of a signal which constitute the orthogonal planes where ...
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Plotting DNA chromatogram trace data
Sanger DNA sequencing produces a chromatogram trace which can be visualized with a number of programs, including FinchTV or ChromasLite. The raw data consists of co-ordinates for each of the four DNA ...
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GCC-PHAT (Generalized cross correlation MATLAB)
I've been trying to implement generalized cross correlation with a PHAT weighting function for a while now, and cannot get it to work. I have tried correlating using MATLAB's xcorr.m file, and it ...
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Variance of periodogram estimate of the power spectrum
I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book.
Some things related to the expectation value of the "periodogram estimate of the power ...
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Black box signal prediction
I have a stateful black box with four real-valued inputs and one real-valued output. My problem is to predict the output at each moment in time, given the sequence of inputs seen up to that point. ...
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Circular Convolution as Cyclic Shift Operator
Given the following signal vectors:
$$ γ=[ψ_0,0,ψ_1,0,ψ_2,0,…,ψ_{N-1},0]^T\in \mathbb{R}^{2N}, ϕ=[1,\frac{1}{2},0,…,0,\frac{1}{2}]^T \in \mathbb{R}^{2N}$$
I want to show that the convolution of $γ$ ...
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Reducing noise from the same frequency band as signal
Sorry for the vague question (as I'm not even quite sure what I want to do is possible), just asking for some general direction to take my research.
For a brief description, my signal resembles ...
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1D Deconvolution with Gaussian Kernel (MATLAB)
Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution.
To get a grasp of the idea I have created a simple ...
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laser speckle noise reduction
I'm trying to process an 1D signal containing a waveform of 100000 pixel.
As it was acquired with a laser scanning system, and therefore it is corrupted by some annoying speckle noise.
I tried to ...
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Discrete (Inverse) Haar (2D) transform implementations
I am interested in implementations of the Haar transform, and its inverse, such that when composed always result in the identity operation. My inputs are discrete ordinals within a given range - and ...
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Converting from stereo to mono by averaging
Hi I'm doing a past exam question about converting from stereo to mono. The scenario is below:
The first question is: Explain why would this result in a noisy encoding. How is the noise introduced ...
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Calculate Phase angle between two signals i.e. digital Phase meter
I want to calculate the phase difference between the two channels(signals) of a stereo audio file.(uncompressed data i.e. PCM samples).
I want to determine whether whether two signals are in phase or ...
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Under what conditions does DFT(f(x)) = f(DFT(x)) hold?
I have encountered a text (a specification) in which $$\text{FFT}\left(f\left(x\right)\right) = f\left(\text{FFT}\left(x\right)\right)$$ is clearly presumed (for the functions they are applying).
Thus,...
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What is the meaning of channel capacity?
If the transmitted information signal takes values from a modulation constellation, then is there a way to know what the channel capacity is?
Is there a connection between the modulation kind and ...
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What is the intuition behind convolution? [duplicate]
I have been using convolution for finding outputs of various systems .I know how to use it.But I still don't know what does convolution exactly means? how one can define convolution ?
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Ways to compute the n-the derivative of a discrete signal
This is a pretty general question about how to compute derivatives of a digital signal $x[n]$.
I would like to know what are the different approaches (from naive to complex) and how are they compared ...