Questions tagged [non-linear]
The non-linear tag has no usage guidance.
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Non Linear Recursive/Online Least Squares
I am searching for a recursive or online non linear least squares algorithm. I want to spread the computation out as new data is sampled like in the linear Recursive Least Squares or the LMS.
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1answer
17 views
Biquad Filter Non-Linearity
I'm using a biquad filter algorithm in my project. I got 3, 16 size variable arrays summing into one and then gets filtered.
Now i want to filter each array seperately and sum after that, which if ...
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2answers
44 views
How to discard deviating values from standard deviation and running average
I'm building a inductive vehicle loop detector. By measuring the frequency of a LC-oscillator where the cars will pass over the inductor of the LC-Oscillator.
If the cars pass over the inductor the ...
3
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1answer
69 views
Can all systems be described by differential/difference equations?
All LCCODEs (linear, constant-coefficient ordinary differential equation) with initial rest conditions describe causal LTI systems (is this a correct statement?)
Is the converse true, i.e. can all ...
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1answer
22 views
Can I use SINAD for THD+N measurements? Are they inverse of each other?
I'm looking for a clarification, which I haven't really been able to find. It's probably obvious but I'd like to be absolutely sure of what I'm calculating.
I noticed that the formula that calculates ...
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1answer
30 views
Computing the gains of a piecewise affine system
I have a piecewise affine (and memoryless) system, e.g., a response like the following one.
I could manually find the gain in each region by applying a ramp signal. However, the system's input must ...
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0answers
25 views
Coherence and non-linear interactions
Reportedly, coherence-based metrics are primarily influenced by linearity in phase. However, Klein et al report that coherence is also:
... very sensitive to fluctuations of linearity in ...
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1answer
40 views
How to implement discrete extended kalman filter in matlab
I have a nonlinear system, and I need to use the extended kalman filter to estimate it. I know I need the jacobian, but once I get that, is everything else the same as the normal kalman filter?
I ...
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1answer
68 views
classify the system if it's linear , non-linear , time variants or invariants [closed]
classify the system if it's linear , non-linear , time variants or invariants
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1answer
23 views
Optimising an input signal for a system to minimise distortion of output signal
I have a discrete time-series signal which I am able to process before passing it through a system which distorts said signal. This system cannot be altered and is non-linear, but a signal can be ...
2
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2answers
235 views
Alias-free digital nonlinear filter design
@Jazzmaniac has a good answer to the question of how to design an alias-free digital nonlinear time-invariant filter here: https://dsp.stackexchange.com/a/28787/18276
Basically, according to that ...
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1answer
96 views
Sequential Non Linear Least Squares Problem
I have the the following non-linear function,
$$s(x;A_k,\mu_k,\sigma_k)=\sum_{k=1}^2 A_k \exp\left(\frac{-(x-\mu_k)^2}{\sigma_k^2}\right)$$
with unknown (but deterministic) parameters $A_k,\mu_k,\...
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0answers
103 views
Improving credit-card-like image scan for OCR
OCR works best for black on white or binary images, where letters have sharp contours, no noise, and solid filling, i.e. they are nothing like this:
For the curious it's a part of a document number ...
4
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1answer
148 views
Extended Kalman Filter for linear systems with non-linear measurements
I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates.
...
3
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1answer
94 views
Why harmonic components appear only after a certain level when a signal is clipped?
I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level.
The Python code to reproduce the effect is given below. The signal has 3 ...
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1answer
5k views
How to determine if the system is linear or nonlinear
Given a signal
$$y(n)=x(n)\cos(wn)$$
How to determine if the given signal is linear or non linear?
I am getting so confused reading the theory. If someone could help step by step to determine this....
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3answers
215 views
How to correct phase of Diagonal Volterra kernels obtained with exponential sweep sine?
I'm trying to model a non-linear system using non-linear convolution with Novak's (2010) synchronized exponential sine weep (SESS) that models them with a Generalized Hammerstein (Volterra diagonal).
...
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3answers
1k views
Volterra Kernel Convolution Method
Here I understand that the first term is a simple convolution of the input signal with first volterra kernel that I have acquired through farina sweep method, my question is if the second term is the ...
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2answers
55 views
Attenuating peaks of a signal in a specific direction
Consider a segment of a time-domain signal shown in the following graph and the two marked peaks, the first one facing downwards (in red) and the second one facing upwards (in black).
I would like to ...
2
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1answer
89 views
Effect of nonlinear transformation on digital signal
Currently, I know that by passing a band-limited baseband digital signal through a nonlinear system results in the expansion of the original signal's bandwidth and creates harmonics.
Therefore, I ...
2
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0answers
100 views
Check if I has right: Is this the Extended Kalman Filter
I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here.
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3answers
1k views
Upsampling - What purpose does the interpolation filter have?
I want to apply some nonlinear processing to a signal, namely: I want to implement a tube emulation which adds warmth/harmonic distortion to a digital audio signal. I am worried about aliasing, so I ...
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3answers
2k views
Why is not Fourier Transform Good for Non-linear Processes
I was reading through slides about Hilbert Huang Transform. In slide 14, which talks about the motivations of a new method instead of Fourier Transform (FT), the author provides those two reasons in ...
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2answers
835 views
Why is aliasing inherently non-linear?
E.g. when having 2 signals $x(t)$ and $y(t)$ and transforming each one with adding their spectra, the operation is linear, as the result would be the same as the transformation of $(x + y)(t)$.
Even ...
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1answer
147 views
Create distortion from basic linear (and non-linear if neccessary) DSP elements
I'm studying mechatronics and I'm intrested in DSP basics. My lecturer said that there are four basic linear DSP elements:
Adder (and other mathematical operations)
Amplification (shown on diagrams ...
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1answer
117 views
Determining invertibility of a system [closed]
Given a system which is either non-linear and/or time variant, Is there any systematic way to determine if this system is invertible?
For example how to determine invertibility of this system?
$$\int_{...
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2answers
183 views
Remove noise on nonlinear signal
This signal represents a drawn line. For some reason, the device showed interference as shown in the figure below:
The question is: how can I remove the interference, making the signal as continuous ...
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2answers
89 views
Modelling the amplitude and phase through an amplifier
I am writing a software simulator to simulate a real physical acoustic interferometer. I now want to write the module to model the microphone amplifier(s). I'd like to be able to specify the frequency ...
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1answer
147 views
What is meant by “Cubic Difference Frequency”?
The cubic difference frequency (or 3rd degree intermodulation product) is given by:
$$D_3 = - 10\log\left(\frac{P_2\left(2 f_{1,2} - f_{2,1}\right)}{P_2\left(f_1,f_2\right)}\right)$$
where $P_2$ is ...
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1answer
139 views
How can I describe a sum of sinusoids by an equivalent lowpass signal?
I consider a sinusoidal signal with fixed amplitude $A_{\rm in}$ and frequency $f_c$.
This signal is sent into a nonlinear amplifier, whose AM/AM and AM/PM characteristics are known. Using these ...
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0answers
34 views
Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?
e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is?
Also, ...
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0answers
39 views
variance of filtered polynomial
Consider the following system:
What is the variance of $y$, $\mathbb{E}(y^2)$ ?
(EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
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0answers
106 views
DAC output SFDR and Harmonics does not meet at particular decimal frequencies
We are using a current output DAC to perform waveform generation in the band of $20\textrm{ MHz}$ to $500\textrm{ MHz}$ and sampling at $1.2\textrm{ GHz}$. SFDR and harmonics suppression requirement ...
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1answer
58 views
Should you include division by coefficient of variation in WV reconstruction for its normed 1D signal?
I make a new ECG time series from WV spectrum of original signal and its L2 energy normalisation.
I am thinking if the reconstruction step benefits from covariance at each time point.
I take later a ...
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1answer
166 views
Discrete time non-linear time invariant system dynamics descriptions (state-space or input-output relationship)
For the sake of simplicity the following notation $a_k := a[k]$ is assumed for time sequences.
A completely general discrete-time (DT) non-linear(NL) time-invariant (TI) dynamical system can be ...
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3answers
735 views
Dynamic convolution vs Volterra series
I'm trying to understand how a dynamic convolution model relates to something like a Volterra series, and what kinds of effects the latter can capture that the former can't (and vice versa). By ...
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2answers
206 views
Power spectral density of $\left(x(t)\right)^2$?
The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as
$$y(t) = (x(t))^2$$
Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation
$$R_x(...
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2answers
100 views
Can white Gaussian noise improve signal level in non-linear device?
In the system shown below, can white Gaussian noise amplify or attenuate the input signal?
Most of the time we check signal level proportional to noise level (such as noise figure) not singly.
I ...
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1answer
68 views
Nonlinear time-invariant frequency doubler
Does there exist a causal nonlinear, time-invariant system that maps each input function $k \cdot\cos(fx)$ to $k \cdot\cos(2fx)$ for all choices of $k, f \in \Bbb R$?
If so, can one represent this ...
4
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1answer
96 views
What subclass of nonlinear systems can be represented by Volterra series?
Can every possible nonlinear time-invariant Volterra series be represented by a Volterra series?
If not, which ones can?
Also, are there any time-variant systems that can be represented by Volterra ...
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2answers
82 views
The frequency spectrum of a static non-linearity driven by colored noise
Does there exist any straight-forward theory that can explain what happens to colored noise that passes through a static non-linearity? That is, if you have colored noise
$$v = H u \, , \; u \sim N(0,\...
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3answers
128 views
Linearizing digital-analog converters
I'm looking at ways to improve the effective resolution of DACs. It seems that element mismatch (i.e. integral non-linearity) is the main contributor to distortion in modern DACs. Apart from ...
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1answer
141 views
Is it possible to use a Volterra series to generate subharmonics?
Taylor series can create harmonics of the frequencies in an input signal. I'm wondering if it is likewise possible to use Volterra series to create sub-harmonics of the frequencies in that signal.
...
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1answer
764 views
Possibilties of chebyshev polynomial waveshaping
When talking about harmonic distortion, or more specifically waveshaping, we say the order of distortion, can be solved from the equation:
$x^n$
Where n is the order of distortion. To my knowledge ...
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1answer
141 views
Counter-example to show that this system is non-linear?
I have a discrete-time system y[n] = x[n]*x[n-1]
I need to show that this system is non-linear by using a counter example rather than by disproving with algebra ...
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1answer
2k views
Kalman Filter to estimate 3D position of a node
Code given on this link works for 1D:
Kalman filter for position and velocity: introducing speed estimates
In my problem I need to estimate 3D position.What is the criteria ?
How F, G ,H,Q and R ...
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0answers
54 views
Spectral density of 1-bit nonlinear detector in terms of analog spectral density
Suppose we have a time dependent noise signal $\theta(t)$.
We sample $\theta(t)$ with a device which has 1 bit of resolution and is itself stochastic in the sense that the readout value $u$ of the ...
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1answer
51 views
Nonlinear tricks for blocking wide band noise
Conventional methods of filtering allow one to block parts of a frequency band while passing others.
But thinking outside of conventional means, and perhaps not based on any frequency methods at all, ...
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3answers
5k views
What is the advantage of weighted median filter over median filter?
I could not find any proof or comparison of weighted median and median filters. Yes the more occurring pixel contributes much but what should be the criteria of choosing weight function. And any ...
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2answers
1k views
How to prove that frequency mixer is a nonlinear system?
I know that frequency mixer $y(t)=x(t)cos(\omega_ct)$ is a nonlinear system since its output has frequency components that are not present in the input. To prove its nonlinearity, it shuldd be shown ...
