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Questions tagged [non-linear]

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How does the “additive operator splitting” exactly work?

I am reading about the non-linear (or non-homogenous) diffusion method (aka anistropic diffusion method). There are several ways of implementing this method. In all cases, we first need to discretise ...
3
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1answer
75 views

SRF-PLL discretization problem

So I've been working on how to digitally implement a static reference frame PLL (SRF-PLL), which is a quite popular PLL used for extracting three-phase grid angle. This PLL works by using the DQ0 ...
1
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3answers
41 views

Why only odd harmonics after non-linear amplification?

Why do I get only odd harmonics appearing? This not only happens at saturation of the transfer curve, but also in the linear portion of the curve. I make a input signal that has too high power that ...
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0answers
25 views

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. ...
0
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1answer
23 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 ...
1
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2answers
51 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 ...
2
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1answer
76 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 ...
0
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1answer
33 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 ...
0
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1answer
31 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
26 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 ...
-1
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1answer
53 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 ...
-2
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1answer
75 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
27 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
243 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 ...
1
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1answer
100 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,\...
0
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0answers
108 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
177 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. ...
2
votes
1answer
105 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 ...
2
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1answer
6k 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....
4
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3answers
231 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). ...
3
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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 ...
1
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2answers
57 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
92 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
105 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. ...
0
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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 ...
5
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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 ...
6
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2answers
842 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 ...
1
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1answer
150 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 ...
0
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1answer
124 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_{...
3
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2answers
186 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 ...
0
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2answers
90 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 ...
1
vote
1answer
150 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 ...
0
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1answer
151 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, ...
1
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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
109 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 ...
0
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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 ...
0
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1answer
175 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
763 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 ...
0
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2answers
207 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(...
3
votes
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 ...
2
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1answer
70 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 ...
3
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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
86 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
141 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 ...
1
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1answer
146 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. ...
1
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1answer
806 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
146 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 ...
0
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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 ...