Questions tagged [non-linear]

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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 ...
7
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1answer
2k views

Precisions on Hilbert Huang transform

After investigating signal analysis methods based on empirical mode decomposition (EMD), I found that recent developments are mostly related to the Hilbert Huang transform (HHT) and the Local Mean ...
6
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3answers
3k 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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1answer
407 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. ...
6
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1answer
900 views

PID With Prediction

First, I just want to start off by saying that I am a programmer, and am no expert in complex algorithms, and will probably not be able to apply complex pseudo-code or other descriptions of a solution....
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2answers
169 views

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, ...
5
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1answer
196 views

Delta-limiting filter

Consider a filter which tracks $x_i$, clipping $|x_i - x_{i-1}| >$ some limit, say 1: ...
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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 ...
4
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1answer
19k 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
326 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

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 ...
3
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1answer
141 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 ...
3
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1answer
260 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 ...
3
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1answer
226 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 ...
3
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2answers
108 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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0answers
106 views

Efficient implementation of spike removal

I have implemented the moving median absolute deviation (moving MAD) and it seems like bit-exact to Matlab's implementation. Nevertheless, I am sure that it is not efficient. The usual median filter ...
3
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2answers
211 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 ...
2
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1answer
140 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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2answers
336 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 ...
2
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1answer
79 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 ...
2
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1answer
4k 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 ...
2
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3answers
7k 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 ...
2
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1answer
121 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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1answer
150 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
132 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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0answers
45 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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3answers
247 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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2answers
313 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
2k 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 ...
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2answers
105 views

How to find the output mean and autocorrelation of a non-linear system

I need help with this question. I am sure this is the right StackExchange forum for this type of question. Consider a nonlinear device such that the output is $Y(t) = aX^2(t)$, where the input X(t) ...
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3answers
4k 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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1answer
1k 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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2answers
45 views

Analysis of the ratio of two moving average filters

I have created a basic segmentation algorithm for 1-D signals (e.g. audio) based on a ratio of energy averages. The classification rule involves comparing the signal energy measured over a short time ...
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1answer
209 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
1k views

Nonlinear wavelets transform?

Is wavelet a Nonlinear transform, or Not? specifically, continuous wavelet transform with morlet function. I am studying behavior of a dynamic system, and it has nonlinear behaviour. can I employ ...
1
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1answer
54 views

Numerical differentiation on circular data

I have multiple time series of position data (x, y, z) and orientation data expressed as Euler/Tait-Bryan angles (yaw, pitch, roll) obtained from a head tracking device. I need to obtain velocity ...
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2answers
67 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 ...
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1answer
167 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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2answers
106 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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1answer
208 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
51 views

Lifting scheme versus filter banks

I am having some trouble understanding the intuitive connection between the two. I worked through all the theory and learned that Sweldens showed how to derive lifting steps when having admissible ...
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1answer
28 views

What does an ADC DNL specification mean, exactly?

I'm looking at the differential non-linearity specification for an Analog-Digital converter. The spec sheet claims that the DNL ranges from -1LSB to +1LSB, with a typical value of $\pm$0.6LSB. What ...
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1answer
218 views

Having difficulty checking for time invariance of discrete system

A system is given with the following equation: $$y(n) = 3y^2 (n-1) - nx(n) + 4x(n-1) - 2x(n+1)$$ I need to check for the linearity and time invariance of the system. By just looking at the equation I ...
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1answer
90 views

Impulse Response Function-Green's Function

Assuming a input-output system $$u(t) = c \cdot \big(h(t)\circledast m(t) \big)$$ where its impulse response function is: $$ h(t) = \begin{cases} \frac{A}{\tau}te^{-\frac{t}{\tau}}, &...
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3answers
152 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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2answers
107 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 ...
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1answer
331 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
242 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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0answers
50 views

STFT Reconstruction After Modification

Why do we want to minimize the difference between the two signals the original one and the modified one when all we want is the modified constructed signal? What is the purpose of making it the ...
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0answers
28 views

How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...