Questions tagged [non-linear]

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Where to start in Nonlinear System Identification

Now that I have accomplished learning and applying various linear system identification techniques to simulated data sets. I am looking now to dig deeper into the world of system identification by ...
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Single Kalman Filter: Resistance based on measurment of current and Voltage [closed]

Given measurement of voltage and current, which contain gaussian noise with known variance and a constant unknown offset $a_0$, I have attempted to estimate the resistance $R=\frac{V}{I}$. The ...
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Advice on seperation of impulse responses for harmonic distortion orders

I am working based on Angelo Farinas paper: Simultaneous measurement of impulse response and distortion with a swept-sine technique. The purpose of the work is part of a loudspeaker measurement and ...
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3 votes
3 answers
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Modeling Analog Filters for Software Implementation

I am curious about software implementation of analog filters. For example, let's say I have a moog low pass filter. What should I do to turn this device into satisfactory, analog sounding software. I ...
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2 votes
1 answer
85 views

Time Shifting, Reversal and Delay

For a signal, $s(t)$ undergoing multiple transformations of time scaling, reversal and delay, how should I approach the problem of finding the resultant output signal? $$s\left(\pm \frac{t-t_0}{T}\...
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Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions?

Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions $y(t)$?? With output I am meaning that $y(t)$ is such ...
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4 votes
1 answer
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How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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2 votes
1 answer
48 views

Designing a controller with hard output limits

I'm trying to put together a control algorithm to use a heater to drive a 2nd order thermal system to the target temperature as quickly as possible. I've done a nice state-space model with an extra ...
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-1 votes
1 answer
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Impulse response $h[n]$ of a non linear I/O equation

my question concerns an assignment that was given to us at school. We have been given a list of I/O equations and it is required, for each of them, to find the impulse response $h[n]$ and the ratio ...
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1 answer
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Time-frequency analysis of a nonlinear system

I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on ...
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How to find a system without an input $x[n]$ is linear or non linear

The question is this: $$ y[n] = \cos\left(\frac{5\pi}{8}n + \frac{\pi}{4}\right)$$ This is what my teacher said when I asked him for help-: In any system, inputs are not given, then we have to assume ...
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what is the correct order of applying a nonlinear operation and downsampling (with anti-aliasing)

In UltraSound imaging, after beam-forming and obtaining the envelope, Log-compression which is a non-linear operation and scan conversion which is a 2D interpolation (with inherent down-sampling) is ...
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2 answers
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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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1 answer
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Applying Superposition Property : $x^{2}[n]$ vs $x[n^{2}]$

If we consider the mapping $\mathcal{H} : x[n]\mapsto y[n]$ and define the following output signal $y_{1}[n]:=\mathcal{H}\{x[n]\}:=x^{2}[n]$, then one can easily verify that such system is non-linear ...
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2 votes
3 answers
195 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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1 answer
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Can I measure non-linearity of a line echo path?

I'm dealing with an echo signal from a hybrid. An echo path includes DAC, the hybrid, ADC and the line infrastructure. I can see, that after using a digital linear echo-canceller the residual echo ...
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1 answer
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Offline State Estimation

Imagine I have a nonlinear system: $$ \frac{\text{d} x}{\text{d} t} = f(x,t)\\ y = g(x). $$ I can design a nonlinear observer to estimate the state $x$ based on the measurements $y$. However, this ...
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Determine if system is linear time variant

The system equation is given as: $$y(n)=(n-1)x(n-1)+(n+1)x(n+1)$$ I solved that the system is time variant: \begin{align} y(n-k)&=(n-k-1)x(n-k-1)+(n-k+1)x(n-k+1)\\ H[x(n-k)]&=(n-1)x(n-k-1)+(n+...
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3 votes
0 answers
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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 ...
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1 vote
1 answer
69 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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1 answer
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How to find the value of regularization parameter/s when having one or multiple priors

I am working on a image reconstruction framework, specifically interferometry. In simple words we have data that is pertubated by noise, say $$ V^o_i = V_i + \sigma_i $$ Where $V^o$ is a complex ...
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1 vote
1 answer
85 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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1 vote
1 answer
37 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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1 answer
60 views

Erosion compotition rule $\left ( f \ominus g \right ) \ominus h = f \ominus \left (g \oplus h \right ) $

I want to prove that erosion of a signal by a function $g$ followed by erosion with another function $h$ is equivalent to erosion of the signal by the dilation of the two functions (Erosion property): ...
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1 vote
0 answers
133 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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0 votes
0 answers
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FSK carrier frequency estimation in non equiprobable data

We know that in equiprobable data,change in phase over a time interval, this result will be directly proportional to frequency: f∝Im(s(n)s(n−1)∗) Where s(n) is the normalized complex FSK time domain ...
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0 votes
1 answer
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Total Harmonic Distortion THD for the rectifier

I have a circuit with rectifier and this cause the non-linearity and consequently harmonic. I show it on the oscilloscope and then collect the signal from the oscilloscope to the computer by using the ...
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0 votes
1 answer
108 views

How to quantify phase distortion of a filter specific to a signal?

For example, a EKG input signal is filtered with a known transfer function that does not have linear phase. How do you quantify the phase distortion of the output signal given you have the input? I ...
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1 vote
0 answers
29 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 ...
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1 vote
1 answer
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Nonlinear model identification [closed]

I need to build nonlinear model having recorded input/output data. The object is not simple and linear model will fail for sure. What other options exist besides Least Mean Squares? I need to ...
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7 votes
2 answers
241 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, ...
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1 vote
1 answer
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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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1 answer
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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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3 votes
1 answer
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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 ...
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1 vote
3 answers
256 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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0 votes
0 answers
127 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. ...
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0 votes
1 answer
61 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 the ...
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1 vote
2 answers
152 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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3 votes
1 answer
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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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1 answer
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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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0 votes
1 answer
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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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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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-1 votes
1 answer
224 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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-2 votes
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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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-1 votes
2 answers
81 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 ...
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3 votes
2 answers
421 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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4 votes
1 answer
168 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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0 votes
0 answers
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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 ...
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6 votes
1 answer
518 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. ...
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2 votes
1 answer
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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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