Questions tagged [non-linear]

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Trying to run an implementation of lsqcurvefit from the Optimization Toolbox from Matlab in python

trying to implement lsqcurvefit from matlab in python with no success. Below is the matlab code I am trying to port to python: ...
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2answers
46 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
77 views

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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1answer
64 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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0answers
17 views

How to solve Lorentzian equation in matlab with once unknown variable

I am trying to solve Lorentzian in maltab but unable to get expected result. My equation is as follow - ...
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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
37 views

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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1answer
46 views

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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1answer
93 views

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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2answers
106 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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2answers
57 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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1answer
151 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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1answer
25 views

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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1answer
58 views

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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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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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 ...
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0answers
33 views

Discrete representation of a signal that has unevenly spaced samples in frequency

I'd like to describe a problem that I've been struggling with for a while. I want to apologize in advance due to the long text. I just want to be as clear as possible in my first post. Consider the ...
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1answer
263 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 ...
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1answer
411 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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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 ...
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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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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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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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1answer
51 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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0answers
52 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
32 views

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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1answer
59 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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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 ...
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2answers
171 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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1answer
39 views

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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1answer
219 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
91 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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0answers
81 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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3answers
155 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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1answer
45 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
110 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
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 ...
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1answer
335 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
229 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
33 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
47 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
207 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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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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1answer
157 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
362 views

Confusion about 'memoryless' meaning

I am reading the book "Multiple input describng functions and nonlinear system design" written by A.Gelb and W.E.Vander Velde. At some point it says: Single-valued characteristics are termed ...
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2answers
337 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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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 ...
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0answers
143 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 ...
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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 ...
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1answer
20k 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....