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Questions tagged [non-linear]

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185 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 ...
1 vote
51 views

lsqcurvefit using dynamic input data

I have input vector $\boldsymbol{u}$ and output vector $\boldsymbol{y}$ of length $N$, and I use $u_k,y_k$ to denote the $k$-th elements of $\boldsymbol{u}$ & $\boldsymbol{y}$ and $u_{k-1}$ as the ...
708 views

Efficient implementation of rolling MAD/Hampel filter

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 ...
86 views

Method to extract a phase between input and output of a nonlinear system

I have a nonlinear (blackbox) system which gets a singular frequency (f) signal as input: input = A*sin(2*pi*f) + B And I get an output signal, which has ...
377 views

INL-THD, DNL-SNR Relation

What do the following statements on pages 13 and 15 in this linked document mean? DNL, a static specification, relates to SNR, a dynamic specification. INL is a static specification and relates to ...
1 vote
110 views

Is heat equation considered as LTI system?

The heat equation $$\frac{\partial u}{\partial t} = \alpha \nabla^2 u + f(x,t) \tag 1$$ Here, $u$ represents the temperature field, $\alpha$ is the thermal diffusivity of the material, $\nabla^2$ is ...
1 vote
507 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 ...
59 views

Linearity of a system to biomedical applications

Suppose $x(t)$ is temperature and $y(t)$ is sweat. If the following equation describes the system, answer if is it linear or not. $y(t) = [H(x)](t)$ . I would say that it isn't linear because we dont ...
1 vote
101 views

second order cross correlation

I have two signal sequences $u$ and $y$, where the former is the input to a system and the latter is the output of the same system. I would like to find second-order correlation between the two ...
41 views

How to check if a NON LTI System is invertible?

$T\left\{x\left(t\right)\right\}=x\left(t\right)cos\left(\omega t\right)+1$ Can I say that? or there is another way? $x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
1 vote
109 views

Using MATLAB's fmincon() Solver for Linear Optimization Problem

If I have a linear optimization problem to be solved, is it correct to use the FMINCON SOLVER? If not, why?
787 views

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 ...
158 views

How to solve optimization problem

I am a newbie in Optimization. I have this Optimization problem, could anyone help how can I analyze it and solve it? \begin{align}\label{Problem_formulation} \mathbb P_1& ~~~~~~\mathop{\max}_{{ \...
133 views

Calculating THD vs. Frequency of an Acoustic System using the Exponential Swept Sine Method

I am working on analyzing the total harmonic distortion (THD) vs. frequency curve for an acoustic system. I am aware of the traditional method of exciting the system with a mono-frequency wave and ...
689 views

How to avoid harmonic distortions in a DAC?

I have a DAC which is assumed to be nonlinear, such that it produces unwanted harmonic distortions at integer multiples of the input frequencies. (EDIT: Any other nonlinear distortions, such as ...
1 vote
60 views

110 views

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 ...
45 views

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 ...
1 vote
67 views

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 ...
87 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 ...
77 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 ...
273 views

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 ...
529 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) ...
271 views

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 ...
112 views

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 ...
1 vote
64 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 ...
790 views

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 ...
181 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 ...
82 views

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 ...
138 views

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 ...
115 views

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 ...