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# Questions tagged [non-linear]

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### 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 ...
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 ...
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1 vote
88 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 ...
• 103
39 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? $x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
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 ...
1 vote
101 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?
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109 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 ...
• 527
157 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}_{{ \...
• 83
553 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 ...
• 183
1 vote
59 views

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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 ...
• 183
749 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 ...
162 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 ...
• 123
108 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 ...
• 17
81 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 ...
130 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 ...
• 157
1 vote
104 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 ...
• 1,327
1 vote
140 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 ...
• 131
156 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 ...
• 117
490 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) ...
123 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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132 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 ...
201 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+...
659 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 ...
• 1,176
1 vote
91 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 ...
• 145
1 vote
63 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 ...
1 vote
131 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 ...
1 vote
116 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 ...
71 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): ...
1 vote
228 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 ...
44 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 ...
198 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 ...
225 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
34 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
48 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 ...
• 11
324 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, ...
1 vote
846 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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1 vote
151 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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537 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 ...
• 107
1 vote