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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 ...
AOJ keygen's user avatar
0 votes
1 answer
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 ...
Panos's user avatar
  • 25
1 vote
0 answers
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 ...
Neuling's user avatar
  • 103
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1 answer
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? $x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
Ben Shaines's user avatar
0 votes
1 answer
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 ...
ValientProcess's user avatar
1 vote
1 answer
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?
Srikanth's user avatar
3 votes
0 answers
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 ...
DSP novice's user avatar
2 votes
1 answer
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}_{{ \...
Hadeel's user avatar
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5 votes
2 answers
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 ...
Harry's user avatar
  • 183
1 vote
0 answers
59 views

Non-linear external effect in Kalman filter

Let's say I have a Kalman filter with this simple state model: $$\begin{pmatrix} x^0_{k+1}\\ x^1_{k+1}\\ \end{pmatrix} = \begin{pmatrix} 1 & \Delta t\\ 0 & 1\\ \end{pmatrix} \begin{pmatrix} x^...
user42865's user avatar
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1 answer
78 views

Show that decomposition does not hold for non-linear system

The solution to an inhomogeneous differential equation can be split up into homogeneous solution and a particular solution (forced response). Another way to split up the solution to an inhomogeneous ...
Carl's user avatar
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1 vote
0 answers
198 views

Derivation of the process noise covariance matrix for non linear system in UKF

I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
macia's user avatar
  • 53
5 votes
2 answers
681 views

Is there a way to compute the spectrum effect of a non-linear function?

I'm interested in developing audio software. I've read the books by Will Pirkle and there's something I'm struggling to understand about how non-linear functions affect the frequency spectrum of a ...
U62's user avatar
  • 153
0 votes
1 answer
299 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 ...
bb0667's user avatar
  • 103
2 votes
1 answer
40 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 ...
SPARSE's user avatar
  • 129
1 vote
0 answers
60 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 ...
doumham's user avatar
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3 votes
1 answer
237 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 ...
Jammus's user avatar
  • 31
3 votes
3 answers
728 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 ...
someoneunimportant's user avatar
2 votes
1 answer
177 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}\...
kdkvcm's user avatar
  • 21
3 votes
3 answers
259 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 ...
Joako's user avatar
  • 183
4 votes
1 answer
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 ...
user1477107's user avatar
2 votes
1 answer
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 ...
Rgaddi's user avatar
  • 123
-1 votes
1 answer
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 ...
canuel's user avatar
  • 17
0 votes
1 answer
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 ...
Ali Baradaran Birjandi's user avatar
0 votes
1 answer
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 ...
achhainsan's user avatar
1 vote
1 answer
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 ...
Mohammad M's user avatar
  • 1,327
1 vote
2 answers
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 ...
machfour's user avatar
  • 131
0 votes
1 answer
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 ...
B E I R U T's user avatar
2 votes
3 answers
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) ...
Kofi Mokome's user avatar
0 votes
1 answer
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 ...
megasplash's user avatar
0 votes
1 answer
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 ...
Ali Baradaran Birjandi's user avatar
0 votes
1 answer
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+...
Cristina Mosanu's user avatar
4 votes
2 answers
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 ...
Gideon Genadi Kogan's user avatar
1 vote
1 answer
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 ...
CD86's user avatar
  • 145
1 vote
1 answer
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 ...
Miguel Cárcamo's user avatar
1 vote
1 answer
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 ...
chronosynclastic's user avatar
1 vote
1 answer
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 ...
Dabbinator420's user avatar
0 votes
1 answer
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): ...
Rog Fed's user avatar
1 vote
0 answers
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 ...
sudhakar Mishra's user avatar
0 votes
0 answers
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 ...
Angelina ha's user avatar
0 votes
1 answer
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 ...
SnowMan's user avatar
0 votes
1 answer
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 ...
pproctor's user avatar
1 vote
0 answers
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 ...
JH Lee's user avatar
  • 11
1 vote
1 answer
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 ...
yozzi's user avatar
  • 11
7 votes
2 answers
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, ...
Mike Battaglia's user avatar
1 vote
1 answer
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 ...
bikalpa's user avatar
  • 211
1 vote
1 answer
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}}, &...
axel's user avatar
  • 53
3 votes
1 answer
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 ...
Chi's user avatar
  • 107
1 vote
3 answers
464 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 ...
Natalie Johnson's user avatar
0 votes
0 answers
169 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. ...
stretch's user avatar