Questions tagged [non-linear]
The non-linear tag has no usage guidance.
88
questions
1
vote
1answer
34 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?
$$s\left(\pm \frac{t-t_0}{T}\...
4
votes
1answer
83 views
How to linearize this state space model and write it in discrete form?
This might not be trivial nor short so in advance thank you all who read this in attempt to help.
I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
2
votes
1answer
41 views
Designing a controller with hard output limits
I'm trying to put together a control algorithm to use a heater to drive a 2nd order thermal system to the target temperature as quickly as possible. I've done a nice state-space model with an extra ...
1
vote
1answer
61 views
Impulse response $h[n]$ of a non linear I/O equation
my question concerns an assignment that was given to us at school.
We have been given a list of I/O equations and it is required, for each of them, to find the impulse response $h[n]$ and the ratio ...
0
votes
1answer
46 views
Time-frequency analysis of a nonlinear system
I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on ...
0
votes
1answer
64 views
How to find a system without an input $x[n]$ is linear or non linear
The question is this:
$$ 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 ...
0
votes
0answers
23 views
EMD code question in finding local max/min points
Trying to understand the following part of the EMD code taken from (https://www.mathworks.com/matlabcentral/fileexchange/55448-empirical-mode-decomposition-animation?s_tid=prof_contriblnk)
...
1
vote
1answer
39 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
vote
2answers
59 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 ...
0
votes
0answers
19 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 -
...
0
votes
1answer
49 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
2answers
138 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) ...
0
votes
1answer
82 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 ...
0
votes
1answer
58 views
Offline State Estimation
Imagine I have a nonlinear system:
$$
\frac{\text{d} x}{\text{d} t} = f(x,t)\\
y = g(x).
$$
I can design a nonlinear observer to estimate the state $x$ based on the measurements $y$. However, this ...
0
votes
1answer
74 views
Determine if system is linear time variant
The system equation is given as:
$$y(n)=(n-1)x(n-1)+(n+1)x(n+1)$$
I solved that the system is time variant:
\begin{align}
y(n-k)&=(n-k-1)x(n-k-1)+(n-k+1)x(n-k+1)\\
H[x(n-k)]&=(n-1)x(n-k-1)+(n+...
3
votes
0answers
189 views
Efficient implementation of spike removal
I have implemented the moving median absolute deviation (moving MAD) and it seems like bit-exact to Matlab's implementation. Nevertheless, I am sure that it is not efficient.
The usual median filter ...
1
vote
1answer
59 views
Lifting scheme versus filter banks
I am having some trouble understanding the intuitive connection between the two. I worked through all the theory and learned that Sweldens showed how to derive lifting steps when having admissible ...
1
vote
1answer
49 views
How to find the value of regularization parameter/s when having one or multiple priors
I am working on a image reconstruction framework, specifically interferometry. In simple words we have data that is pertubated by noise, say
$$
V^o_i = V_i + \sigma_i
$$
Where $V^o$ is a complex ...
1
vote
1answer
71 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
1answer
29 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 ...
0
votes
1answer
59 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
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0answers
107 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 ...
0
votes
0answers
35 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 ...
0
votes
1answer
104 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 ...
0
votes
1answer
88 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 ...
1
vote
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 ...
1
vote
1answer
42 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 ...
5
votes
2answers
199 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
1answer
346 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)$$
I need to check for the linearity and time invariance of the system.
By just looking at the equation I ...
1
vote
1answer
111 views
Impulse Response Function-Green's Function
Assuming a input-output system
$$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}}, &...
3
votes
1answer
330 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 ...
1
vote
3answers
199 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 ...
0
votes
0answers
112 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.
...
0
votes
1answer
55 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 ...
1
vote
2answers
131 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 ...
3
votes
1answer
272 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 ...
1
vote
1answer
403 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 ...
0
votes
1answer
37 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 ...
1
vote
0answers
55 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 ...
-1
votes
1answer
222 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 ...
-2
votes
1answer
200 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
0
votes
2answers
72 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 ...
3
votes
2answers
382 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 ...
3
votes
1answer
162 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 $A_k,\mu_k,\...
0
votes
0answers
150 views
Improving credit-card-like image scan for OCR
OCR works best for black on white or binary images, where letters have sharp contours, no noise, and solid filling, i.e. they are nothing like this:
For the curious it's a part of a document number ...
6
votes
1answer
473 views
Extended Kalman Filter for Linear Systems with Non Linear Measurements
I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates.
...
2
votes
1answer
142 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 ...
4
votes
1answer
22k 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....
4
votes
3answers
372 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).
...
4
votes
3answers
2k views
Volterra Kernel Convolution Method
Here I understand that the first term is a simple convolution of the input signal with first volterra kernel that I have acquired through farina sweep method, my question is if the second term is the ...
