Questions tagged [non-linear]
The non-linear tag has no usage guidance.
77
questions
1
vote
1answer
28 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 ...
0
votes
1answer
29 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
43 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
26 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
47 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
0answers
32 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
10 views
Non-linear system identification with random lag errors
I've been researching this topic for a little while and I haven't found anything particularly concrete. I'd very interested to know if there is an accepted solution for this problem, and whether there ...
0
votes
0answers
29 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
43 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
43 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
26 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
38 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 ...
0
votes
0answers
28 views
Decorrelation for Adaptive Feedback Cancellation: How does it work?
I am going through lecture slides on adaptive feedback cancellation right now, and several decorrelation measures are mentioned.
As I understand, these are important in order to avoid a bias in filter ...
5
votes
2answers
113 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
80 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
61 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:
$$
h(t) =
\begin{cases}
\frac{A}{\tau}te^{-\frac{t}{\tau}}, &...
0
votes
0answers
31 views
what is the co-variance of system output cooresponding to a non-iid random variable
Consider the following system.$\DeclareMathOperator{\sign}{sign}$
$$
\begin{aligned}
&\dot{e_1}=c_1e_1+c_2e_2+\eta\\
&\dot{e_2}=c_3e_1+c_4e_2-c_5 \sign(e_1)+a \eta
\end{aligned}
$$
which $\eta$...
0
votes
0answers
123 views
Using Kalman filter vs Extended Kalman filter for differential drive robot with IMU
I have an IMU that provides me with a heading that is pretty accurate and accurate encoders on the wheels of my differential drive robot which provides me with pretty accurate velocity but has ...
2
votes
0answers
46 views
How does the “additive operator splitting” exactly work?
I am reading about the non-linear (or non-homogenous) diffusion method (aka anistropic diffusion method). There are several ways of implementing this method. In all cases, we first need to discretise ...
3
votes
1answer
181 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
94 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
69 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
36 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 ...
1
vote
2answers
79 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
156 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 ...
0
votes
1answer
229 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
31 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
38 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
184 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
124 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
46 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 ...
2
votes
2answers
302 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 ...
2
votes
1answer
139 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)$$
with unknown (but deterministic) parameters $A_k,\mu_k,\...
0
votes
0answers
136 views
Improving credit-card-like image scan for OCR
OCR works best for black on white or binary images, where letters have sharp contours, no noise, and solid filling, i.e. they are nothing like this:
For the curious it's a part of a document number ...
4
votes
1answer
346 views
Extended Kalman Filter for linear systems with non-linear measurements
I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates.
...
2
votes
1answer
134 views
Why harmonic components appear only after a certain level when a signal is clipped?
I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level.
The Python code to reproduce the effect is given below. The signal has 3 ...
4
votes
1answer
13k views
How to determine if the system is linear or nonlinear
Given a signal
$$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
287 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
1k 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 ...
1
vote
2answers
63 views
Attenuating peaks of a signal in a specific direction
Consider a segment of a time-domain signal shown in the following graph and the two marked peaks, the first one facing downwards (in red) and the second one facing upwards (in black).
I would like to ...
2
votes
1answer
109 views
Effect of nonlinear transformation on digital signal
Currently, I know that by passing a band-limited baseband digital signal through a nonlinear system results in the expansion of the original signal's bandwidth and creates harmonics.
Therefore, I ...
2
votes
0answers
128 views
Check if I has right: Is this the Extended Kalman Filter
I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here.
...
0
votes
3answers
3k views
Upsampling - What purpose does the interpolation filter have?
I want to apply some nonlinear processing to a signal, namely: I want to implement a tube emulation which adds warmth/harmonic distortion to a digital audio signal. I am worried about aliasing, so I ...
6
votes
3answers
3k views
Why is not Fourier Transform Good for Non-linear Processes
I was reading through slides about Hilbert Huang Transform. In slide 14, which talks about the motivations of a new method instead of Fourier Transform (FT), the author provides those two reasons in ...
7
votes
2answers
970 views
Why is aliasing inherently non-linear?
E.g. when having 2 signals $x(t)$ and $y(t)$ and transforming each one with adding their spectra, the operation is linear, as the result would be the same as the transformation of $(x + y)(t)$.
Even ...
1
vote
1answer
188 views
Create distortion from basic linear (and non-linear if neccessary) DSP elements
I'm studying mechatronics and I'm intrested in DSP basics. My lecturer said that there are four basic linear DSP elements:
Adder (and other mathematical operations)
Amplification (shown on diagrams ...
0
votes
1answer
245 views
Determining invertibility of a system [closed]
Given a system which is either non-linear and/or time variant, Is there any systematic way to determine if this system is invertible?
For example how to determine invertibility of this system?
$$\int_{...
3
votes
2answers
203 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 ...
0
votes
2answers
97 views
Modelling the amplitude and phase through an amplifier
I am writing a software simulator to simulate a real physical acoustic interferometer. I now want to write the module to model the microphone amplifier(s). I'd like to be able to specify the frequency ...
1
vote
1answer
162 views
What is meant by “Cubic Difference Frequency”?
The cubic difference frequency (or 3rd degree intermodulation product) is given by:
$$D_3 = - 10\log\left(\frac{P_2\left(2 f_{1,2} - f_{2,1}\right)}{P_2\left(f_1,f_2\right)}\right)$$
where $P_2$ is ...
