Questions tagged [non-linear]
The non-linear tag has no usage guidance.
81
questions
0
votes
0answers
17 views
How to prove that this signal function doesn't perform as a linear system?
The below signal function is given.
$$y[n]=x[n]+x[n-1]+2$$
I defined the below 2 functions.
$y_{1}[n]:=T[x_{1}[n]]=x_{1}[n]+x_{1}[n-1]+2$
$y_{2}[n]:=T[x_{2}[n]]=x_{2}[n]+x_{2}[n-1]+2$
I tried below.
$...
0
votes
0answers
15 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
46 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
104 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
65 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
23 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
55 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+...
0
votes
0answers
33 views
Discrete representation of a signal that has unevenly spaced samples in frequency
I'd like to describe a problem that I've been struggling with for a while. I want to apologize in advance due to the long text. I just want to be as clear as possible in my first post.
Consider the ...
3
votes
0answers
101 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
51 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
37 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
53 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
28 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
51 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
43 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
32 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
87 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
58 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
39 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
164 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
208 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
87 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
251 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
140 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
79 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
44 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
104 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
212 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
323 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
33 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
47 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
204 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
154 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
57 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
336 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
150 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)$$
with unknown (but deterministic) parameters $A_k,\mu_k,\...
0
votes
0answers
141 views
Improving credit-card-like image scan for OCR
OCR works best for black on white or binary images, where letters have sharp contours, no noise, and solid filling, i.e. they are nothing like this:
For the curious it's a part of a document number ...
6
votes
1answer
403 views
Extended Kalman Filter for Linear Systems with Non Linear Measurements
I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates.
...
2
votes
1answer
140 views
Why harmonic components appear only after a certain level when a signal is clipped?
I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level.
The Python code to reproduce the effect is given below. The signal has 3 ...
4
votes
1answer
19k views
How to determine if the system is linear or nonlinear
Given a signal
$$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
316 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
67 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
119 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
132 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.
...
1
vote
3answers
4k 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
1k 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
209 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 ...
