Questions tagged [non-linear]
The non-linear tag has no usage guidance.
101
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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 ...
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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 ...
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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, ...
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Precisions on Hilbert Huang transform
After investigating signal analysis methods based on empirical mode decomposition (EMD), I found that recent developments are mostly related to the Hilbert Huang transform (HHT) and the Local Mean ...
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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.
...
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6
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PID With Prediction
First, I just want to start off by saying that I am a programmer, and am no expert in complex algorithms, and will probably not be able to apply complex pseudo-code or other descriptions of a solution....
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2
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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 ...
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356
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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 ...
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257
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Delta-limiting filter
Consider a filter which tracks $x_i$, clipping $|x_i - x_{i-1}| >$ some limit, say 1:
...
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4
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3
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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 ...
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Dynamic convolution vs Volterra series
I'm trying to understand how a dynamic convolution model relates to something like a Volterra series, and what kinds of effects the latter can capture that the former can't (and vice versa). By ...
- 507
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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....
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What subclass of nonlinear systems can be represented by Volterra series?
Can every possible nonlinear time-invariant Volterra series be represented by a Volterra series?
If not, which ones can?
Also, are there any time-variant systems that can be represented by Volterra ...
- 507
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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 ...
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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,\...
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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).
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4
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Can white Gaussian noise improve signal level in non-linear device?
In the system shown below, can white Gaussian noise amplify or attenuate the input signal?
Most of the time we check signal level proportional to noise level (such as noise figure) not singly.
I ...
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3
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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 ...
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2
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Is it possible to use a Volterra series to generate subharmonics?
Taylor series can create harmonics of the frequencies in an input signal. I'm wondering if it is likewise possible to use Volterra series to create sub-harmonics of the frequencies in that signal.
...
- 507
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2
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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 ...
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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 ...
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3
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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 ...
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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 ...
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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 ...
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150
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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 ...
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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 ...
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532
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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 ...
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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 ...
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3
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407
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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) ...
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Possibilties of chebyshev polynomial waveshaping
When talking about harmonic distortion, or more specifically waveshaping, we say the order of distortion, can be solved from the equation:
$x^n$
Where n is the order of distortion. To my knowledge ...
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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 ...
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What is the advantage of weighted median filter over median filter?
I could not find any proof or comparison of weighted median and median filters. Yes the more occurring pixel contributes much but what should be the criteria of choosing weight function. And any ...
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1
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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 ...
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1
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Nonlinear time-invariant frequency doubler
Does there exist a causal nonlinear, time-invariant system that maps each input function $k \cdot\cos(fx)$ to $k \cdot\cos(2fx)$ for all choices of $k, f \in \Bbb R$?
If so, can one represent this ...
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Kalman Filter to estimate 3D position of a node
Code given on this link works for 1D:
Kalman filter for position and velocity: introducing speed estimates
In my problem I need to estimate 3D position.What is the criteria ?
How F, G ,H,Q and R ...
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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}_{{ \...
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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 ...
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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.
...
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Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?
e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is?
Also, ...
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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?
$$s\left(\pm \frac{t-t_0}{T}\...
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3
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Linearizing digital-analog converters
I'm looking at ways to improve the effective resolution of DACs. It seems that element mismatch (i.e. integral non-linearity) is the main contributor to distortion in modern DACs. Apart from ...
- 1,035
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Power spectral density of $\left(x(t)\right)^2$?
The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as
$$y(t) = (x(t))^2$$
Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation
$$R_x(...
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How to prove that frequency mixer is a nonlinear system?
I know that frequency mixer $y(t)=x(t)cos(\omega_ct)$ is a nonlinear system since its output has frequency components that are not present in the input. To prove its nonlinearity, it shuldd be shown ...
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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 ...
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1
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319
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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 ...
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Nonlinear wavelets transform?
Is wavelet a Nonlinear transform, or Not?
specifically, continuous wavelet transform with morlet function.
I am studying behavior of a dynamic system, and it has nonlinear behaviour. can I employ ...
- 1,307
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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 ...
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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 ...
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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 ...
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2
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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 ...
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