Questions tagged [non-linear]
The non-linear tag has no usage guidance.
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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 ...
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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?
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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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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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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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Applying a frequency and phase sensitivity post-recording
I have a particle velocity sensor that I'm recording, which has a non-linear frequency and phase response. I have frequency and phase correction curves for it, however, the proprietary acquisition ...
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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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Non-linear external effect in Kalman filter
Let's say I have a Kalman filter with this simple state model:
$$\begin{pmatrix} x^0_{k+1}\\ x^1_{k+1}\\ \end{pmatrix} = \begin{pmatrix} 1 & \Delta t\\ 0 & 1\\ \end{pmatrix} \begin{pmatrix} x^...
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Show that decomposition does not hold for non-linear system
The solution to an inhomogeneous differential equation can be split up into homogeneous solution and a particular solution (forced response).
Another way to split up the solution to an inhomogeneous ...
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Derivation of the process noise covariance matrix for non linear system in UKF
I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
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Is there a way to compute the spectrum effect of a non-linear function?
I'm interested in developing audio software. I've read the books by Will Pirkle and there's something I'm struggling to understand about how non-linear functions affect the frequency spectrum of a ...
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Is it possible to use a Volterra series to generate subharmonics?
Taylor series can create harmonics of the frequencies in an input signal. I'm wondering if it is likewise possible to use Volterra series to create sub-harmonics of the frequencies in that signal.
...
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Time Shifting, Reversal and Delay
For a signal, $s(t)$ undergoing multiple transformations of time scaling, reversal and delay, how should I approach the problem of finding the resultant output signal?
$$s\left(\pm \frac{t-t_0}{T}\...
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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 ...
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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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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 ...
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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 ...
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Should you include division by coefficient of variation in WV reconstruction for its normed 1D signal?
I make a new ECG time series from WV spectrum of original signal and its L2 energy normalisation.
I am thinking if the reconstruction step benefits from covariance at each time point.
I take later a ...
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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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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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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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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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+...
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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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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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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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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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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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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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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 ...
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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 ...
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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):
...
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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 ...
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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 ...
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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 ...
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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 ...
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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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