Skip to main content

Tag Info

Hot answers tagged non-linear

10 votes
Accepted

Why is not Fourier Transform Good for Non-linear Processes

Because complex exponentials $e^{\jmath \omega t}$, which are results of Fourier transform, are the eigenfunctions for linear, time invariant (LTI) systems. See eigenfunction of LTI. Also see this ...
• 116
7 votes
Accepted

Volterra Kernel Convolution Method

Yes the MATLAB code is correct. Be careful though, the bandwidth of the signal squared is twice that of the signal itself, which may lead to aliasing if the sampling frequency is too low compared to ...
• 13.6k
7 votes
Accepted

Is there a way to compute the spectrum effect of a non-linear function?

is there any way to calculate the rate at which the harmonics decrease in power for a given function Yes, but it's complicated and typically not worth the bother. If the non-linearity is static, i.e. ...
• 47k
6 votes

Why is aliasing inherently non-linear?

I think you mean "images", not "aliases". They become aliases if there is foldover from resampling. It's because you are not adding two signals, $x(t)$ and $\operatorname{III}(t)$, you are ...
6 votes

Is there a way to compute the spectrum effect of a non-linear function?

Stealing$^\dagger$ from this answer: For non-linear functions that admit a series expansion (e.g. Taylor/Maclaurin), you can get a decent intuition for how fast the harmonics decay. The Maclaurin ...
5 votes

How to determine if the system is linear or nonlinear

As Matt L. says you'll need to check for homogeneity and, possibly, additivity. Homogeneity That test says that if: $$y[n] = f(x[n])$$ then $$A \cdot y[n] = f(A \cdot x[n])$$ for all scalar $A$. ...
• 25.9k
5 votes
Accepted

Power spectral density of $\left(x(t)\right)^2$?

Since the question has been raised as to whether the hint that I had given to the OP in a comment on the original question was appropriate for a newcomer to signal processing, here goes. Stripped of ...
• 20.7k
5 votes
Accepted

What subclass of nonlinear systems can be represented by Volterra series?

The system must be time invariant and smooth in the functional derivative sense. That doesn't guarantee that the Volterra series converges (like with Taylor series, there are pathological counter ...
• 4,593
5 votes

As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

It is very strange phenomena that one object is completely dropped out of attention of researchers. It is Urysohn operator. First of all Urysohn is equivalent to multiple parallel Hammersteins and ...
• 301
5 votes

Modeling Analog Filters for Software Implementation

Modeling real analog components with their non-linear behavior can be a challenge to do digitally. I suggest starting with wave digital filters. Quoting from the linked source: A Wave Digital Filter ...
• 1,183
4 votes

Why is aliasing inherently non-linear?

Hints: Can an LTI system generate components in some frequency $\omega_0$ if the input signal $x(n)$ was such that $X(e^{j\omega_0})=0$? Does aliasing do such thing? The answers to these questions ...
• 5,040
4 votes
Accepted

Create distortion from basic linear (and non-linear if neccessary) DSP elements

Using those four basic elements will allow you to implement linear systems, which can change the magnitude and phase of the input signal, but which will not add the harmonics that are expected from a ...
• 91.1k
4 votes

Is it possible to use a Volterra series to generate subharmonics?

Many years later I was asked to write some of what I've learned on this. The short answer is that it depends on what the term "subharmonics" means - things are very different if we're ...
4 votes
Accepted

Dynamic convolution vs Volterra series

A flavor of dynamic convolution (is that a trademark by the way?) has a different impulse response $g_i$ associated with each range of instantaneous input. A number of ranges can be defined by fuzzy ...
• 13.6k
4 votes

As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

The easiest is Urysohn adaptive filter: http://www.ezcodesample.com/UAF/UAF.html It can build nonlinear model by few lines of code. The theoretical details can be found here http://www.ezcodesample....
• 301
4 votes
Accepted

How to find the output mean and autocorrelation of a non-linear system

The OP's updated working is incorrect. Following up what Hilmar suggested gives \begin{align} Y(t) &= a\left(X(t)\right)^2\\ &= a\left(S(t) + N(t)\right)^2\\ &= a\left(S(t)\right)^2 + 2aS(...
• 20.7k
3 votes

• 12.9k
3 votes
Accepted

How to avoid harmonic distortions in a DAC?

Frequency Planning in Radio Design The OP has clarified in comments that his question is focused on what would I believe would be commonly referred to as frequency planning in the process of radio ...
• 53.8k
2 votes
Accepted

• 768
2 votes

Dynamic convolution vs Volterra series

Dynamic convolution is a model for systems that can be written as follows: $$S[x] = \sum_k (L_k \circ N_k)[x]$$ where $L_k$ are linear time-invariant systems and $N_k$ are non-linear memoryless ...
• 4,593
2 votes
Accepted

What is meant by "Cubic Difference Frequency"?

After skimming through the paper, I can see more clearly now. The measure $D_3$ quantifies the relative strength of the 3rd order intermodulation product. If two sinusoidal signals with frequencies \$...
• 91.1k
2 votes

Determining invertibility of a system

In general there is no systematic way and you simply have to analyze the given system. In the case of the system in your question, it's easy to see that it can't be invertible, because the output is ...
• 91.1k

Only top scored, non community-wiki answers of a minimum length are eligible