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 ...
mascara's user avatar
  • 116
7 votes
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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 ...
Olli Niemitalo's user avatar
7 votes

Linearizing digital-analog converters

well i'm assuming you mean "conventional" DACs and not $\Sigma \Delta$ DACs. in a conventional DAC (like an R-2R ladder or something), there are the micro errors that occur between neighboring DAC ...
robert bristow-johnson's user avatar
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. ...
Hilmar's user avatar
  • 44.8k
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 ...
robert bristow-johnson's user avatar
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
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 ...
Jazzmaniac's user avatar
  • 4,584
5 votes
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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 ...
Dilip Sarwate's user avatar
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 $A$. ...
Peter K.'s user avatar
  • 25.7k
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 ...
Andrew Polar's user avatar
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 ...
GrapefruitIsAwesome's user avatar
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 ...
Tendero's user avatar
  • 5,020
4 votes
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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 ...
Matt L.'s user avatar
  • 90k
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 ...
Olli Niemitalo's user avatar
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 ...
Mike Battaglia's user avatar
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....
Andrew Polar's user avatar
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(...
Dilip Sarwate's user avatar
3 votes

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

For this problem you can't use the formula involving $|H(f)|^2$ because it only applies to linear time-invariant (LTI) systems, and a squarer is obviously a non-linear system. The only way to solve ...
Matt L.'s user avatar
  • 90k
3 votes

Linearizing digital-analog converters

Another typical approach, that independently of my other answer works, is predistortion, for example with the look-up table mentioned by robert, or with a correction polynomial. If you can really ...
Marcus Müller's user avatar
3 votes

Volterra Kernel Convolution Method

I think actually your code is not correctly implementing the equation you gave. What you are actually imeplementing in matlab is this: $$ y(n) = \sum_{m_1=0}^{M-1} h_1(m_1)x(n-m_1) + \sum_{m_1=0}^{M-...
kippertoffee's user avatar
3 votes
Accepted

Why harmonic components appear only after a certain level when a signal is clipped?

Is this a well-known phenomenon? Yes, of course. You will see harmonics as soon as your clip point is lower than the maximum amplitude in the time domain. The latter is a function of the relative ...
Hilmar's user avatar
  • 44.8k
3 votes

Why only odd harmonics after non-linear amplification?

An ideal amplifier would have a transfer characteristic of $f(x)=Ax$: the input signal comes out amplified and otherwise undistorted. A real amplifier will deviate from this and go into saturation. We ...
Florian's user avatar
  • 2,463
3 votes

SRF-PLL discretization problem

I faced the same problem in the past. Perhaps there is a way without adding a delay but I haven't found it. You need to realize that your 3 first solutions (delay after vq, delay at the delta_freq ...
Ben's user avatar
  • 3,777
3 votes
Accepted

How to linearize this state space model and write it in discrete form?

You have $$ f\left(\mathbf x, u\right) = \begin{bmatrix}\frac{-1}{T}\tau+\frac{K}{T} u \\ \frac{\tau}{mr} \\ 0 \end{bmatrix} \tag a $$ From which you (eventually) derive $$ \mathbf {A}_d=\begin{...
TimWescott's user avatar
  • 12.7k
3 votes

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 ...
Dan Boschen's user avatar
  • 51.4k
2 votes

Linearizing digital-analog converters

So, the intuitive reaction to this situation is oversampling. Basically, if you use twice the sampling rate, you can always average to samples to get one "output sample value" (thanks, Nyquist!). ...
Marcus Müller's user avatar
2 votes
Accepted

The frequency spectrum of a static non-linearity driven by colored noise

If your nonlinearity can be expressed as a polynomial (i.e., in terms of addition and multiplication), you can make use of: The linearity of the Fourier transform, i.e., if $f$ and $g$ are (benign) ...
Wrzlprmft's user avatar
  • 138
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 ...
Jazzmaniac's user avatar
  • 4,584
2 votes
Accepted

Nonlinear time-invariant frequency doubler

As already suggested by Robert and Olli, a system that maps $x(t)=k\cos(2\pi f_0t)$ to $y(t)=k\cos(4\pi f_0 t)$ can be formalized as $$y(t)=|x(t)|_{max}\left(2\left(\frac{x(t)}{|x(t)|_{max}}\right)^2-...
Matt L.'s user avatar
  • 90k

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