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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 Urysohn followed by static nonlinearity is a model of any deterministic dynamic object, it maps any given input to any provided output. I obtained Ph.D. in ...


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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 and delay after the frequency) will yield the same result as omega_g is a constant and because your PI controller has fixed coefficients. Anyway, place the ...


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No the converse is not true in general. Take for example the discrete-time ideal lowpass filter with impulse response $$ h[n] = \frac{ \sin( \omega_c n) }{ \pi n } ~~~,~~~-\infty < n <\infty$$ which describes an LTI system but it does not correspond to a difference equation of any kind. Indeed $h[n]$ is derived based on the inverse discrete-time ...


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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.com/NAF/index.html The site has downloadable coding sample. Besides UAF, the other common methods are: Kernel LMS, Voltera LMS, Neural networks, Point cloud. ...


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For a phase distortion metric I recommend using “group delay variation”. The definition of Group Delay is the negative derivative of phase with respect to frequency. The Group Delay is the delay in time that “group” of signals over a band of frequencies would have. A frequency response that is linear in phase (constant group delay with no variation) is not ...


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You did everything correctly. I think that part of your confusion comes from the way you chose the notation. Let me use $v_k[n]$ to denote the system's response to a delayed input $x[n-k]$. $v_k[n]$ is described by the following difference equation: $$v_k[n]=3v_k^2[n-1]-nx[n-k]+4x[n-k-1]-2x[n-k+1]\tag{1}$$ On the other hand, the delayed response $y[n-k]$ ...


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A simple way to derive the differential equation from the impulse response is to transform the latter to the frequency domain, rewrite the input/output relation, and then transform the resulting equation back to the time domain. The Laplace transform of the given impulse response $h(t)$ is $$\begin{align} H(s) &=\frac{A}{\tau}\frac{1}{\left(s+\frac{1}{\...


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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 could model it by a polynomial $f(x) = \sum_{n} a_n x^n$. Now, what we would still expect is that the amplifier treats positive and negative values the same ...


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Let's ignore the issue that you already have a discrimination problem in your hands (bus/car/truck/van) there is an initial discrimination problem that has to be solved for the data to be considered valid for any moving object. The issue is one of rate of change, so the problem should probably be moved into derivative space. That is, ignore the mean ...


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Add a DC signal to your sinusoidal input, so that the input falls in the middle of each line segment of the input-output curve. Then choose the amplitude of the input sinusoid in order to avoid "spilling over" into the other segments. Measure the amplitude of the output sinusoid (neglecting its DC component, of course). Lastly, compute the gain.


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