13
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Why eigen values and poles of a system are equivalent?
Let's consider a discrete-time state space model (the derivation for a coninuous-time system is completely analogous):
$$\begin{align}\mathbf{q}[n+1]&=\mathbf{Aq}[n]+\mathbf{b}x[n]\\
y[n]&=\...
- 79.2k
12
votes
Accepted
Who first understood the importance of poles?
If you consider poles of an integral transform domain to be important to the solution of differential equations: (as usual,) Euler did it first, 1753.
One "importance" of poles is that they're part of ...
- 25.8k
11
votes
Digital filter coefficients from low-pass to high-pass
You can apply a so-called all-pass transformation to a discrete-time low-pass prototype filter in order to convert it to other standard filters (such as high-pass, band-pass, and band-stop). This is ...
- 79.2k
9
votes
What is the relationship between poles and system stability?
I agree with Peter K.'s answer, but I would like to add one important point: the two statements in the question are only true for causal systems. The most general statement about stability for LTI ...
- 79.2k
8
votes
Do Causal Discrete-time systems have proper transfer functions?
Note that a stable and causal continuous-time transfer function does not need to be strictly proper but only proper, i.e. the degree of the numerator does not exceed the degree of the denominator, but ...
- 79.2k
7
votes
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Understanding the $\mathcal Z$-transform
Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose):
$$a_0y[n]+a_{1}y[...
- 4,105
7
votes
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Why does reversing the order of these two transfer functions give me different outputs?
If the input is a unit step, then the output of the first block in system 1 is not zero, but it is a Dirac delta impulse $\delta(t)$. Intuitively, the derivative is infinite at $t=0$ because of the ...
- 79.2k
7
votes
Accepted
Basic Questions on Wiener Filtering
The task is to filter x(t) when given y(t), where y(t) = x(t) + n(t).
Great but first we need to build an appropriate filter. At this point:
No. The task is to filter $y[n]$ to achieve $x[n]$. Your ...
- 26.6k
6
votes
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Poles and zeros of a transfer function
The "poles-inside-unit-circle" stability criterion only applies to causal systems. Your system is not causal because it uses one sample from the future owing to the $z$ term.
The general technique to ...
- 4,004
6
votes
Accepted
Transfer function intuition
Normally, in electrical enginnering, we apply the term "transfer function" and "filter" to an operation that belongs in the class we call Linear Time-Invariant systems (LTI).
Sometimes you might read ...
- 16.8k
6
votes
Accepted
Is this system causal or not?
Note that in this case you can see that the system is causal only from the given implementation. It's important to understand that you can't see it from the difference equation (if no initial ...
- 79.2k
6
votes
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Transfer function with blackbox modelling is too slow compared to real expectation
In your original code you defined the sampling interval to be $T_s=0.05$ (idd1 = iddata(ddout, ddin, 0.05);). Yet, according to the data file, the time step between ...
- 79.2k
6
votes
Accepted
How accurate is the dominant poles approximation in higher order control systems?
It depends entirely on how close the less dominant poles are to the dominant poles. A simple way to understand what is happening is consider poles on the real negative axis for continuous time systems:...
- 36.1k
5
votes
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Estimate the Transfer Function of an Unknown System
Here's the way I think about a discrete Wiener Filter
Consider a sequence of observations $\mathbf{y} \in \Re^n $
Form a matrix from the input $\mathbf{x} \in \Re^{n+r-1}$ by shifting columns one ...
- 2,880
5
votes
Accepted
What is the relationship between poles and system stability?
The two are both true, but they are for different cases. Case 1 is true for continuous-time systems, and the transform is the Laplace transform and the variable is the derivative operator, $s$. Case ...
- 21.7k
5
votes
transfer function of wiener filter
In general, an ideal Wiener filter (i.e. a non-causal filter with an infinitely long impulse response) has the following frequency response
$$W(\omega)=\frac{S_{dx}(\omega)}{S_x(\omega)}\tag{1}$$
...
- 79.2k
5
votes
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Deconvolution Using Response to an Heavy Side
If we can assume no noise (Or the SNR is very high) you can get the response by applying the inverse filter in frequency domain.
Lets say $ y [n] $ are the signal samples.
Given $ x [n] $ the samples ...
- 39.3k
5
votes
How frequency response related to a transfer function
An LTI system's "frequency response" tells you how the system acts on the amplitude and phase of a sinusoidal input. If the frequency response is $H(f)$, then an input $x(t)=e^{j2\pi f_0t}$ produces ...
- 13.6k
5
votes
Accepted
determining type of filter given its pole zero plot
You'd have to figure out the frequency response of the filter. Here are two methods. I prefer Method 2 because it's quick and dirty, and you don't really care about the exact gain values in the ...
- 4,004
5
votes
determining type of filter given its pole zero plot
In this answer I'll try to show you how to qualitatively evaluate a given pole-zero plot by just looking at it. Of course, this method has its limits, but for relatively simple pole-zero plots you can ...
- 79.2k
5
votes
Accepted
Why do we assume zero mean noise in sensor data?
The brutally honest answer here is: The noise is considered zero-mean because that's what the author decided to do. Without looking deeper into the signal model employed, it's impossible to answer.
...
- 25.8k
5
votes
A question about the meaning of pole in time domain
Let $H(s)$ be a transfer function of the form
$$H(s) = \frac{1}{s-p}$$
where $p$, which is a pole of $H(s)$, can be written as a complex number $a+jb$. Taking the inverse Laplace transform of $H(s)$ ...
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5
votes
Can someone explain waveshaping to me?
In the audio domain, waveshaping is simply applying a memoryless nonlinear function to an input signal.
$$ y(t) = g\big( x(t) \big) $$
The waveshaping function, $g(x)$, is most often a continuous ...
- 16.8k
5
votes
What is the zero in this transfer function?
$$2s+1=2\left(s+\frac12\right)$$
That's all I can say.
- 79.2k
5
votes
How to realize Poles and zeros at infinity??especially through transfer function?
It's actually quite straightforward: positive powers of $s$ (or, in discrete-time, $z$), correspond to poles at infinity. Negative powers give you zeros at infinity.
Let's look at some examples. In ...
- 79.2k
5
votes
Accepted
Finding the Transfer Function of a Multiplicative Distortion in MATLAB
Basically the transfer function is given by (Continuous time case):
$$ H \left( j \omega \right) = K \frac{ \left( j \omega - {q}_{1} \right) \left( j \omega - {q}_{2} \right) }{ \left( j \omega - {p}...
- 39.3k
5
votes
Filter odd or even harmonics with notch or inverse notch filter
What you are looking for are what we, in the audio space, call comb filters. Comb filters may or may not have a feedback path, just like FIR and IIR filters. In fact, there is a generalized theory ...
- 16.8k
4
votes
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Output of a system given it's transfer function and input (beginner)
For an LTI system, output $y(t)$ is given by
$$y(t) = h(t)\otimes x(t)$$
Where $x(t)$ is input and $h(t)$ is impulse response of the system. The operator $\otimes$ represents convolution.
Convolution ...
- 447
4
votes
Accepted
Block diagram transfer function of a line
The transfer function of a line is 1.
And hence you can reduce your blocks into a single block with transfer function
$$\frac{C(s)}{R(s)} = \frac{G(s)}{1+G(s)}$$
where, $$G(s) = \frac{K}{s(s+2)(s+...
- 447
4
votes
How to compute the impulse response from a transfer function
Your filter is the all-poles IIR, this simplifies things a bit. Normally you can write transfer function in following form:
$H(z)=\dfrac{\sum_{i=0}^{P}b_{i}z^{-i}}{\sum_{j=0}^{Q}a_{j}z^{-j}} $
Going ...
- 10.4k
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