Questions tagged [transfer-function]
Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.
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Implementation of a time-domain solution of a transfer function
I have the the following transfer function (TF):
$$
G(s) = \frac{b_2 s^2 + b_1 s + b_0}{a_3 s^3 + a_2 s^2 + a_1 s + a_0}
$$
I want to program the numerical solution of the underlying system of ODEs ...
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Finding the impulse response between two microphones
I have made recordings of a single source (musical instrument) with multiple microphones and in the interest of limiting the size of the final project, I would like to find a way to get the impulse ...
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What is the denominator of the transfer function when PI-regulator is connected?
A system is described by the transfer function
$$G_p(s)=\frac{s+2}{(s+1)(s+3)}.$$
A PI-regulator is connected to the system making it a closed loop system.
So the transfer function for the PI-...
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Understanding how to implement high-pass filter with cascaded biquad filters
I'm trying to understand how to implement a high-pass filter using, quote:
a cascasded biquad direct form II IIR filter
with a cut-off of 8kHz.
DSP is a complete new field for me, and the ...
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Desired trajectory generation from transfer function in control theory
I am trying to implement the backstepping techniques for quadrotor described in this article : Backstepping control for a quadrotor helicopter: Madani & Benallegue 2006
Since I am new to the ...
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Function Transfer of Block Diagram Discrete System
I need to find out the transfer function in Z from this diagram, how can I extract this information from this diagram
Obs: Doing the math, my H_z gave, H_z = 1 + 0.5z^-1 + 2z^-2 + 2z^-3 + 0.5z^-4 + z^-...
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Extracting transfer function from output measurement
Let's say I am generating pure sine oscillations with a laboratory instrument on which vibration frequency and amplitude are tunable (there are uncertainties +/- 1 % with my inputs), and I get my ...
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Bode plot phase shift equation when poles and zeros are not at the origin
Let $$H(s)=\frac{s^{n}}{s^{m}}$$
For $n \ne m$ the phase shift between output and input will be
$\frac{\pi}{2}(n-m)$.
For situations where the poles and zeros are not at the origin, I could find the ...
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Generate a continuous time system with desired bode diagram
I have a fluid mechanics model that is heavy to simulate. Its main output is a scalar $q$ related to some energy transfer, and its input is a pressure $P$. This model, noted system 2, is coupled with ...
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Theory behind transfer function transforms of the type $H(s) \rightarrow H(f(s))$
My brother wanted me to derive a high-pass version of a Butterworth low-pass filter. I found that the transform $H \left( s \right) \rightarrow H \left( j - j s \right)$ does the thing, but I can't ...
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Simulate Op-Amp low-pass transfer function in Python
I am struggling to simulate the frequency response of a simple op-amp low-pass transfer function in Python. The results I get are not accurate. The transfer function is $H(s)=\frac{1}{1 + s\tau}$, ...
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Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?
In signal processing, we define an analytic signal as a complex-valued signal which has no frequency components for $\omega<0$. It can be shown that the real part and the imaginary part of an ...
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Why does causality imply that the system function is analytic?
It is cited in multiple places that the fact that a filter is causal (i.e. the impulse response is zero for t < 0) implies that the system function is analytical.
I couldn't find any proof of this, ...
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control system : time domain analysis
This is the question. According to this, when we solve for transfer function we will get $20/s^2+5s+24$. but this is not the correct format as numerator should be equal to the last term, i.e., 24, in ...
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If the convolution of two signals is a unit impulse, what does this tell us?
I have two discrete-time LTI systems whose transfer functions satisfy $h_1[n] * h_2[n]= \delta[n]$. We also know that system 1 is causal and stable. Does $h_1[n] * h_2[n]= \delta[n]$ tell us anything ...
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Help with Implementation of Transfer Function using Python or MATLAB
Relatively new to the DSP side and wanted some help to implement this approach using Python (with NumPy, SciPy libraries) or via MATLAB.
Background of the problem:
I'm running a linear dynamic loads ...
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How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator
How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator.
The bottom equation is supposed to be the answer.
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Transfer Function Estimate
This is related to this post: https://engineering.stackexchange.com/questions/56050/obtaining-the-open-loop-gain-estiamte-the-gain-and-phase-frequency-response
Using python, I would like to write a ...
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Average of a set of transfer functions: how should I treat the phase?
I have a set of transfer functions obtained by impacting an instrumentation hammer against a mass, measuring the acceleration on a set of accelerometers; the result is shown below. I want to get a ...
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Deriving Step Response from Input and Output Data for Quadcopter PID Controller
I have logged gyroscope sensor data for roll(x), pitch(y) and yaw(z) axis and i want to plot their step response with Python to be able to tune the pid controller of my quad better.
1. I have found ...
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Why can't I use the differentiation property of the Fourier transform?
I have some question about the function in frequency domain and I'd like to know its inverse fourier transform (IFT)
$$G(jw) = \dfrac{jw\cdot (jw+1)}{(2+jw)(3+jw)}$$
I know that:
$$\dfrac{d}{dt}x(t)\...
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Calculating transfer function of a linear time varying system?
If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
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Max input of a system given it's transfer function and an assumed step change (beginner)
I have an exercise that gives me the following transfer function
$$
\frac{0.5}{s+0.5}
$$
and an assumed step change in the target of 20
I am asked to calculate the maximum input for the assumed step ...
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How to compute modular transfer function (MTF) from line spread function (LSF) with given discretization
I have an optical system, which is commonly characterized by its point spread function. Somehow by the method, which resemble slanted edge method, I have end up with discretized line spread function ...
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Why does scipy introduce its own convention for H(z) coefficients?
Conventionally, the definition of the system function for a IIR digital system is:
$$H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\cdots}{1-a_{1}z^{-1}-a_{2}z^{-2}-\cdots}$$
where coefficients are the ...
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Feedback stabilizes unstable systems?
Can feedback stabilize a unstable system?I guess so since we may get rid of any poles in the positive complex plane by feedback but I am not sure.
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Factorization of transfer function using its roots
I'm missing a step to understand the factorization of the FIR filter transfer function:
$$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$
From DSP First:
The $z$-transform of a finite-length signal, ...
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Linear Linearly Time Varying Systems properties?
Yesterday I asked a question about LTV Systems and how the impulse response h(t,t0) is found.
I was thinking about it and realized there is a subsclass of LTV systems which I call Linear Linearly Time ...
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Remove over and undershoot from an output signal by manipulating the input
I have an experiment for which I want to generate a high-power short-voltage pulse with no over and undershoot. For this, I am using an amplifier. I set a pulse with the desired width as input (I use ...
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How to determine if a system is minimum phase or not?
I'm studying for an exam and this is an old exam question that I don't understand:
Is the following system non-minimum phase?
$$G(s) = \frac{e^{-2s}}{s+2}$$
I can see that the real part of the pole is ...
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Finding the inverse $z$-transform
I have the transfer function: $$H(z) = \frac{z^2 + 0.75z + 0.125}{z^2+0.5625}, |z| > 0.75 = \frac{(z-0.5) (z-0.25)}{(z - 0.75j) (z + 0.75 j)}$$
I attempted partial fraction expansion in order to ...
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Is it possible to use AMIGO tuning rules with relay control?
I am trying to control a plant with PID using tuning rules such as the Ziegler-Nichols rules. However, it is not always easy just to send a step to your plant
source of the image.
Another method to ...
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Can you plot an irrational transfer function on matlab?
For example if I have the following transfer function:
$$H(s) = \frac{1}{\cosh(\sqrt{s/10})}$$
Can I do the bode plot it in matlab or do I need to rationalize it beforehand?
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LTI system: can I infer the system is causal based only on the transfer function without the ROC?
Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
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How is the transfer function of a state space representation computed in practice?
I know that if you have a linear time invariant system defined by
$$ \dot{X} = AX+BU $$ $$Y = CX$$ by "Laplacing" the previous equations, you get the following transfer function in the ...
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Z - Transform of a non recursive block diagramm
i am currently struggling to find the Transfer Function of the following Block Diagram, since i have never done it for a non recursive System, could somebody please walk me through the process of it?
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Finding transfer functions from a system of multiple inputs
If I have a system: $$sX(s) = AX(s)+BY(s)+CZ(s)$$ How would I find the transfer functions $\frac{X(s)}{Y(s)}$ and $\frac{X(s)}{Z(s)}$?
Do I simply disregard one of the inputs? I am quite confused and ...
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How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response
I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
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How to find zeros of a transfer function
Given the following transfer function,
$$H(z) = \frac{6 + 4z^{-1}}{2 + 5z^{-1} - 3z^{-2}}$$
How do we find the zeros of the transfer function? We can write the above expression as
$$\frac{3(1+\frac{2}{...
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Relation between Causality and the Phase response of an Amplifier
I am trying to model the response of an amplifier. As per the main answer on this question, if one wishes to do so, they have to look at the Fourier decomposition of the input signal $x(t), \, \tilde{...
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Why does a root locus show that system is stable but unit step response of a system does not have a stable output?
From what I know about root locus is that if all roots are located on the Left Half of the S-plane the system is stable. That's why I expected the unit step response of a system to be stable.
...
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Why does drawing bode plots on poles or zeros give different results?
Why does drawing bode plots on poles or zeros give different results?
For example I have a transfer function, I could write it for pole as $$\frac{1}{\left(1+\frac{s}{\omega_0}\right)} \tag 1$$ or ...
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How to write transfer function?
I am an engineering student. I have some data stored in matlab. I need to build low pass filter to process my data. How can I write the transfer function? In my understanding transfer function is the ...
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Z domain transfer function including time delay to difference equation
How can get the difference equation of a $\mathcal{Z}$-transform transfer function with time delay? How does a time delay influence the difference equation?
For example:
$$H(z) = \frac{8z^{94}}{z-0.9}...
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First Order State Space Question
I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response
$$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$
In this ...
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How should I interpret $z_1^{-1}$ if $z = e^{j\omega(i)T}$?
I'm trying to understand how I should create all these $z$ values.
Each $z$ values is equal to $z = e^{j\omega(i)T}$ were $j$ is the complex number (instead of $i$), $\omega(i)$ is the i:th wrequency ...
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Obtain transfer function from FEM Model
I'am getting Transfer function from FEM Model of Simply supported rectangular plate
i do random vibration input force $x(t)$ and measured displacement $y(t)$
In matlab, because that is noise free data,...
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How to get the impulse response of from input and output data?
We know that
$$x(t) \star h(t) = y(t) $$
and
$$X(\omega)H(\omega) = Y(\omega).$$
But in real world, $X(\omega)$ and $H(\omega)$ are DFTs. So to prevent circular convolution, we do zero padding before ...
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Why do I need to multiply the frequencies with a number, to get correct "shift" in the bode plot?
Assume that we got a sine wave function
$$u(t) = A\sin(2\pi \omega(t)t)$$
Where the frequency $\omega(t)$ changes over time $t$ and $A$ is the amplitude.
Assume that we apply that $u(t)$ signal onto a ...
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The frequency function for $Y_t-18=0.4X_t+0.9X_{t-1}+e_t$
I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white ...
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