# 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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I'm mixed about the concepts of analog filters, so I hope someone can explain me, or point to information, to unentangle the ideas. I know there are filters (analog) as Chevyshev, Butterworth, ...
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### How can we obtain the input signal in Python given the output signal and transfer function?

I have the following transfer function $$H(s) = \frac{R}{sRC + 1}$$ where $V$ is the output and $I$ is the input. We can write $$V(s) = I(s) H(s)$$ or $$V( j \omega ) = I(j \omega) H(j \omega)$$...
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### Help with setting up transfer function correct format

I have a transfer function as: H(s) = R / (sRC + 1) V is the output and I is the input so we can write: V(s) = I(s)*H(s) Now the thing is that, I want to obtain I(t) for the given V(t). So I write: I(...
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### How can I use an irrational transfer function to convolve a signal?

I have the irrational transfer function $$H(s)=\mathrm{e}^{-a\sqrt{s}}$$ With the inverse Laplace transform $$h(t) = \frac{a\,\mathrm{e^{-a^2/(4t)}}}{2\sqrt{\pi}~t^{3/2}}$$ For $a > 0$ How can I ...
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### How to determine the dynamic response of a spring-mass system? [migrated]

The Problem I have the following system for which I would like to determine its dynamic response, taken from these lecture notes pg.20: where the forcing functions are $u_1 = 1-U(t - t_0)$, $u_2=0$, ...
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### Mismatch between the frequency response of a transfer function and bode plot

I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)): <...
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### Derivation of Strehl ratio

I am in trouble proving the following fact: The Strehl ratio is the ratio of the volume of the aberrated OTF (optical transfer function) and the ideal OTF, i.e. \begin{align} \mathcal{S}=\frac{\int\...
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### State-space model and/or TF for a $K$-th order linear system given the signal sequence

The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential: \begin{equation} x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
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### Digital IIR LPF Difference Equation from Transfer Function

I want a digital IIR filter with f0=225kHz and fs=53.125GHz. I can come up with the transfer function and plot it using Matlab. ...
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### Realize the given system in cascade form of 2nd order section in signal flow graph representation(with complex exponents)?

I know how to solve cascade form for normal case, but I don't know how to solve cascade form if I get complex exponentials. How do I solve this? Can you provide me 1 solved example or some hint or ...
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### Difference equation to FIR filter coefficients

I have a difference equation $$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$ According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ...
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### Trying to plot frequency response of a filter Transfer Function in MATLAB, it looks wrong

I have the transfer function below which is for a IIR filter and trying to plot its frequency response for omega<pi. r=0.99 and theta=pi/3: Here is my attempt at implementing it in MATLAB: ...
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### Filter odd or even harmonics with notch or inverse notch filter

Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ...
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### Real Data Complex Transfer Function using H0, H1, H2 Estimators

BACKGROUND: This question is attempting to consolidate material discussed in two previous topics. These are: Understanding the H1 and H2 estimators @Pontus S Frequency-domain deconvolution: "...
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### Coupled system instability

Suppose there are two linear devices (containing some multi-physics but the details don't matter here), and these devices are given to us as two black boxes that can be studied experimentally. Black ...
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### Stabilizing an unstable system and removing oscillations from step response

I have a system with the transfer function given in this MATLAB code ...
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### Confusion regarding terminology?

While studying the topic of filter design,i came across following terms: 1)Factored form 2)SOS(second order sections)form 3)Rational form 4)Transfer function form What is the difference between all ...
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### Developing Lead Compensator to Decrease Settle Time

This is a follow up to this question. I've approximated the transfer function for a system to be H = zpk([0.012 -1.05 18],[-0.22 -0.22 -45 -1000],10000);. My goal ...
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### Get the transfer function when using the "designfilt" command in MATLAB

To put things into perspective, I initially had these four graphs in MATLAB, whose data were sampled with a rate of 10 samples/sec :- I wanted to remove some of the spikes on the blue graphs, so I ...
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### Tuning a PID Controller

I have the following transfer function $$10000 \cdot\frac{(s-0.012)(s+1.05)(s-18)}{(s+0.22)^2(s+45)(s+1000)}$$ For which I am trying to tune a PID controller for. I'm using the pidTuner in MATLAB to ...
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### Adding noise to frequency response

I have the dynamics of a 2nd order system, mass-spring-damper for example, in the transfer-function format. For the analysis that I am doing, I am calculating the frequency response of the system by ...
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### Creating Bode Plot from Experimental Data

I have a blackbox system in which I can input a function and obtain the output signal (in MATLAB). I'm attempting to reconstruct a Bode diagram and have had success with the Magnitude plot, however, I'...
does anybody know how to take a second order transfer function with no zeros (no s terms in the numerator): $$g(s) = K\frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2}$$ and represent it using ...