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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Digital control: Exercise solution

Can you help me (show me how) to solve the following exercise? For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
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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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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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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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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 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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Error in the computation of PSF?

I am in trouble computing a PSF of an optical system in optical turbulence. Background The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
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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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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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Practical implementation of IIR/biquad filters following non-textbook transfer function of real-wold analog filter

I am trying to program a DSP filter to study prototypes of loudspeaker filters, which will be implemented as passive analog circuits in the final speaker system. This process involves simulation of ...
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real refractive index from Kramers Kronig relation

I have a measurement of the complex part of the refractive index $k$ (where the refractive index is $m = n + i\,k$) measured at a nonlinear grid of wavelengths or frequencies that span several orders ...
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How can I compute the inverse digital of a nonrational transfer function?

My $G(s)=1-e^{-s/\tau}$, $\tau$ is very small, say of order $10^{-4}$. I need to compute a $H(z)$ (a digital filter) such that $H(z)$ has the inverse response of $G(s)$. Is ok even if $G(z)$ has the ...
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Difference between state space and transfer function model response (in Simulink)

Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values ($...
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Does calculating the phase margin when the phase is positive has any meaning?

I want to calculate the phase margin and the gain margin of my transfer function to have an idea about the system's stability. The transfer function is quite complicated since it contains an ...
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How to tune the coefficients of Polynomial Models in MatLab System Identification toolbox

I have such setting: Where $Y_M(S)$ is the transfer function of the model I am trying to approximate with $Y_U(S)$, what I have is the data of the signal corrupted with noise. I am trying to create a ...
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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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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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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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How can I find a transfer function between two signals in python?

If we call one signal $x$ and the other signal $y$. I want to find a transfer function that takes $x$ as input and gives $y$ as output. I have recorded data of signal $x$ and $y$. $$x(t) \overset{H}\...
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What is the difference between sending pulses and modulating waves?

If you look for amplitude, frequency, phase modulation, you typically get some picture saying you have a wave and you modulate the corresponding parameter (amplitude, frequency, phase). On the other ...
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Poles and zeros from step reponse?

Is there a numerically robust method for calculating the poles and zeros of a discrete-time causal LTI SISO system given its response to a unit-step input? In the specific example I'm working on all ...
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Taking transfer function out of real heating system

I have some king of heating system: heater (that I can control current for final power control) and a thermocouple (for measuring the temperature). I also have a device that can record temperatures ...
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Vary poles/zeros of digital IIR filter

Many applications that produce sound, such as software synthesizers, are able to apply a filter that varies with time, such as applying a low pass filter that varies with an LFO. I currently have a ...
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Powers of $z$ in a discrete transfer function

I have been working with discrete-time systems and I am not yet able to understand the reason behind using powers of $z^{-1}$ in transfer functions. I get that $z^{-1}$ means a delay, but when we ...
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Region of convergence for discrete system

I am confused by two questions on the region of convergence (ROC) when applying the $Z$-transform. Consider a discrete-time linear system $$x[n+1] = Ax[n]+Bu[n], \qquad y[n]=Cx[n]+D$$ whose transfer ...
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How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?

For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
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How do I convert a two-pole two-zero transfer function from the s-domain to the z-domain?

I'm trying to convert the following IIR transfer function from the s-domain to the z-domain: $$ H(s) = \displaystyle\frac{\frac{s^2}{\omega_z^2} + 2\zeta_z\frac s\omega_z + 1}{\frac{s^2}{\omega_p^2} + ...
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Real-time implementation of cascaded all-pass filters from given transfer function

I am working on real-time implementation of spring reverb based on scientific paper called Parametric Spring Reverberation Effect by Välimäki, Vesa; Parker, Julian; Abel, Jonathan S. One block of ...
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Calculating Transfer Functions From Harmonic Distortion Percentage

Hi I am working on emulating a piece of analog audio equipment and would like to be able to create a transfer function based on the measured percentages of harmonic distortion. I know that harmonic ...
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Solve for Transfer Function Coefficients Embedded in a Non Linear System

Given a complex input signal $x$ and real input signal $v$, a 4th order (for simplicity) transfer function $H(z)$ is first applied to $v$ to obtain $w$, which in the time domain is represented by the ...
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How can I find the transfer function from this Bode diagram?

I've been given this bode diagram : I've been asked to find the transfer function only by using the bode diagram. It's the first time I'm doing this so here's what I thought. The starting value is ...
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Deriving the transfer functions of a heating system

I'm tying to develop a model for a heated system that consists of a small steel block (~25 sq. in.) with a heating element embedded in it. The block acts as a sort of hot-plate that is used to deform ...
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Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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How to eliminate audio device transfer function from recording?

I'm working on a project which requires analysis of filter transfer function of vocal tract. The vocal tract is excited by a source signal that is a frequency sweep. The source signal is provided ...
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Parameter identification for PI controller

I have a PI temperature controller being used in experiments, which I am also trying to simulate. However, using the proportional gain and integral time as used in the experiments gives different ...
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Matlab's invfreqs won't fit at low frequencies

I'm wondering of anyone can explain why invfreqs() is unable to fit a polynomial to the data in the image below. The red line is the measured frequency response of an analog system. I should mention ...
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Convert Gaussian Like Histogram into Uniform Analytically

If I have the histogram of an input image as Gaussian probability density function of the form: $$P_r(r)=\dfrac{1}{\sqrt{2\pi}\sigma}e^{-\dfrac{(r-\mu)^2}{2\sigma^2}} $$ where: $\mu$ and $\sigma$ ...
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Difference between natural response and forced response?

Reference Second post on EdaBoard.com Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time. Natural response ...
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How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?

Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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Butterworth Bandpass Filter Design

Determine the transfer function for the Butterworth bandpass filter? (At the Transfer Function Factoring and Sp Substitution stage) The Parameter $$a_{pass} = - 1dB$$ $$a_{stop} = - 20dB$$ $$f_{pass1} ...
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Signal reconstruction of time domain data via transfer function of a quadripole

Dear signal processing community, I hope my question finds you all well. I have an electrical network, consisting of three complex impedances. These impedances basically form a simple voltage divider. ...
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Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
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Causality and Stability of a discrete-time LTI system which has ROC = {z : 4/3 < |z| < 2}

The transfer function H(z) of a discrete-time LTI system has ROC={z ∈ C : 4/3 <|z|< 2}. The system is... a) Causal and stable b) Stable but non-causal c) Unstable but causal d) Neither causal ...
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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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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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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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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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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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