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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Who first coined "Direct Form I" and "Direct Form II"?

I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
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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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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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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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41 views

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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1answer
87 views

Transfer Function to go from a Step Input to a Linear Ramp between the two step values

I want a very basic simulation of a linear axis that can be given a position demand, and it will move to that position at a constant speed. At this point, I do not care about acceleration, but if I ...
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1answer
180 views

Why does this transfer function estimation not work? System identification

Goal: I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses. Method: I begun first with creating the ...
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307 views

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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1answer
358 views

Why I don't get the right PSD

I need to model a noise with a given PSD. To do this, I am starting from a white gaussian noise (WGN) and feed with the WGN a transfer function, which will act like a filter. In fact,it's easy to ...
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827 views

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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49 views

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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9k views

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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65 views

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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78 views

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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1answer
162 views

Given a system with Transfer Function and its desired output. Is it possible to find the required Input?

I'm currently working on an DC servomotor. I managed to find it transfer function using System Identification theory and Matlab. The transfer function is given as $$H(Z) = \frac{1 - 0.4952z^{-1} + 0....
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23 views

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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104 views

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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156 views

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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126 views

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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1answer
554 views

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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70 views

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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308 views

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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243 views

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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109 views

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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99 views

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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2answers
600 views

Design discrete controller for zero steady state error

I have the following system where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ...
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62 views

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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3k views

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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317 views

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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42 views

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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75 views

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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1k views

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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118 views

Gonzalez question solution

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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54 views

Discrepancy in frequency response of biquad filter (in Python)

I have written a simple biquad filter class but when I check its frequency response, I get different results with different methods. If I check it "empirically" (by taking the FFT of its ...
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1answer
54 views

Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab

I have been given an input and output signal. input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1) output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n). or x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
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How to find response of step function in matlab and plot transfer function?

I have an transfer function: Y(s)/F(s) = (s^2+2s+3) / (s^4+6s^3+13s^2+12s+9) How can I find Y(s) response of step function if f(t)=sin(5t) in MATLAB. And how can I plot the transfer function? Thank ...
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41 views

Is it allowable to place a zero to cancel out a complex pole?

Consider the following transfer function : $$ T(s)=\frac{4}{s^{2}+2s+4} $$ I wish to design a lead-lag compensator satisfying a set of requirements. What matters for now is the process done to meet ...
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Bode plot of transfer function with vs without feedback

I am looking at some old exams. Particularly, one question where there is a Bode plot of a transfer function $G(s)$, and some questions about the Bode plot. So far so good. However, part b) of the ...
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Poles and Zeros of a DiscreteTimeModelFunction with delay in Wolfram Mathematica

help me please, I have a problem with this TransferFunctionModel, When I want to obtain the poles from the Discrete Model Wolfram gives me an error, what am I doing wrong? Could it be the delay of the ...
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1answer
46 views

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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25 views

Filter a signal with a complex dB SPL filter

I've been tasked with filtering a sound with a filter that looks something like this. I don't have any real DSP training, so I'm not sure if my attempt at tackling this is correct. I can filter ...
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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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46 views

How to find H(z) from just zeros and poles

I have a system with a DC gain of 8, poles at z = +- j/2 and zeroes at e^+-j5, I need to find the H(z). I have tried this but not sure if it is right. $$ H(z) = G_o * z^{-1} \frac{(z-z_0)(z-z_1)}{(z-...
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48 views

Digtial FIR Impulse response & transfer function

I am currently working the figure through below. as it is an FIR Filter i have worked out using convolution that the output is 4,2,4,6,0,0. i am trying to obtain the 'z' domain transfer function of ...
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79 views

SPL dB to voltage conversion misunderstanding

base on these links: https://electronics.stackexchange.com/questions/96205/how-to-convert-volts-to-db-spl https://electronics.stackexchange.com/questions/302833/convert-digital-and-analog-values-to-...
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Gradient of transfer function (z-transform) with respect to coefficients/parameters?

my problem is perhaps very simple but I just can not find the answer, even though this is used (though not explained) in several books: What is $\frac{\partial G (z, \theta)}{\partial \theta}$ when $G$...
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47 views

Why the transfer function is equal to the output in this case

In this description of transfer functions on the z-plane (image linked), I'm confused by equation 1.49, which says that $H(f)=v_{out}(f)$ when $v_{in}(f)= 1 * e^{j 2 \pi (f/f_s)}$. (For another matter ...
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How to handle cross products in feedback loop?

I'm trying to simplify the following block diagram from to the following block diagram However, h(t), H(s) in time domain, has a cross product in it (gyroscopic torque). How can I represent the ...
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71 views

Transfer function model to frequency response

I have a problem, I wanted to filter the signal with a Butterworth filter built on the basis of a prototype. I have zeros and poles and an $H (s)$ answer, and I do not have the frequency response. How ...