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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Using ROC to find stability of system in specific example

I've started learning about finding the ROC from the transfer function, but I'm confused about an example. $$H(Z) = \frac{2Z + 1}{Z^2 + Z - \frac{5}{16}}$$ I understand the poles lie at $z = \frac{-...
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Finding poles of an abstract transfer function

When finding the poles of something like the following transfer function, would I be able to write $z=\sqrt[L]{\mu}$ since square roots aren't technically defined on the complex plane? $$Y(z) = \frac{...
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Recovering a Differential Equation From the Transfer Function of a Cascaded System

With respect to the below discussion, consider that we are talking about LTIC systems characterized by constant coefficient ODEs. Consider a cascaded system whose transfer function H(s) is given by ...
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How do I find the transfer function of a speaker by analysing the audio produced by it?

I have the original audio signal(MATLAB GENERATED) and the recorded audio signal (anechoic conditions). The setup consists of a DAC with a power amp plugged into the speaker. The audio is recorded via ...
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Who first understood the importance of poles?

Who first understood (or at least published papers on) the importance of poles in understanding transfer functions in the frequency domain? If I had to guess, I'd suggest Nyquist or Bode but I know ...
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Determine the system function H(s) of a system and find out the differential equation

I have created the following system for practice purposes. From this system I want to determine the system function H(s). In the picture I have worked with auxiliary (dummy) variables, which should ...
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How to applly Hanning window on S parameter results?

I am working on Time domain computation. I have S parameter results simulated, using these results I do the Inverse FFT to get results in time domain. I want to filter/window results using Hanning ...
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What is the slope of a transfer function?

Lets say I have a Transfer function (H) plot as below. I need to find the SLOPE of the transfer function in dB/MHz. That is... i need a plot (db/MHz) vs frequency. How can i go about it ? ...
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Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler integral ...
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Draw a structure for IIR Filter given H(z)

This is the transfer function for the Direct Form 1 of the IIR Filter: I'm trying to understand the rules to convert $H(z)$ into its corrispondent structure I've just understood how to draw $H_1(z)$,...
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Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
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Forward Euler Discretization

I don't understand why the substitution $s=\frac{z-1}{T}$ allows us to discretize a transfer function from laplace to z-transform through Forward Euler Discretization. Can you explain to me ?
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Non-polynomial Z-transform

My prof said that when a transfer function described by a z-transform is not polynomial, then i can't perform the anti-transformation. But, what does it means to be not polynomial ? Can you explain to ...
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bode plot, zero at 0Hz

I'm learning to draw magnitude bode plots from transfer functions: $$ H(s) = \frac{sRC}{sRC+1} $$ So I can see that I have a zero at s = 0, which corresponds to 0 Hz. I know this will add a +20dB/...
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Unstable plant transfer function identification

I would like to find the transfer function of an unknown unstable SISO plant. If it was a stable plant, I would input a sine sweep and measure the frequency response at the output; but I cannot do ...
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How do I find transfer functions from a state space representation?

Suppose I have a MIMO system in state space representation, for example: $A=\begin{bmatrix} 1 &2 &3 \\ 4&5 &6 \\ 7&8 &9 \end{bmatrix}$ $B=\begin{bmatrix} 2 &3 \\ ...
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When is a discrete time transfer function unrealizable?

I don't understand why the following makes sense: Given a second-order mass damper system in continuous time: $H(s) = \frac{1}{ms^{2}+cs}$ Its inverse $H^{-1}(s)$ is unrealizable as a transfer ...
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Transfer function given as z-Domain fraction: gain calculation

I am stuck on a question regarding transfer functions. I have the answer and have attempted the question but am having trouble solving it. Q: Given the transfer function of a digital filter is (5z-5)/...
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Limitations in Backing Out a Transfer Function

Suppose you have an LTI system for which the (complex) frequency response $H(j\omega)$ has been measured in some frequency window $[\omega_1,\omega_2]$. Now imagine that you want to provide an input $...
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What real object could be modeled by this transfer function? [closed]

What object from real world could be modeled by this transfer function? What could parameters b, p1 and p2 stand for?
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How is time or sampling rate accounted for in this model?

A basic model of coupled strings (eg. piano) is provided here as: The principle is that it has two identical string simulations each formed by a delay line and LPF. The outputs of these are summed at ...
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Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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Doubt on inversion of the dynamics

I am studying control system and I have encountered the topic of the inversion of the dynamics. So I have seen that the ideal situation would be $C(s)=P(s)^{-1}$ but there are some problem with ...
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How to Determine if FIR has a Linear_Phase Response w/o Matlab

Given the FIR transfer function: h(z) = $ .36 + .384z^{-1} + .1608z^{-2} +.9712z^{-3} + .352z^{-4} + .18z^{-5} - .2z^{-6} $ How do you determine if this transfer function has a linear - phase ...
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Is it impossible to determine the inverse Z-transform without any other information?

Suppose I give you this as my transfer function $H(z)$: $$ H(z) = \frac{1} { 1 - az^{-1}}$$ With no other information given, is it even possible to determine the inverse Z-transform? The reason I'...
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How can I obtain the response signal for this question?

In particular I am having trouble with 6b). From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. ...
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Steady-State Output from Transfer Function

The progress I have made is as follows: $\sin(t)$ is our signal therefore $\omega = 1 = 2\pi f$ and $f$ = $\frac{1}{2 \pi}$ Also, $f_s$ = 10Hz therefore T = $\frac{1}{f_s}$ = 0.1s $H(z) = \frac{z}{...
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Lead compensator vs lag compensator?

I already know that lag compensator acts like PI controller and improves steady state and lead compensator acts like PD controller improves transient state but how they achieve their goal? Despite ...
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Magnitude and phase response and cut-off frequency of a moving average filter

The frequency response of a typical moving average filter of length $N$ is given by $H(\omega)=\frac{1}{N}\frac{\sin(\omega N/2) e^{-j \omega ((N-1)/2)}}{\sin(\omega/2)}$. Firstly, isn't the cut off ...
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Pole Zero plot given a Transfer function

I've been looking at how to plot zeros/poles based on a transfer function. I found a couple of Tutorials online. In the first youtube tutorial, the author brilliantly explains how to plot the zeros/...
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A signal $g(t)$ is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0

I am solving a question, where a signal g(t) is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0. I understand that since for this filter the ...
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Finding the impulse response of a system

I have the following transfer function. $$ H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$ I'm trying to find the impulse response of the system. ...
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Are MATLAB function zp2tf() and tf2zp() are complementary or not?

I was under impression that given, pole, zero and gain the transfer function (filter coefficients b and a) is fixed. Therefore, ...
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How would I calculate the DC Gain for a Chebyshev Type 2 filter?

I'm currently working on an implementation of a Chebyshev Type 2 filter but the gain is all over the place when playing around with the order and ripple. I haven't found anything online but (as far as ...
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How to realize Poles and zeros at infinity??especially through transfer function?

I have a question regarding the poles and zeros at infinity I often read here in DSP SE and also in some textbooks about poles and zeros at infinity This question also answers somehow (but not in ...
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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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Closed Loop AGC

Interested to develop an AGC for the RF RX chain below. Using the Matlab code as a reference have developed an open loop AGC. Equations as well as block diagram are provided below. Wondered how can ...
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Determining the transfer function from discrete signals

I have measurements of a discrete in- and output signals, and I want to find the transfer function of the system. Is there a good method for finding the transfer function of an LTI system from ...
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Two different answers while doing Inverse Z-transform

Given, $$X(z) = \frac{z}{3z^2 - 4z + 1}$$ Question 1 I need to calculate inverse z-transform for ROC $|z|>1$ When I try to calculate inverse $z$-transform using partial fraction of $X(z)$ and ...
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Inverting Sensor Transfer Functions?

When you see software packages that read in data from sensing equipment, does the software do something to inverse the transfer function? Correct me if I'm wrong in my understanding, but this is how ...
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Calculate transfer function of two parallel transfer functions in a feedback loop

I have rational transfer functions: $$H_1(z) = \frac{ b_0 + b_1z^{-1} + b_2z^{-2} }{a_0 + a_1z^{-1} + a_2z^{-2}}$$ $$H_2(z) = \frac{ q_0 + q_1z^{-1} + q_2z^{-2} }{p_0 + p_1z^{-1} + p_2z^{-2}}$$ And ...
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Step response of third-order continuous-time transfer function

I have a transfer function of the form: $$H(s) = \frac{b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}{s^3 + b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}$$ If it matters, $a=b=2$. Is anyone aware of ...
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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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Second Order Transfer Function : Imaginary component in $R$?

I have been looking at the following transfer function: $$ H(z) = \tfrac12 - \tfrac12 z^{-2} $$ Given the usual method for finding $\theta$ and $R$ in the complex plane, I calculate that $\theta = \...
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Compensating the Group Delay of an Analog Filter using DSP

I am having a problem in my current project where I need to measure different biological signals (like ECG) simultaneously. As the instrumentation hardware is developed by different people over time, ...
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Basic Questions on Wiener Filtering

I read a lot about Wiener Filters (focusing on discrete time case). I understand the math, but I am quite disconnected from the real life assumptions behind using such a filter. Unfortunately ...
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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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Similarity or Relation between Walsh Hadamard Transform and Slant Transform

Is there any relation between Walsh Hadamard Transform and Slant Transform? Or is there any common property or similarity?
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Missing delay in heavyside step function

I found the following task that was inspired by an example in the book A. V. Oppenheim and R. W. Schafer, "Discrete-Time Signal Processing", 3rd Edition, 2014. Task: Consider the 2nd-order IIR ...
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Cascade filter realization equivalence? [closed]

Given $$H(z) = \frac{11 +4.6z^{-1} -26z^{-2}-3.75z^{-3}}{1-z^{-1}-8.75z^{-2}}$$ I'd like to know whether this realization: Is equivalent to this one? In short, is the direct form realization ...

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