# 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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### 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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### 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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### Significance of poles in a Transfer Function

Sorry for asking this basic question, but I am new to signal processing and have this doubt for a long time. I have been studying signal modelling and have $$H(z) = B_q(z)/A_p(z)$$ where $A_p(z)$ ...
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### Does the definition of stable system contradict itself?

A system is said to be stable when any of its poles are <0. However I don't get why that is the case. Negative poles mean negative angular frequency, and negative angular frequency is equal to ...
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### Find transfer function of physical system

I want to detect an impact at a table using accelerometers. I thought a useful thing to do was to find the transfer function of the table I am using, so that I have an idea of how signals in the table ...
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### Impulse response from the transfer function

The discrete system has poles at points $z_{1,2} = 0.8e^{\pm{i\pi /6}}$ and $z_{3,4}=0.8e^{\pm{i\pi/2}}$, and two-fold zeros at $1$ and $-1$. The task is to determine the impulse response of the ...
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### Calculating and controlling the location and bandwidth of individual notches in an allpass phaser

I'm currently working on a phaser implementation with the intention of adding some parameters that generate unique effects, namely effects that involve the precise placement of the phaser notches (e.g....
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### What methods allow learning "changes" in data, and then generating synthetic output?

Suppose I'm interested in a process of the sort: Original data -> Something happened to data -> Result data More particularly, consider that we observe many results of "something happened ...
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### Slope of phase function

Would appreciate some help understanding if I take the phase function of some transfer function and derivative it in the linear part of it which is around the resonant frequency what does this slope ...
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