# 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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### Calculation of an impulse response of h[n]

I am currently looking at the z-transform and am using a great youtube reference to help me, however I am struggling on some basic step. How do I get the impulse response array of h[n] = [ ... ] shown ...
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### How to I get transfer function?

there is a ODE $dx/dt-ax(t)=u(t)$ Firstly, I have to find the transfer function $u$ to $x$ using exponential input. So I put $u(t)=e^{st}$ to the ODE, and I got $x(t)=x(0)e^{at}+1/(s-a)e^{st}$. In ...
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### How to approximate the transfer function of compensator using root locus?

I have the root locus of a system with and without compensator. The system is consist of a PD-controller and the process, the output is fed back to the controller via $G_s(s) = 1$. The upper graph is ...
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### Digital filter coefficients from low-pass to high-pass

Given I have coefficients a0, a1, a2, b1, and b2, defining the difference equation for a digital filter as: ...
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### Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results

I'm confused due to the fact that the Nyquist stability criterion and looking at the transfer function doesn't give the same results whether a feedback system is stable or not. When I have the system ...
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### How to estimate the modulation transfer function of images?

I'd like some way to estimate the modulation transfer function in images. This is the observed drop in amplitude vs increase in frequency of spatial details - nice illustration here: (from https://...
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### How can I find the transfer function of the following block diagram?

I've the following image and I want to find the transfer function from input $x(t)$ to output $y(t)$. I know that I have to apply Laplace Transform, so the integrator becomes $\dfrac{1}{s}$, but I don'...
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### How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?

How to compute transfer function $$G(s) = \exp \left( - \sqrt{s} \right)$$ in Matlab / Simulink? I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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### Calculating IIR Filter gain at given frequency

Let's consider an IIR filter with transfer function: $H(z)$. Given the sampling frequency $F_s$ how can I calculate gain at say $F$ ? When I was dealing with analog systems when I wanted to calculate ...
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### What is the DFT of a binomial filter?

I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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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 \$...