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# 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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### Flatten noise floor of spectrum by reference/dark measurement

I'm currently stuck with a problem and would appreciate any input or guidance in this regard. Background information In a laser experiment, an amplitude signal in volts and a position signal are ...
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### Low pass Thiran filter difference equation in Python

I'm attempting to build a time domain low-pass Thiran filter (in Python if that is relevant) based on the original article: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1083363&tag=...
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### Decay of the impulse response for poles contained in the unit circle

I've been struggling with the following exercise in Ljung's "System Identification: Theory for the User" (Problem 3G.1): Given a rational transfer function $G(z)$ such that its poles are all ...
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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. ...
1 vote
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### Why is there a phasor in the transfer function of an ideal LPF?

I'm learning about Low Pass Filters. My professor said the following is the transfer function of an ideal LPF: $$H_{LPF}(f) = G\Pi\left(\frac{f}{2B_{pass}}\right) e^{-j2\pi ft_0}$$ However, i don't ...
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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 ...
1 vote
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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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### Calculating transfer function of a linear time varying system?

If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
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### Max input of a system given it's transfer function and an assumed step change (beginner)

I have an exercise that gives me the following transfer function $$\frac{0.5}{s+0.5}$$ and an assumed step change in the target of 20 I am asked to calculate the maximum input for the assumed step ...
1 vote
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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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### Why does scipy introduce its own convention for H(z) coefficients?

Conventionally, the definition of the system function for a IIR digital system is: $$H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\cdots}{1-a_{1}z^{-1}-a_{2}z^{-2}-\cdots}$$ where coefficients are the ...
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### Feedback stabilizes unstable systems?

Can feedback stabilize a unstable system?I guess so since we may get rid of any poles in the positive complex plane by feedback but I am not sure.
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### Factorization of transfer function using its roots

I'm missing a step to understand the factorization of the FIR filter transfer function: $$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$ From DSP First: The $z$-transform of a finite-length signal, ...
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### How to determine if a system is minimum phase or not?

I'm studying for an exam and this is an old exam question that I don't understand: Is the following system non-minimum phase? $$G(s) = \frac{e^{-2s}}{s+2}$$ I can see that the real part of the pole is ...
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### Finding the inverse $z$-transform

I have the transfer function: $$H(z) = \frac{z^2 + 0.75z + 0.125}{z^2+0.5625}, |z| > 0.75 = \frac{(z-0.5) (z-0.25)}{(z - 0.75j) (z + 0.75 j)}$$ I attempted partial fraction expansion in order to ...
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### Is it possible to use AMIGO tuning rules with relay control?

I am trying to control a plant with PID using tuning rules such as the Ziegler-Nichols rules. However, it is not always easy just to send a step to your plant source of the image. Another method to ...
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### Can you plot an irrational transfer function on matlab?

For example if I have the following transfer function: $$H(s) = \frac{1}{\cosh(\sqrt{s/10})}$$ Can I do the bode plot it in matlab or do I need to rationalize it beforehand?
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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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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 ...