# 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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### Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
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### How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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### What Is the Transfer Function of a Moving Average (FIR Filter)?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
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### What is the zero in this transfer function?

What is the zero for the following transfer function, $-1/2$ or $-2$? $$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$ This appears to give a zero of $-1/2$. I can transform this into the standard form ...
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### Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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### Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
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### Understanding $\mathcal Z$-transforms and pole locations

I am trying to gain a better understanding of pole locations in the $z$-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the $\mathcal Z$-...
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### Does “improper” imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
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I have the following inverse system $$G(s)= s^2 + 2s + 3$$ How do I implement it in Simulink? Note that the transfer function is only accepted if and only if the order of the numerator is less than ...
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### Applying a filter on an audio signal with Python

Let's say I have a filter described by its transfer function: $$H(\omega) = \frac{1}{1 + j\frac{\omega}{\omega_0}}$$ And I want to apply this filter to an audio signal (a .wav file) using Python. ...
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### Why more poles than zeroes?

I read that an "improper system" "has more zeros than poles; it is not causal, cannot be implemented, has a strictly proper inverse and has infinite high-frequency gain." Does causality fail due to ...
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### Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...
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### Can I determine a system's $z$-domain transfer function from its pole-zero plot?

Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
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### Anti-causal systems

If Anti-causal systems are defined as those whose output depends solely upon future inputs.(Is this definition correct as I understand) So i see that $y[n] = x[n+2]$ ; is anticausal system How is a ...
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### Estimate the Transfer Function of an Unknown System

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
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### Why does this transfer function has a second zero

I'm learning about $\mathcal Z$-transforms in DSP and I have a transfer function of the following form: $$H(z)=\frac{2-3z^{-1}}{1-1.6z^{-1}+0.8z^{-2}}$$ When I calculate zeros and poles of this ...
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### derivative filter transfer function

In many of the papers it is said that the derivative filter transfer function is given by: $$H(z) = \dfrac{1}{8T}\left(-z^{-2} - 2z^{-1} + 2z + z^{2}\right)$$ But no one gave the detailed information ...
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### How to find poles of transfer function by looking at the step response?

How to find poles of transfer function by looking at the step response? Given a step response graph like such: How would I find the sketch for its poles on the complex plane? The only thing I can ...
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### How to establish transfer function of a speaker?

I'm working on a signal processing project about vocal system, and I'm trying to use controlling theories to solve the problem. I need to get the transfer function, $H(s)$, of a speaker, from ...
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### Response of a system to a step function (heaviside)

I'd like to compute the response to a step function of a electrical/thermal system. Generally I can "easily" compute the transfer function $H$: $$H(\omega) = \frac{V_{out}(\omega)}{V_{in}(\omega)}$$ ...
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### Transfer function determination from input and output data

I have some input and output data that I believe adequately includes excitation of the important dynamics of a system. I know it is at most a 4th-order transfer function. How can I identify the ...
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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 optical anti-aliasing filters work from a frequency domain perspective?

To prevent aliasing caused by the finite number of pixels on a sensor, a blurring filter is commonly used. How does that work from a frequency domain perspective? What is the transfer function of such ...
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### Poles and zeros of a transfer function

What are the poles and zeros of this transfer function (in $z$): $$H(z)=z+2+z^{-1}$$ and how would you approach the resolution of such problem? Personally, I would write H(z)=\displaystyle\frac{...
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### What do we know about the transfer function away from its zeros?

So lets say I have a transfer function for an FIR filter $H(z) = (z-a)...(z-n)$ where $a,...,n$ are points along the unit circle. But what about other points along the unit circle that correspond to ...
Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...