# 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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### Convolution with an impulse response does not give the same result as the frequency response

Context I am trying to design a linear-phase FIR filter with the following frequency and phase responses: Designing the filter Given its characteristics (peak filter at 1kHz with 9dB gain and Q=7), ...
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### Transfer function and difference equations: why does $H(z)$ numerator polynomial not correspond to $Y(z)$?

For a discrete time LTI system, I understand that from a difference equation description of the system in the form $$\sum\limits_{k=0}^N{a_k y[n-k]}=\sum\limits_{k=0}^M{b_k x[n-k]}$$ I can ...
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### 1st order filter output

Two 1st order filters : ...
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### What is $H_2$ and $H_{\infty}$ control? [closed]

I can create a Linear Quadratic Gaussian Integral(LQGI) controller very easy by using GNU Octave. LQGI is in the area of Optimal Control Theory. But there is something called Robust Control Theory. ...
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### Could someone please explain how to get frequency response of a given Bode Plot?

Having trouble with bode plots. I understand that the is to be converted to $dB$ but after that I'm stuck. Could someone please show me how this graph gives a frequency response of $10/1+jw10$
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### Design discrete controller for zero steady state error

I have the following system where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ...
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### Find transfer function given impulse

I am given the following discrete time transfer function : $$G_d(z^{-1})=z^{-d}\frac{b_0+b_1z^{-1}}{1+a_1z^{-1}}$$ which has the following impulse response $$g_d[n]=\{0,1,-0.1,-0.05,...\}$$ How can I ...
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### How can I find the transfer function from this Bode diagram?

I've been given this bode diagram : I've been asked to find the transfer function only by using the bode diagram. It's the first time I'm doing this so here's what I thought. The starting value is ...
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### First derivative analog filter

I'm reading about fault detection via signal processing in time domain. One possibility is to check that first derivative of the signal is in some predefined bounds. The text says that to obtain the ...
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### Estimate transfer function from Bode curve

I have measured the magnitude response Y_mag(f) and phase response Y_phase(f) of an unknown physical system. Is it possible to ...
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### Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
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### FIR Filter - Transfer Function

I am dealing with the transfer function of an FIR filter: $$H(z) = (1-0.5z^{-1})(1-2z^{-1})$$ I am having trouble determining which type of Linear-phase FIR filter it is, Type 1-4. I believe it ...
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### Given a causal LTI system with a transfer function, determine if the system is an all-pass filter

We are given a transfer function of a causal LTI system and must determine if it is an all-pass filter: $$H(z) = \frac{1 + 4z^{-2}}{4 - z^{-2}}$$ To the best of my recollection to determine if a ...
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### A question about the meaning of pole in time domain

Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as: $$H(s) = \frac{1}{s - (-1-j)}$$ So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good. Now ...
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### (How to ask a Homework Question): Define poles by using proportional controller

Given is a process with the transfer function $$G(s) = \frac{s - 1}{s^2 + 3s + 2}$$ I want to create a controller so that the poles of the controlled system are $$p_{1,2} = -4 \pm i$$ Is it ...
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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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### Finding DC gain of a signal

I have a gray scale image produced by an optical photon simulation and I am trying to find the DC gain of the image using Matlab. For that, I simulate a slant edge image in the simulation where N ...
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### Why is the dB plot of a signal usually non-positive?

Almost every decibel plot of a signal is usually below 0. Why is this the case? I recently just plotted a transfer function with a very high decibel plot above 0.
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### Simplify equation of single pole IIR transfer function

Example - Consider the causal stable IIR transfer function $$H(z)=\frac{K}{1-\alpha z^{-1}}, \quad 0 < \lvert \alpha\rvert 1$$ where $K$ and $\alpha$ are real constants Its square-...
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### How to find analytic description of filtered signal

I am looking for an exact analytic description of a filtered signal. I have an electronic circuit whose input is a monoexponential decay. First (1) the signal gets filtered by a simple RC-Lowpass. ...
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### Control design: under what conditions can closed-loop poles be placed arbitrarily?

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., ...
I've forgotten how to get the frequency response function out of a Bode Plot. The phase component of $H(j\omega) = e^{j\pi/2}$, right? But I am having trouble finding $|H(j\omega)|$. How would I get ...