Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.

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Hardware Transfer Function Estimation

Suppose you have the ability to inject any arbitrary waveform into a piece of analog rf hardware and collect and digitize the output for analysis. If you wanted to characterize/estimate the transfer ...
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Lorentzian signal fit

A plot showing two S21 peaks through a resonator is given below: As you can see, the first resonance peak occurs at 4.43GHz. The fit applied to this peak is given below. $$y = A - 10 \log_{10} ...
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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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Stability of transfer function

Now K(s) is obviously the negative feedback loop which is ${H(s) \over 1+H(s)G(s)}$ When I substitute ${H(s) = {1 \over s-2}}$ I get K(s) = ${ 1 \over s-2 +G(s) }$ For the system to be stable ...
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Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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Output of a system given it's transfer function and input (beginner)

I have an exercise that gives me the transfer function of a system $$H(s) = \frac{3s^2+27}{s^4+8s^3 + 16s^2} $$ and an input $$x(t) = \frac13 cos(3t) $$ An ask's what is the output I don't whant ...
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Block diagram transfer function of a line

What is the transfer function of a line, can i ignore it? After simplification i got the diagram: I don't know what to do with the empty feedback
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IIR filter SOS and Direct Forms doubt

I have below doubts, so confusing! As I don't want to assume from what I read, I am asking for help here! Are Second Order Sections another name for biQuads ? If I have 2 single pole transfer ...
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66 views

Given input and output time series, obtaining filter design

Say I have 5 minutes of input and output audio. One method I know is to do FFT on windows from input and output. Then divide FFT output into bins and find average energy in various bands for all the ...
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167 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
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Describing a time delay at a maximum for maxima and minima but tends to 0 elsewhere

I have two force-time signals obtained from a couple of force plates, corresponding to input/output signals for some system. Plotting the two together one of the first things I noticed was a time ...
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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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Step response overshoot

given step response: $\frac {0.04 \cdot K} {(0.04 \cdot K+1.63 \cdot 10^{-3})}$ how do I find $K$ so the step response never have overshoot?
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Obtaining an expression for the transfer function when using FFT

Say I have two signals, a(t) and b(t) where the former is the input and the latter in the output. These signals are both recorded by sampling at every 0.01s. The Fast Fourier Transform was applied to ...
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How to compute the impulse response from a transfer function

Say I have a transfer function, for example: $$H(z)=\frac{1}{1+0.1z^{-30}}$$ How can I compute the impulse response? (This is just an example, the important thing is that it is in closed symbolic ...
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Digital filters with more zeros than poles

I am having trouble wrapping my head around digital filters with different orders of numerator and denominator. Let me know if any of these points is wrong: All (digital or analog) transfer ...
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What is the general form of a transfer function

I repeatedly see two representations of the general transfer function in the literature. The first is the following which is factorization of the numerator and denominator polynomials: ...
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How to find transfer function by state space representation matrices

A state space representation is given by: $$\dot{x}= \begin{bmatrix}0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 \\ 0&0&-2&-4\\0&0&1&0\end{bmatrix}x+\begin{bmatrix} ...
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Conversion from laplace transform to z-transform [closed]

I would like to know if $$ \text {Z-Transform ( } G(s)H(s) \text{ )} = \text {Z-Transform (}G(s) \text{)} \text { Z-Transform (} H(s) \text{) } = G(z)H(z) $$ where G(s), H(s) are the Laplace ...
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How can I compute the inverse digital of a nonrational transfer function?

My $G(s)=1-e^{-s/\tau}$, $\tau$ is very small, say of order $10^{-4}$. I need to compute a $H(z)$ (a digital filter) such that $H(z)$ has the inverse response of $G(s)$. Is ok even if $G(z)$ has the ...
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Understanding 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 Z-transforms ...
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Why is state-space representation more numerically stable than zeros-poles representation?

Matlab documentation says things like: For high order filters, the state-space form is the most numerically accurate, followed by the zero-pole-gain form. The transfer function coefficient form is ...
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Using goertzel confuses me

I am having some troubles understanding the algorithm. My algorithm looks like this. how come am i able to compute the DFT coefficient using this algoritm. As far as i know $$ X[k] = ...
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Difference between natural response and forced response?

Reference Second post on EdaBoard.com Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time. ...
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Attempting to use the trapezoidal rule to form a difference equation representing a circuit

I have a differential equation that has been proven to be correct. The transfer function obtained by Laplace domain analysis and Matlab freqs match up and all is well. The problem is somewhere in ...
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WIDELY UNKNOWN?? Wireless Channel Transfer Function or freq response - frequency vs attenuation

We know that the signal attenuates out with distance and according to the channel transfer function or frequency response, the signal frequency components attenuate to different values based on ...
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256 views

Calculate cut-off frequency of lowpass IIR-filter

Given a an IIR lowpass-filter in z-space: $ H(z) = \frac{\sum_{i=0}^P b_{i} z^{-i}}{1+\sum_{j=1}^Q a_{j} z^{-j}} $ How to calculate it's 3dB cut-off frequency? I about evaluating it's fourier ...
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Difference between state space and transfer function model response (in Simulink)

Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values (Kp ...
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Implementing headphone transfer function (HPTF)

This document on HRTFs, A Spherical Far Field HRIR/HRTF Compilation, of the Neumann KU 100, talks about headphone compensation filters. Searching Google returns ...
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Is any time-domain vector stored on a digital machine always intrinsically causal? [closed]

Reading up on causality, I understand the mathematical definition, in so far as that a causal system, is one where the output depends only on the current time, and possibly the past time, but never ...
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295 views

Inverse system in Simulink

I have a inverse system: $G(s)= s^2 + 2s + 3$. How do I apply it in a Simulink model? (the transfer function is only accepted if and only if the order of the numerator < order of denominator).
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Build discrete IIR from a transfer function which is not in terms of $s$

Firstly I should state that my maths knowledge is limited. I'm currently designing an acoustics modelling application which uses a rectilinear FDTD grid for modelling pressure variations - but I've ...
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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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Converting mel spectrogram to Spectrogram

I have a set of songs for which I extracted the STFT (Short Time Fourier Transform) and used the magnitude spectrum $|S|$ to calculate the mel spectrogram by using a mel filterbank matrix $M$, so ...
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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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Transfer function between voltage and decibel output for in-ear headphones

What would be a decent formula for approximating the connection between voltage and decibel output for a typical set of unpowered in-ear headphones? I'm generating sine waves from the computer: an ...
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z-space replaces multiplication with convolution and frequency eigenvectors

The frequency domain is allegedly preferred because it replaces convolution of complexity $n^2$ with a diagonal matrix multiplication. Yet, I see that in z-domain we have multiplication of ...
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Cascade Transfer Function; Odd or Even Transfer Function

suppose we have a cascade realization of a transfer function of a higher order. What difference does it make if the order of the transfer function is an Even or an Odd number?
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Transfer Function from input to node [closed]

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node:
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Finding the frequency response of a filter defined as a Z-domain transfer function

I am software engineer studying DSP on my own. I came across this question in a graduate textbook and am not sure how to proceed. ...
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Why is a feedback loop not represented by the least order transfer function?

I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(Z)C(z)}$. $H(z) = h$ and $C(z) = \frac{K}{z-\alpha}$. If I manually calculate the transfer function, I get: $L(z) = ...
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Digital control: Exercise solution

Can you help me (show me how) to solve the following exercise? For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
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Fill matlab “ellip” function through transfer function magnitude response

The matlab "ellip" function can be used to design the unquantised coefficient set. From matlab website: $ [b,a]=ellip(n,Rp,Rs,Wp) , $ n: order of filter Wp: normalized passband edge ...
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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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How to show that this filter is a HP filter

i got a system with transfer function given by: $$H(\omega)=1-e^{-j\omega}$$ I already plot it, and that seems to be a periodic function with $H(0)=0$, $H(\pi)=2$, , is that enough to show that this ...
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479 views

Determine the type of filter from the transfer function

i got that system $x_n \to x_n-x_{n-1}$, so $h_n=[.....,0,1,-1,0,...]$, with $h_0=1$ and $h_1=-1$, so the transfer function given by: $$\sum_{i=-\infty}^{\infty} h_ne^{-jwn} = ...
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If exponentials are eigenfunctions, where does the transient term come from?

Here you can see that the transfer function applied to a cosine input will give you a sinusoid and a transient term: $$ x(t) = \underbrace{(x(0) + x'(0))(2 e^{-t} - e^{-2t}) + \frac{2}{5} e^{-t} - ...
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Find the frequency response if i have the magnitude response?

if i have the transfer function of magnitude response is there a method that i could calculate the frequency response? For example the transfer function of the magnitude response is: $ 3db \pm ...
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Z-domain transfer function question

For the difference equation below: $y(k)=1/2{x(k)+x(k-1)}$ How i can find he z-domain transfer function? Thanks.
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Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...