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

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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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For a standard second order transfer function, what is the equivalent time domain significance of $\zeta>0.707$?

In frequency domain $\zeta>0.707$ implies no resonant peak in frequency response. But I am unable to correlate what is the exact time domain effect of this? If $\zeta=0.707$ acts like an ...
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to find transfer function for experimental data and check its correctness

http://www.sciencedirect.com/science/article/pii/0167610587900225 http://www.sciencedirect.com/science/article/pii/0167610579900266 paper which i refered for calibration of pressure sensors i want to ...
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How to compute transfer function (Frequency Response Function) from experimental data

I have a set of data, in the freqeuncy domain, corresponding to a structural test. I have amplitude, phase and frequency for both the measured output and the input signal (accelerations are measured ...
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How to find roll-off from its transfer function equation?

I want to find roll-off (unit dB/decade) of highpass filter $H(z) = 1 - a \cdot z^{-1}$. I derived magnitude response to be $1+a^2 - 2a\cdot \cos(\omega)$ To find out roll-off factor from above ...
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Why is my discretized transfer function unstable when my discretized state-space model is stable?

I am working with a 30-state, 14-input linear model that is described by a state-space model: model_state_space = ss(A, B, C, D); The model is extremely slow (it ...
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45 views

Biquad Filter Transfer Function Frequency Response

$H(z) = G\cdot\displaystyle\frac{2b_0\left(1-z^{-2}\right)}{1-2a_1z^{-1}-2a_2z^{-2}} + 1$ I have a data sheet with the above transfer function, I need to calculate its frequency response in code. I ...
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Symmetry of Walsh matrix

Walsh matrix is abtained by sorting the rows of Hadamard matrix by number of sign changes (1st row had 0 changes, 2nd has 1 change of sign etc). Walsh matrix is symmetric. Meaning the sorting the ...
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Gonzalez question solution

If I have the histogram of an input image as Gaussian probability density function of the form: $$P_r(r)=\dfrac{1}{\sqrt{2\pi}\sigma}e^{-\dfrac{(r-\mu)^2}{2\sigma^2}} $$ where: $\mu$ and $\sigma$ ...
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52 views

Equivalence of FFT and PSD based output based on the Frequency Response Function

Correct me please if I am wrong... I have just started working in the domain of signal processing using the Fourier Transform ($\mathbf{FFT}$) and Power Spectral Density ($\mathbf{PSD}$). I am trying ...
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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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47 views

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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58 views

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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77 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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206 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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42 views

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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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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238 views

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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303 views

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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394 views

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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216 views

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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293 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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432 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) = ...