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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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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How is the transfer function of a state space representation computed in practice?

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 ...
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Z - Transform of a non recursive block diagramm

i am currently struggling to find the Transfer Function of the following Block Diagram, since i have never done it for a non recursive System, could somebody please walk me through the process of it? ...
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Finding transfer functions from a system of multiple inputs

If I have a system: $$sX(s) = AX(s)+BY(s)+CZ(s)$$ How would I find the transfer functions $\frac{X(s)}{Y(s)}$ and $\frac{X(s)}{Z(s)}$? Do I simply disregard one of the inputs? I am quite confused and ...
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How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response

I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
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How to find zeros of a transfer function

Given the following transfer function, $$H(z) = \frac{6 + 4z^{-1}}{2 + 5z^{-1} - 3z^{-2}}$$ How do we find the zeros of the transfer function? We can write the above expression as $$\frac{3(1+\frac{2}{...
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Relation between Causality and the Phase response of an Amplifier

I am trying to model the response of an amplifier. As per the main answer on this question, if one wishes to do so, they have to look at the Fourier decomposition of the input signal $x(t), \, \tilde{...
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Why does a root locus show that system is stable but unit step response of a system does not have a stable output?

From what I know about root locus is that if all roots are located on the Left Half of the S-plane the system is stable. That's why I expected the unit step response of a system to be stable. ...
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Why does drawing bode plots on poles or zeros give different results?

Why does drawing bode plots on poles or zeros give different results? For example I have a transfer function, I could write it for pole as $$\frac{1}{\left(1+\frac{s}{\omega_0}\right)} \tag 1$$ or ...
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How to write transfer function?

I am an engineering student. I have some data stored in matlab. I need to build low pass filter to process my data. How can I write the transfer function? In my understanding transfer function is the ...
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Z domain transfer function including time delay to difference equation

How can get the difference equation of a $\mathcal{Z}$-transform transfer function with time delay? How does a time delay influence the difference equation? For example: $$H(z) = \frac{8z^{94}}{z-0.9}...
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First Order State Space Question

I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response $$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$ In this ...
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How should I interpret $z_1^{-1}$ if $z = e^{j\omega(i)T}$?

I'm trying to understand how I should create all these $z$ values. Each $z$ values is equal to $z = e^{j\omega(i)T}$ were $j$ is the complex number (instead of $i$), $\omega(i)$ is the i:th wrequency ...
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Obtain transfer function from FEM Model

I'am getting Transfer function from FEM Model of Simply supported rectangular plate i do random vibration input force $x(t)$ and measured displacement $y(t)$ In matlab, because that is noise free data,...
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How to get the impulse response of from input and output data?

We know that $$x(t) \star h(t) = y(t) $$ and $$X(\omega)H(\omega) = Y(\omega).$$ But in real world, $X(\omega)$ and $H(\omega)$ are DFTs. So to prevent circular convolution, we do zero padding before ...
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Why do I need to multiply the frequencies with a number, to get correct "shift" in the bode plot?

Assume that we got a sine wave function $$u(t) = A\sin(2\pi \omega(t)t)$$ Where the frequency $\omega(t)$ changes over time $t$ and $A$ is the amplitude. Assume that we apply that $u(t)$ signal onto a ...
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The frequency function for $Y_t-18=0.4X_t+0.9X_{t-1}+e_t$

I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white ...
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Significance of poles in a Transfer Function

Sorry for asking this basic question, but I am new to signal processing and have this doubt for a long time. I have been studying signal modelling and have $$H(z) = B_q(z)/A_p(z)$$ where $A_p(z)$ ...
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Does the definition of stable system contradict itself?

A system is said to be stable when any of its poles are <0. However I don't get why that is the case. Negative poles mean negative angular frequency, and negative angular frequency is equal to ...
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Find transfer function of physical system

I want to detect an impact at a table using accelerometers. I thought a useful thing to do was to find the transfer function of the table I am using, so that I have an idea of how signals in the table ...
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Impulse response from the transfer function

The discrete system has poles at points $z_{1,2} = 0.8e^{\pm{i\pi /6}}$ and $z_{3,4}=0.8e^{\pm{i\pi/2}}$, and two-fold zeros at $1$ and $-1$. The task is to determine the impulse response of the ...
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How can I find a transfer function between two signals in python?

If we call one signal $x$ and the other signal $y$. I want to find a transfer function that takes $x$ as input and gives $y$ as output. I have recorded data of signal $x$ and $y$. $$x(t) \overset{H}\...
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What is the intuitive interpretation of the transfer function of this system?

If I have the system that could be observed in the next Image: I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
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Phase Response Function / Plotting in Excel (IIR Filter)

Using formula from Audio EQ Cookbook I implemented biquad IIR filters in Excel. I can now plot every transfer function and total of 8 band EQ with shelvings and peakings. My problem is, I can not ...
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Confusions regarding expressions of transfer functions of ideal integrator and ideal differentiator?

The ideal integrator has differentiator has transfer function H(s)= -1/RCs while ideal differentiator has transfer function H(s)= -RCs It is often said regarding above integrator that it has a zero at ...
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What does it mean for a transfer function matrix to be real, rational, and stable?

In a book I'm reading, the author writes For example, all real rational stable transfer matrices are analytic in the right-half plane I'm not sure of the definitions of "real", "...
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Amplitude ratio is larger than 0.5 on a RC-filter if RC = 1.7684e-03

I have two signals ...
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How can I learn more about this equation?

I have come across an undocumented slide detailing the system response based on a time vs amplitude input signal. The transfer function $$G(jw)$$ and $$w_{n} = 2\pi f_{n} $$ $$h(t) = \sum_{k=0}^{n} A(...
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Wrong cut-off frequency of IIR low-pass filter

The transfer function $$H_{LPF}=\frac{b_0}{1+a_1z^{-1}}$$ becomes a multiplier-less low-pass filter if $b_0=2^{-M}$ and $a_1=2^{-M}-1$. According to this paper, the cut-off frequency is then given by $...
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How/why is the relative degree of a transfer function related to the causality of the system it represents?

A transfer function can be classified as strictly proper, proper or improper depending on its relative degree, i.e. the difference between the degree of the polynomial in the denominator and the ...
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How does the phase/gain margin method work?

We have the closed loop transfer function: $$T(s)=\frac{L(s)}{1+L(s)}$$ So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
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Proper notation for frequency response between $H(\omega)$ and $H(j\omega)$

Short version: which notation is formally correct between $H(\omega)$ and $H(j\omega)$? Disclaimer: I know that no one cares in the industry. I am asking out of curiosity and care for rigorous ...
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Time invariance in transfer functions

I read this in a book: here ${\cal L}[x(t-a)u(t-a)]$ is the laplace transform of a time shifted function $x(t)$ shifted by $a$ seconds and we know that transfer functions have the formula $H(s)=Y(s)/...
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Calculating and controlling the location and bandwidth of individual notches in an allpass phaser

I'm currently working on a phaser implementation with the intention of adding some parameters that generate unique effects, namely effects that involve the precise placement of the phaser notches (e.g....
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What methods allow learning "changes" in data, and then generating synthetic output?

Suppose I'm interested in a process of the sort: Original data -> Something happened to data -> Result data More particularly, consider that we observe many results of "something happened ...
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Slope of phase function

Would appreciate some help understanding if I take the phase function of some transfer function and derivative it in the linear part of it which is around the resonant frequency what does this slope ...
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Poles and zeros form of a transfer function

I know that a transfer function for a discrete-time LTI system can be written in the form $$ H(z) = \frac{Y(z)}{X(z)} = \frac { \displaystyle\sum_{m=0}^M {b_m z^{-m}}} {1 + \displaystyle\sum_{n=1}^...
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Python Bode plots frequency response of transfer function

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Impulse response of IIR low-pass filter

(Disclaimer. I have started doing some DSP. The last time I worked with this was in the eigthies. And I wasn't much of a specialist then, either.) Is the impulse response different for IIR and FIR ...
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Find transfer function from frequency and phase response [duplicate]

Given a desired frequency and phase response, is it possible to find a transfer function that matches/approximates both the frequency and phase response? Basically once you have a Bode plot, invert it ...
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Calculate the Gain of a fixed-point filter

As the title already says, I would like to know how to calculate the Gain and Phase of a given fixed-point filter at a given frequency. What I've achieved so far: Let's say for example that I have a ...
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Matlab: How to design digital equivalent for a lowpass Bessel filter (Thiran filter)?

In the process of applying a lowpass Bessel filter to my signal, I realized that besself function does not support the design of digital Bessel filters and the bilinear function can be used to convert ...
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Alternative derivation for a Thiran filter

Following this reasoning (link on ee.se) I'm trying to derive the transfer function for a Thiran filter, but I get stuck. I know of the original paper, I just thought I'd go this way. This is what I'm ...
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Normalize Bessel filter

I am applying a low pass filter to my signal and I should make sure the transfer function of my filter is one. How can I normalize my filter? I am learning about filters and I appreciate any help. <...
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L1-norm of a stable, proper but not strictly proper transfer function

in the literature I find the statement, that the L-norms exist for every strictly proper and stable transfer function. I ask myself, if the L1-norm also exists for a transfer function, that has as ...
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How do I calculate offset functions of these circuts? (Matlab results vs analytical results vary)

I am trying to calculate offset functions of these circuts but, the offsets results I got from matlab vary from those I calculated in python(analitically). So I have three circuts, and after each ...
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Scipy tf2zpk doesn't return zeros

I have the following transfer function: $$H(z) =\frac{\alpha z}{(z-(1-\alpha))}$$ I'd like to find zeros and poles of it by scipy.signal.tf2zpk: ...
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Simulated Room Transfer Function

I need help obtaining a simulated transfer function in a simulated room. I have created image sources for first and second order reflections, and am assuming a point source for my source. I have the ...
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What is the difference between sending pulses and modulating waves?

If you look for amplitude, frequency, phase modulation, you typically get some picture saying you have a wave and you modulate the corresponding parameter (amplitude, frequency, phase). On the other ...
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How to design fir filter from transfer function

Transfer function is this equation in frequency domain: $$G(f) = \frac{1}{4\pi d} e^{i2 \pi d f/c}$$ or Hankel function d : constant (distance), c : 340 We may think we know complex number of ...
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