Questions tagged [transfer-function]

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
25 views

Implementation of a time-domain solution of a transfer function

I have the the following transfer function (TF): $$ G(s) = \frac{b_2 s^2 + b_1 s + b_0}{a_3 s^3 + a_2 s^2 + a_1 s + a_0} $$ I want to program the numerical solution of the underlying system of ODEs ...
ch101112's user avatar
0 votes
0 answers
34 views

Finding the impulse response between two microphones

I have made recordings of a single source (musical instrument) with multiple microphones and in the interest of limiting the size of the final project, I would like to find a way to get the impulse ...
arno sica's user avatar
0 votes
1 answer
32 views

What is the denominator of the transfer function when PI-regulator is connected?

A system is described by the transfer function $$G_p(s)=\frac{s+2}{(s+1)(s+3)}.$$ A PI-regulator is connected to the system making it a closed loop system. So the transfer function for the PI-...
per persson's user avatar
1 vote
1 answer
55 views

Understanding how to implement high-pass filter with cascaded biquad filters

I'm trying to understand how to implement a high-pass filter using, quote: a cascasded biquad direct form II IIR filter with a cut-off of 8kHz. DSP is a complete new field for me, and the ...
DannyNiu's user avatar
  • 125
0 votes
0 answers
25 views

Desired trajectory generation from transfer function in control theory

I am trying to implement the backstepping techniques for quadrotor described in this article : Backstepping control for a quadrotor helicopter: Madani & Benallegue 2006 Since I am new to the ...
aRedDish's user avatar
0 votes
0 answers
40 views

Function Transfer of Block Diagram Discrete System

I need to find out the transfer function in Z from this diagram, how can I extract this information from this diagram Obs: Doing the math, my H_z gave, H_z = 1 + 0.5z^-1 + 2z^-2 + 2z^-3 + 0.5z^-4 + z^-...
Pedrimbus's user avatar
2 votes
0 answers
50 views

Extracting transfer function from output measurement

Let's say I am generating pure sine oscillations with a laboratory instrument on which vibration frequency and amplitude are tunable (there are uncertainties +/- 1 % with my inputs), and I get my ...
aRedDish's user avatar
0 votes
0 answers
43 views

Bode plot phase shift equation when poles and zeros are not at the origin

Let $$H(s)=\frac{s^{n}}{s^{m}}$$ For $n \ne m$ the phase shift between output and input will be $\frac{\pi}{2}(n-m)$. For situations where the poles and zeros are not at the origin, I could find the ...
Cerise's user avatar
  • 143
2 votes
1 answer
51 views

Generate a continuous time system with desired bode diagram

I have a fluid mechanics model that is heavy to simulate. Its main output is a scalar $q$ related to some energy transfer, and its input is a pressure $P$. This model, noted system 2, is coupled with ...
Laurent90's user avatar
  • 121
0 votes
1 answer
77 views

Theory behind transfer function transforms of the type $H(s) \rightarrow H(f(s))$

My brother wanted me to derive a high-pass version of a Butterworth low-pass filter. I found that the transform $H \left( s \right) \rightarrow H \left( j - j s \right)$ does the thing, but I can't ...
Emanuel Landeholm's user avatar
1 vote
0 answers
34 views

Simulate Op-Amp low-pass transfer function in Python

I am struggling to simulate the frequency response of a simple op-amp low-pass transfer function in Python. The results I get are not accurate. The transfer function is $H(s)=\frac{1}{1 + s\tau}$, ...
MisterFilter's user avatar
12 votes
1 answer
1k views

Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?

In signal processing, we define an analytic signal as a complex-valued signal which has no frequency components for $\omega<0$. It can be shown that the real part and the imaginary part of an ...
Matt L.'s user avatar
  • 89k
4 votes
2 answers
504 views

Why does causality imply that the system function is analytic?

It is cited in multiple places that the fact that a filter is causal (i.e. the impulse response is zero for t < 0) implies that the system function is analytical. I couldn't find any proof of this, ...
David Cian's user avatar
0 votes
0 answers
35 views

control system : time domain analysis

This is the question. According to this, when we solve for transfer function we will get $20/s^2+5s+24$. but this is not the correct format as numerator should be equal to the last term, i.e., 24, in ...
stuti's user avatar
  • 1
7 votes
2 answers
1k views

If the convolution of two signals is a unit impulse, what does this tell us?

I have two discrete-time LTI systems whose transfer functions satisfy $h_1[n] * h_2[n]= \delta[n]$. We also know that system 1 is causal and stable. Does $h_1[n] * h_2[n]= \delta[n]$ tell us anything ...
tonythestark's user avatar
2 votes
1 answer
67 views

Help with Implementation of Transfer Function using Python or MATLAB

Relatively new to the DSP side and wanted some help to implement this approach using Python (with NumPy, SciPy libraries) or via MATLAB. Background of the problem: I'm running a linear dynamic loads ...
ganondorf29's user avatar
0 votes
1 answer
75 views

How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator

How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator. The bottom equation is supposed to be the answer.
Oliver Becquart's user avatar
2 votes
1 answer
260 views

Transfer Function Estimate

This is related to this post: https://engineering.stackexchange.com/questions/56050/obtaining-the-open-loop-gain-estiamte-the-gain-and-phase-frequency-response Using python, I would like to write a ...
user68884's user avatar
2 votes
1 answer
196 views

Average of a set of transfer functions: how should I treat the phase?

I have a set of transfer functions obtained by impacting an instrumentation hammer against a mass, measuring the acceleration on a set of accelerometers; the result is shown below. I want to get a ...
Julio's user avatar
  • 43
1 vote
1 answer
200 views

Deriving Step Response from Input and Output Data for Quadcopter PID Controller

I have logged gyroscope sensor data for roll(x), pitch(y) and yaw(z) axis and i want to plot their step response with Python to be able to tune the pid controller of my quad better. 1. I have found ...
Cenk's user avatar
  • 13
0 votes
1 answer
71 views

Why can't I use the differentiation property of the Fourier transform?

I have some question about the function in frequency domain and I'd like to know its inverse fourier transform (IFT) $$G(jw) = \dfrac{jw\cdot (jw+1)}{(2+jw)(3+jw)}$$ I know that: $$\dfrac{d}{dt}x(t)\...
miguel747's user avatar
1 vote
2 answers
284 views

Calculating transfer function of a linear time varying system?

If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
Volpina's user avatar
  • 295
0 votes
1 answer
34 views

Max input of a system given it's transfer function and an assumed step change (beginner)

I have an exercise that gives me the following transfer function $$ \frac{0.5}{s+0.5} $$ and an assumed step change in the target of 20 I am asked to calculate the maximum input for the assumed step ...
Tom Callan's user avatar
1 vote
0 answers
158 views

How to compute modular transfer function (MTF) from line spread function (LSF) with given discretization

I have an optical system, which is commonly characterized by its point spread function. Somehow by the method, which resemble slanted edge method, I have end up with discretized line spread function ...
VojtaK's user avatar
  • 111
3 votes
2 answers
923 views

Why does scipy introduce its own convention for H(z) coefficients?

Conventionally, the definition of the system function for a IIR digital system is: $$H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\cdots}{1-a_{1}z^{-1}-a_{2}z^{-2}-\cdots}$$ where coefficients are the ...
mins's user avatar
  • 443
1 vote
2 answers
53 views

Feedback stabilizes unstable systems?

Can feedback stabilize a unstable system?I guess so since we may get rid of any poles in the positive complex plane by feedback but I am not sure.
Volpina's user avatar
  • 295
1 vote
2 answers
232 views

Factorization of transfer function using its roots

I'm missing a step to understand the factorization of the FIR filter transfer function: $$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$ From DSP First: The $z$-transform of a finite-length signal, ...
mins's user avatar
  • 443
0 votes
0 answers
46 views

Linear Linearly Time Varying Systems properties?

Yesterday I asked a question about LTV Systems and how the impulse response h(t,t0) is found. I was thinking about it and realized there is a subsclass of LTV systems which I call Linear Linearly Time ...
Volpina's user avatar
  • 295
0 votes
0 answers
35 views

Remove over and undershoot from an output signal by manipulating the input

I have an experiment for which I want to generate a high-power short-voltage pulse with no over and undershoot. For this, I am using an amplifier. I set a pulse with the desired width as input (I use ...
JJJJeb's user avatar
  • 1
1 vote
1 answer
113 views

How to determine if a system is minimum phase or not?

I'm studying for an exam and this is an old exam question that I don't understand: Is the following system non-minimum phase? $$G(s) = \frac{e^{-2s}}{s+2}$$ I can see that the real part of the pole is ...
student's user avatar
  • 13
2 votes
1 answer
2k views

Finding the inverse $z$-transform

I have the transfer function: $$H(z) = \frac{z^2 + 0.75z + 0.125}{z^2+0.5625}, |z| > 0.75 = \frac{(z-0.5) (z-0.25)}{(z - 0.75j) (z + 0.75 j)}$$ I attempted partial fraction expansion in order to ...
MeljahU's user avatar
  • 33
1 vote
1 answer
60 views

Is it possible to use AMIGO tuning rules with relay control?

I am trying to control a plant with PID using tuning rules such as the Ziegler-Nichols rules. However, it is not always easy just to send a step to your plant source of the image. Another method to ...
NokiYola's user avatar
  • 487
0 votes
2 answers
63 views

Can you plot an irrational transfer function on matlab?

For example if I have the following transfer function: $$H(s) = \frac{1}{\cosh(\sqrt{s/10})}$$ Can I do the bode plot it in matlab or do I need to rationalize it beforehand?
FISqrt's user avatar
  • 25
1 vote
1 answer
42 views

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 ...
Algo's user avatar
  • 13
2 votes
0 answers
59 views

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 ...
NokiYola's user avatar
  • 487
2 votes
2 answers
136 views

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? ...
ricardo's user avatar
  • 23
0 votes
2 answers
300 views

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 ...
user66077's user avatar
1 vote
1 answer
72 views

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 ...
Heath's user avatar
  • 131
0 votes
2 answers
119 views

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}{...
MaxFrost's user avatar
  • 359
2 votes
2 answers
122 views

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{...
Heath's user avatar
  • 131
0 votes
1 answer
110 views

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. ...
Eric Saginashvili's user avatar
0 votes
1 answer
59 views

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 ...
jjk's user avatar
  • 3
0 votes
1 answer
104 views

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 ...
jjk's user avatar
  • 3
0 votes
1 answer
185 views

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}...
Essi Mimizama's user avatar
1 vote
2 answers
141 views

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 ...
solo's user avatar
  • 13
0 votes
1 answer
52 views

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 ...
euraad's user avatar
  • 403
0 votes
0 answers
45 views

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,...
gg h's user avatar
  • 101
2 votes
2 answers
279 views

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 ...
gg h's user avatar
  • 101
0 votes
2 answers
182 views

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 ...
euraad's user avatar
  • 403
0 votes
0 answers
30 views

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 ...
Bigggie's user avatar
  • 11

1
2 3 4 5
11