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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Butterworth Bandpass Filter Design

Determine the transfer function for the Butterworth bandpass filter? (At the Transfer Function Factoring and Sp Substitution stage) The Parameter $$a_{pass} = - 1dB$$ $$a_{stop} = - 20dB$$ $$f_{pass1} ...
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Does calculating the phase margin when the phase is positive has any meaning?

I want to calculate the phase margin and the gain margin of my transfer function to have an idea about the system's stability. The transfer function is quite complicated since it contains an ...
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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 ...
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Extracting Transfer function from Bode's gain plot

Let the figure of the Bode's Gain plot of a certain transfer function, estimate what could this transfer function be: Here is what I tried to do: since at $\omega = 0 , |G(j \omega)|_{db} = 20\log(K) ...
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3 answers
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Filter odd or even harmonics with notch or inverse notch filter

I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencies or disturbing signals are contained). What I'm looking for is a kind of filter which is able to ...
2 votes
2 answers
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Bandwidth of a complex pole

Text from "Fundamentals of Speech Recognition (Rabiner)". A complex pole of the LPC model spectrum can be expressed as $Z_i = > r_i \cdot e^{j \omega_i} $, where $r_i$ and $\omega_i$ are ...
1 vote
2 answers
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Poles and Zeros in Time Domain

I was looking at this forum: A question about the meaning of pole in time domain, and I still have some doubts about the time domain input that would lead to a pole or zero. Let's say I have this TF $$...
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Signal reconstruction of time domain data via transfer function of a quadripole

Dear signal processing community, I hope my question finds you all well. I have an electrical network, consisting of three complex impedances. These impedances basically form a simple voltage divider. ...
1 vote
1 answer
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Why is there a phasor in the transfer function of an ideal LPF?

I'm learning about Low Pass Filters. My professor said the following is the transfer function of an ideal LPF: $$H_{LPF}(f) = G\Pi\left(\frac{f}{2B_{pass}}\right) e^{-j2\pi ft_0}$$ However, i don't ...
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1 answer
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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 ...
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Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
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How to tune the coefficients of Polynomial Models in MatLab System Identification toolbox

I have such setting: Where $Y_M(S)$ is the transfer function of the model I am trying to approximate with $Y_U(S)$, what I have is the data of the signal corrupted with noise. I am trying to create a ...
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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 ...
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1 answer
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Nyquist plot of $1/[s(s+1)(s+2)(s+3)]$

I am trying to learn how to plot by hand Nyquist plots. I took $$G(s) = \frac{1}{s(s+1)(s+2)(s+3)}$$ I converted it to $G(jw)$ : $$G(jw) = \frac{i w (-11 + w^2)}{(1 + w^2) (4 + w^2) (9 + w^2)} + \frac{...
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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-...
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Causality and Stability of a discrete-time LTI system which has ROC = {z : 4/3 < |z| < 2}

The transfer function H(z) of a discrete-time LTI system has ROC={z ∈ C : 4/3 <|z|< 2}. The system is... a) Causal and stable b) Stable but non-causal c) Unstable but causal d) Neither causal ...
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System identification/ Filter estimation to mimic frequency equalizer of audio with Scipy

At the current problem I'm working on, I have two signals: One "original" signal that contains audio (voice). The second signal is the same audio file but edited with a frequency equalizer, for ...
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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 ...
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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 ...
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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 ...
2 votes
1 answer
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How do I find the difference equation from a transfer function?

Most of the resources I found online go the other way. If I have the transfer function $$ H(z) = 1 - \cos(\theta) \, z^{-1} + z^{-2} $$ How do I get the difference equation from it, so that I can ...
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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 ...
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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^-...
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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 ...
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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 ...
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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 ...
4 votes
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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, ...
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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 ...
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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 ...
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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 $H(s)=\frac{1}{1 + s\tau}$, ...
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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 ...
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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 ...
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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.
2 votes
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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 ...
2 votes
1 answer
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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 ...
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Convert Gaussian Like Histogram into Uniform Analytically

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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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 ...
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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)\...
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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 ...
2 votes
1 answer
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Transfer Function to go from a Step Input to a Linear Ramp between the two step values

I want a very basic simulation of a linear axis that can be given a position demand, and it will move to that position at a constant speed. At this point, I do not care about acceleration, but if I ...
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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 ...
3 votes
2 answers
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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 ...
9 votes
5 answers
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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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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.
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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, ...
29 votes
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Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
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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 ...
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1 answer
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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 ...
1 vote
1 answer
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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 ...
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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?

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