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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How to handle cross products in feedback loop?

I'm trying to simplify the following block diagram from to the following block diagram However, h(t), H(s) in time domain, has a cross product in it (gyroscopic torque). How can I represent the ...
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Ending points of the root locus

Let $$D(s) + KN(s) = 0 \tag{1}$$where $D(s)$ and $N(s)$ are polynomials of $s \in \mathbb{C}$ such that $\text{Deg}(D) = n, \ \text{Deg}(N) = m$ and $n\ge m$. The root locus method tells us how the ...
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Can we choose a sampling frequency to remove unwanted noise at a specific frequency?

I am studying for my exam in signal processing. In one of the old exam papers I am told to find a sampling frequency, which will remove 80 Hz noise. The filter the exam question is based around has an ...
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Interpreting Nyquist Plot for Phase and Gain Margins

I have an open-loop system transfer function given by $G(s) = \frac{K(ABs^2+As+1)(Cs+1)}{s^2A(s(C+D)+1)}$ so I'd expect two poles at the origin and one at $s=\frac{-1}{C+D}$. After using Matlab to ...
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Converting Audacity Filter Curve EQ into transfer function and applying it to a signal via python

First of I am very new to Signal Processing and to python in general. I am trying to write a script where I would feed a voice recording into it, internally apply an eq and have the modified signal ...
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Creating a prediction from data in MATLAB

How can I create a closed loop system that can guess the input value that is going to return 0 from unknown transfer function. The output of this transfer function is either a positive constant, a ...
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What is the relation between input and output PSDs given system transfer function $H(s)$

If I have the system transfer function $H(s)$ in the complex frequency domain, how would I relate the input/output power spectral densities? I have come across the relation $P_{out}(f) = |H(f)|^2P_{in}...
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Is this an error in Oppenheim and Schafer's Discrete-Time Signal Processing (3rd edt)?

Q: According to Fig 71, y[n]=something+e[n] and hence the transfer function from e[n] to y[n] denoted as He(z) should be 1. Am I wrong?
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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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Poles and zeros from step reponse?

Is there a numerically robust method for calculating the poles and zeros of a discrete-time causal LTI SISO system given its response to a unit-step input? In the specific example I'm working on all ...
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Finding the Transfer Function of a Multiplicative Distortion in MATLAB

I have the frequency response of two signals shown above. One is uncontaminated, and the other is the same signal contaminated by a multiplicative distortion with two poles and two zeros. I need to ...
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Uncountable Set of Poles?

It is easy to define an (ideal) LTI system that would have an infinite number of poles - for instance, if the transfer function is $$ H(z)=\frac{1}{\cos(z)-1} $$ However, this would only define a ...
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Why can't this system be adequately represented using a z-domain transfer function?

According to this question and answer the following system cannot be adequately captured by a z-transform transfer function. $$y[n] = y[n-1] + F_{\psi}(y[n-1)) + F_{\phi}(x[n-1])$$ where $F_{\alpha}(z)...
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RoC and Stability of a Rectangular Signal

If we have a system with an impulse defined as: $$h(t)=u(t)-u(t-2)$$ Then the Laplace Transform of h(t) would be the transfer function: $$H(s)=\frac{1}{s}-\frac{e^{-2s}}{s}, \quad Re(s)>0$$ We also ...
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Transfer function model to frequency response

I have a problem, I wanted to filter the signal with a Butterworth filter built on the basis of a prototype. I have zeros and poles and an $H (s)$ answer, and I do not have the frequency response. How ...
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Matlab filter implementation

I have a filter response in the $z$-domain. $$H_0(z) = 2 + 6z^{−1} + z^{−2} + 5z^{−3} + z^{−5}$$ How do I implement this filter on MATLAB? I can do this if I have the coefficients but I do not know ...
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How to model transfer functions using Python (without using higher level packages) and plot the magnitude and phase response?

I'm trying to model a transfer function in Python and thought I could do it by simply plotting the transfer function at many frequencies. This seemed to work for a 2nd order LPF. See the below figure. ...
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Calculation of an impulse response of h[n]

I am currently looking at the z-transform and am using a great youtube reference to help me, however I am struggling on some basic step. How do I get the impulse response array of h[n] = [ ... ] shown ...
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How to I get transfer function?

there is a ODE $dx/dt-ax(t)=u(t)$ Firstly, I have to find the transfer function $u$ to $x$ using exponential input. So I put $u(t)=e^{st}$ to the ODE, and I got $x(t)=x(0)e^{at}+1/(s-a)e^{st}$. In ...
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How to approximate the transfer function of compensator using root locus?

I have the root locus of a system with and without compensator. The system is consist of a PD-controller and the process, the output is fed back to the controller via $G_s(s) = 1$. The upper graph is ...
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Digital filter coefficients from low-pass to high-pass

Given I have coefficients a0, a1, a2, b1, and b2, defining the difference equation for a digital filter as: ...
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Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results

I'm confused due to the fact that the Nyquist stability criterion and looking at the transfer function doesn't give the same results whether a feedback system is stable or not. When I have the system ...
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How to estimate the modulation transfer function of images?

I'd like some way to estimate the modulation transfer function in images. This is the observed drop in amplitude vs increase in frequency of spatial details - nice illustration here: (from https://...
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How can I find the transfer function of the following block diagram?

I've the following image and I want to find the transfer function from input $x(t)$ to output $y(t)$. I know that I have to apply Laplace Transform, so the integrator becomes $\dfrac{1}{s}$, but I don'...
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How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?

How to compute transfer function $$G(s) = \exp \left( - \sqrt{s} \right)$$ in Matlab / Simulink? I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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Calculating IIR Filter gain at given frequency

Let's consider an IIR filter with transfer function: $H(z)$. Given the sampling frequency $F_s$ how can I calculate gain at say $F$ ? When I was dealing with analog systems when I wanted to calculate ...
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Can time-invariance be determined from a given a transfer function?

I've the following function. $$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$ Calculating it's inverse using $\mathcal Z$-Transform, I get the following function: $$g[n] = 2\delta[n] + 8u[n] ...
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Deriving of magnitude, phase response and impulse response of transfer function

I have a transfer function as $$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$ I want to derive magnitude and phase response of this equation. can someone help me from here I ...
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How to plot poles, zeros and impulse response of a transfer function

I want to plot poles and zeros as well as impulse response of a transfer function that is given below: $$H(z) = -0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z -\frac{0.0625}{z^4}$$ For poles and zeros, I ...
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Determine causality and stability from given filter structure

I have the diagram above. I found the transfer function below from it; The question asks me to find out if the system is causal and stable, but didn't it have to indicate whether it was left-sided or ...
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Why is my MATLAB's bode plot wildly off?

I will give out all the details in case it is relevant. I have a MIMO state space system. I find its bode plot using MATLAB and separately using Mathematica. The plot from MATLAB is wildly off ...
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calculate fft convolution for an LTI system given its input (in time domain) and its poles and zeros

I have considered taking the fft (MatLab) of the input (x) and create frequency bins for the first half (problems with an odd number of samples, tried solution zero paddings) and evaluate the transfer ...
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Is there a simpler way to calculate the amplitude response of the following filter

I would like to calculate the amplitude response $|H(z)|$, $z=e^{j\omega}$, of the following filter: $$H(z)=\frac{\frac{b}{2}+z^{-2}}{2+bz^{-2}}$$ and I would like to avoid using Euler's formula and ...
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Apply Transfer Function in Continuous Domain in Matlab

I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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Is it possible to prove that dither VS PWM can result the same output?

Assume that we have a SISO transfer function model $G(s)$ and we want to look how the output looks like when we have a input signal $u(t)$ that looks like this: $$u_1(t) = \left\{\begin{matrix} 50 + ...
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What is the DFT of a binomial filter?

I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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Transfer function coefficients and impulse response - FIR filter

I am currently working on a FIR filter (varying in time). I have the real coefficients of the filter, but I would like to know if they correspond to the coefficients from the impulse response (as $b[k]...
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Given a system with Transfer Function and its desired output. Is it possible to find the required Input?

I'm currently working on an DC servomotor. I managed to find it transfer function using System Identification theory and Matlab. The transfer function is given as $$H(Z) = \frac{1 - 0.4952z^{-1} + 0....
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How to determine whether a filter is high/low or band pass from the Z transform?

How to solve questions of these kind? I have tried by replacing $z=re^{jw}$ and taking the limits from $0$ to $\infty$. But I am not sure what $e^{j\infty}$ is.
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How to invert FFT these magnitude equations to get FIR filters?

I need filter designs that will reproduce or approximate each of the following: 1) ${\rm magnitude} = e^{-cf^{2}}$ 2) ${\rm magnitude} = e^{-\frac{a+b\sqrt{gf}}{df}}$ Where: $a$, $b$, $c$, $d$ and $...
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How to convert my transfer function to the frequency domain

I have the following transfer function in the time domain: $h\left(t\right) = B x\left(t\right) + a x^2\left(t\right) + b x^3\left(t\right)$. My simulation is in the frequency domain, so I would ...
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Why does this transfer function estimation not work? System identification

Goal: I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses. Method: I begun first with creating the ...
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How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
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How can I find the transform function, amplitude and frequency response of a digital filter in python?

I have applied a laplace filter mask to an image and now I want to find the amplitude and freqency response of a laplacian filter: [[1,1,1], [1,-8,1], [1,1,1] ]. I know I need to first find the ...
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Characterizing an unknown LTI system

What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
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When to choose ZoH over Tusin method to transform continuous to discrete

I have a continuous transfer function here: a 2nd Order Butter Worth filter $$\frac{1}{6.416\cdot10^{-11}s^2+1.33\cdot10^{-5}s+1}$$ How would one choose which discrete method to use to transform ...
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Using ROC to find stability of system in specific example

I've started learning about finding the ROC from the transfer function, but I'm confused about an example. $$H(Z) = \frac{2Z + 1}{Z^2 + Z - \frac{5}{16}}$$ I understand the poles lie at $z = \frac{-...
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Finding poles of an abstract transfer function

When finding the poles of something like the following transfer function, would I be able to write $z=\sqrt[L]{\mu}$ since square roots aren't technically defined on the complex plane? $$Y(z) = \frac{...
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Recovering a Differential Equation From the Transfer Function of a Cascaded System

With respect to the below discussion, consider that we are talking about LTIC systems characterized by constant coefficient ODEs. Consider a cascaded system whose transfer function H(s) is given by ...
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How do I find the transfer function of a speaker by analysing the audio produced by it?

I have the original audio signal(MATLAB GENERATED) and the recorded audio signal (anechoic conditions). The setup consists of a DAC with a power amp plugged into the speaker. The audio is recorded via ...

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