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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Confusion regarding terminology?

While studying the topic of filter design,i came across following terms: 1)Factored form 2)SOS(second order sections)form 3)Rational form 4)Transfer function form What is the difference between all ...
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Developing Lead Compensator to Decrease Settle Time

This is a follow up to this question. I've approximated the transfer function for a system to be H = zpk([0.012 -1.05 18],[-0.22 -0.22 -45 -1000],10000);. My goal ...
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Get the transfer function when using the “designfilt” command in MATLAB

To put things into perspective, I initially had these four graphs in MATLAB, whose data were sampled with a rate of 10 samples/sec :- I wanted to remove some of the spikes on the blue graphs, so I ...
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Tuning a PID Controller

I have the following transfer function $$10000 \cdot\frac{(s-0.012)(s+1.05)(s-18)}{(s+0.22)^2(s+45)(s+1000)}$$ For which I am trying to tune a PID controller for. I'm using the pidTuner in MATLAB to ...
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Adding noise to frequency response

I have the dynamics of a 2nd order system, mass-spring-damper for example, in the transfer-function format. For the analysis that I am doing, I am calculating the frequency response of the system by ...
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Creating Bode Plot from Experimental Data

I have a blackbox system in which I can input a function and obtain the output signal (in MATLAB). I'm attempting to reconstruct a Bode diagram and have had success with the Magnitude plot, however, I'...
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how to take a second order transfer function without any zeros and represent it using two first order transfer functions

does anybody know how to take a second order transfer function with no zeros (no s terms in the numerator): $$ g(s) = K\frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2} $$ and represent it using ...
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How to find H(z) from just zeros and poles

I have a system with a DC gain of 8, poles at z = +- j/2 and zeroes at e^+-j5, I need to find the H(z). I have tried this but not sure if it is right. $$ H(z) = G_o * z^{-1} \frac{(z-z_0)(z-z_1)}{(z-...
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Transfer function estimation from frequency response

Let's assume that we know that we are dealing with a SISO second order system for which we have the frequency response (magnitude and phase for a known frequency range ω). What methods would people ...
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Amplitude spectrum (transfer function) of signal?

I have one question related to finding amplitude spectrum (transfer function) of signal knowing that output signal is time derivative of input signal. I have the answer graph but I don't understand ...
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How do I get a faster system response?

I have this model in simulink (the graph is my output): The step input has amplitude 0.5 m/s, and it steps up after 0.1 seconds. The gain $K_p=5$. The saturation block is to keep the voltage between -...
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Digtial FIR Impulse response & transfer function

I am currently working the figure through below. as it is an FIR Filter i have worked out using convolution that the output is 4,2,4,6,0,0. i am trying to obtain the 'z' domain transfer function of ...
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Transfer function with blackbox modelling is too slow compared to real expectation

I collected this data from a robot that drives with its wheels up. The blue curve is the voltage and that is my input. The orange curve is the wheel velocity and that is my output. I want to create a ...
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SPL dB to voltage conversion misunderstanding

base on these links: https://electronics.stackexchange.com/questions/96205/how-to-convert-volts-to-db-spl https://electronics.stackexchange.com/questions/302833/convert-digital-and-analog-values-to-...
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how to find frequency response of microphone

hello I want to find the frequency response of a microphone. I give the input signal to my speaker and it produces a specific SPL with specific frequency. on the other side, I read the microphone ...
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Additive disturbance in block diagram representation

Drawing the open loop block diagram between valve and pump is straightforward (please see illustration). But why should $v$ be an additional disturbance in this system (please see solution)? $v$ is ...
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From transfer function to differential equation

I have the below detailed solution (boxed in blue) that I don't understand completely: I can reconstitute the differential equation from: $$ (1+Ts) X(s) = K_v U(s) $$ $$ x(t) + T\dot x(t) = K_v u(t) $...
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Is this system causal or not?

My efforts of solving this question are below. I came to a conclusion that this system is causal, since: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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Gradient of transfer function (z-transform) with respect to coefficients/parameters?

my problem is perhaps very simple but I just can not find the answer, even though this is used (though not explained) in several books: What is $\frac{\partial G (z, \theta)}{\partial \theta}$ when $G$...
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Why the transfer function is equal to the output in this case

In this description of transfer functions on the z-plane (image linked), I'm confused by equation 1.49, which says that $H(f)=v_{out}(f)$ when $v_{in}(f)= 1 * e^{j 2 \pi (f/f_s)}$. (For another matter ...
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Part 2: Root Locus, Transfer Functions and Unit Step Response?

I'm continuing my question referenced here: Part 1 Question / Problem Description Say I have a new Root Locus shown below Consider the generic feedback loop, and the transfer function $G(s)$ shown by ...
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Root Locus, Transfer Functions and Unit Step Response?

Consider the generic feedback loop, and the transfer function $G(s)$ shown by the following root locus plot. Where $\mathbf{x}$ denotes the open-loop poles and $\square$ denotes the closed loop poles....
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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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181 views

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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