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 about analog filters

I'm mixed about the concepts of analog filters, so I hope someone can explain me, or point to information, to unentangle the ideas. I know there are filters (analog) as Chevyshev, Butterworth, ...
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How can we obtain the input signal in Python given the output signal and transfer function?

I have the following transfer function $$ H(s) = \frac{R}{sRC + 1} $$ where $V$ is the output and $I$ is the input. We can write $$ V(s) = I(s) H(s) $$ or $$ V( j \omega ) = I(j \omega) H(j \omega) $$...
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Help with setting up transfer function correct format

I have a transfer function as: H(s) = R / (sRC + 1) V is the output and I is the input so we can write: V(s) = I(s)*H(s) Now the thing is that, I want to obtain I(t) for the given V(t). So I write: I(...
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How can I use an irrational transfer function to convolve a signal?

I have the irrational transfer function $$H(s)=\mathrm{e}^{-a\sqrt{s}}$$ With the inverse Laplace transform $$ h(t) = \frac{a\,\mathrm{e^{-a^2/(4t)}}}{2\sqrt{\pi}~t^{3/2}} $$ For $a > 0$ How can I ...
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How to determine the dynamic response of a spring-mass system? [migrated]

The Problem I have the following system for which I would like to determine its dynamic response, taken from these lecture notes pg.20: where the forcing functions are $u_1 = 1-U(t - t_0)$, $u_2=0$, ...
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Mismatch between the frequency response of a transfer function and bode plot

I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)): <...
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Derivation of Strehl ratio

I am in trouble proving the following fact: The Strehl ratio is the ratio of the volume of the aberrated OTF (optical transfer function) and the ideal OTF, i.e. \begin{align} \mathcal{S}=\frac{\int\...
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State-space model and/or TF for a $K$-th order linear system given the signal sequence

The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential: \begin{equation} x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
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Digital IIR LPF Difference Equation from Transfer Function

I want a digital IIR filter with f0=225kHz and fs=53.125GHz. I can come up with the transfer function and plot it using Matlab. ...
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Realize the given system in cascade form of 2nd order section in signal flow graph representation(with complex exponents)?

I know how to solve cascade form for normal case, but I don't know how to solve cascade form if I get complex exponentials. How do I solve this? Can you provide me 1 solved example or some hint or ...
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Z domain Transfer function to magnitude

How would one go about calculating the Magnitude of... $\mathcal{Z}$-transform = $$\frac{1}{1-z^{-2}}$$ I understand that z can be replaced with $${exp}^{j\omega}$$ and I am aware of the identities $${...
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Determine transfer function based on a diagram with ai coefficients given

From a diagram with input $x(n)$ a summer and three feedback delay taps I get the difference equation... $$y(n) = x(n)+a_1y(n-1)+a_2y(n-2)+a_3y(n-3)$$ Then I am given values for ai coefficients. Case1:...
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How to estimate multidimensional linear response function from measured input and output signals?

Problem definition: I measure N sources of noise $x_i$ and one output signal $y$ which contains real signal $y_0$ plus noise from all these sources $x_i$ transformed by linear response functions $h_i$ ...
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What does it mean for a transfer function to have multiple sets of zeros in the numerator?

I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
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Phase Response of $N$-th order Digital All-Pass Filter

I am having trouble reconciling my derivation of the phase response of an N-th order all-pass filter with those I am finding in the literature, and I figured someone here could help me. Real Version: ...
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Amplitude-and phasefunctions for a system

I am studying a course in signalanalysis and have run into som trouble with a exercise. I am to dimension the circuit below in such a way that the DC-amplification is 1 and that the frequencies $\...
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Meaning of term in notch filter coefficient

I have a discrete implementation of a notch/bandstop filter that allows me to specify the stop band frequency, the width of the notch and the attenuation of the stop band frequency. I've been tasked ...
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how to calculate $H_{lp} = z(1- H_{hp}) $ , given coefficients for $H_{hp}$?

Given a high pass transfer fn of the form $H_{hp}=a_{1}*z^0 +a_{2}*z^{-1} + ... a_{n}*z^{-n}$ Is it possible to calculate a causal low pass filter using $H_{lp} = z*(1-H_{hp})$ ? attempting $H_{...
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Transfer functions for Scipy and Matlab's Butterworth filter don't seem to match theory

The squared transfer function for a Butterworth filter of order $n$ should be $$ |H(f)|^2 = \frac{1}{1+\left(\frac{f}{f_c}\right)^{2n}} $$ where $f_c$ is the cut-off frequency. (Here's one of many ...
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Who first coined "Direct Form I" and "Direct Form II"?

I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
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Filter a signal with a complex dB SPL filter

I've been tasked with filtering a sound with a filter that looks something like this. I don't have any real DSP training, so I'm not sure if my attempt at tackling this is correct. I can filter ...
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57 views

Definition of frequency response

I studied various signal processing materials for a long time, and I have a question. Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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Zeros and poles from transfer function

I have a transfer function $$ H(z) = \frac{Y(z)}{X(z)} = 1 - 0.5z^{-1} \text{.}$$ I'm interested in zeros and poles. I know I need to adjust the function to $$ H(z) = \frac{\prod_i(z-n_i)}{\prod_i(z-...
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Difference equation to FIR filter coefficients

I have a difference equation $$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$ According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ...
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Finding transfer function from bode plot

Given a bode diagram From the figure, I see that when $\omega = 100 \text{ rad/s}$ the magnitude response starting to go down and when $\omega = 1000 \text{ rad/s}$ the slope become higher. Then $$H(...
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A system having impulse response $ h(t)=u(t) $ stable or not?

I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess) I proceeded as$$ \int_{-\...
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Trying to plot frequency response of a filter Transfer Function in MATLAB, it looks wrong

I have the transfer function below which is for a IIR filter and trying to plot its frequency response for omega<pi. r=0.99 and theta=pi/3: Here is my attempt at implementing it in MATLAB: ...
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I tried two approaches and gained the different conclusions of judging the stability of the transfer function of the system

We want to judge whether the system is stable or not. Given the below transfer function. $$ H\left( z \right) =\frac{\left( 1+2 z^{-1} \right) }{\left( 2+z^{-1} \right) } $$ $$ H\left( z \right) ...
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Seemingly no division operation is done of the diagram of the transfer function

Given the below system. $$ y\left[n \right] =2 x\left[n \right] -x\left[n -1\right] +0.5 y\left[n -2 \right] $$ We'll find out the transfer function of it. So, easiely using z-transform, $$ Y(z) ...
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Filter odd or even harmonics with notch or inverse notch filter

Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ...
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104 views

Real Data Complex Transfer Function using H0, H1, H2 Estimators

BACKGROUND: This question is attempting to consolidate material discussed in two previous topics. These are: Understanding the H1 and H2 estimators @Pontus S Frequency-domain deconvolution: "...
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Coupled system instability

Suppose there are two linear devices (containing some multi-physics but the details don't matter here), and these devices are given to us as two black boxes that can be studied experimentally. Black ...
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Stabilizing an unstable system and removing oscillations from step response

I have a system with the transfer function given in this MATLAB code ...
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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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127 views

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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