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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Discrepancy in frequency response of biquad filter (in Python)

I have written a simple biquad filter class but when I check its frequency response, I get different results with different methods. If I check it "empirically" (by taking the FFT of its ...
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Error in the computation of PSF?

I am in trouble computing a PSF of an optical system in optical turbulence. Background The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
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How accurate is the dominant poles approximation in higher order control systems?

From what I have learnt from control systems classes, the dominant poles of a system are those that can be used to analyze a higher order system in terms of the formulas of a 2nd order system. I took ...
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Find Transfer Function and Appropriate Coefficients of the Transfer Functions from Pole Zero Plot

I got a Transfer function problem and I am confused in finding a solid solution step. Below is the problem description: 1st and 2nd order discrete-time filters with different pole-zero locations shall ...
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Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab

I have been given an input and output signal. input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1) output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n). or x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
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Measure Frequency-Response of Sensor using a Signalsource and Reference-Sensor

Cheers, I want to measure the frequency response of an acceleration sensor. I have: A signal source (device similar to a loudspeaker that shakes the acceleration sensor), of which I do NOT know the ...
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Recursive equation Of Euler's Backward PID With Derivative Filter

I'm doing the implementation of the PID with derivative filter using the Euler's backward method, but I got stuck in this part since I have z in the denominator of most terms. I didn't realize yet how ...
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How to find response of step function in matlab and plot transfer function?

I have an transfer function: Y(s)/F(s) = (s^2+2s+3) / (s^4+6s^3+13s^2+12s+9) How can I find Y(s) response of step function if f(t)=sin(5t) in MATLAB. And how can I plot the transfer function? Thank ...
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Is there a simple way to express this DTFT in polar form?

Consider the discrete-time system $$ H(z) = a_0 + a_1 z^{-1} + a_2 z^{-2} $$ To compute the DTFT, let $z = e^{j\omega}$ such that $$ H(e^{j\omega}) = e^{-j\omega} \left(a_0 e^{j\omega} + a_1 + a_2e^{-...
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Calculating numerator and denominator polynomials of a transfer function

I was reading this passage in a Doctoral Thesis about Adaptive cancellation. Using MATLAB, if i were to write a simple code, it would look something like this. ...
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How can you see from the transfer function of a system that it has feed forward/feedback elements?

Furthermore, how can you see from the pole/zero plot if the system has feed forward/feedback elements?
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Is it allowable to place a zero to cancel out a complex pole?

Consider the following transfer function : $$ T(s)=\frac{4}{s^{2}+2s+4} $$ I wish to design a lead-lag compensator satisfying a set of requirements. What matters for now is the process done to meet ...
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How to design a Controller that would adjust the steady-state error of a system?

I have a simple model (input-plant-output) with a transfer function : $$ T(s)=\frac{4}{s^{2}+2s+4} $$ The goal of this problem is to design a system such that it has the following specification for a ...
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Difference equation from a transfer function of a low pass filter

I need to get the difference equation from this transfer function: $H(z) = g \frac{1+a_1}{1+a_1z^-1}$ My math skills are too many years old, but I remember I need to get the Y(output) on one side and ...
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Bode plot of transfer function with vs without feedback

I am looking at some old exams. Particularly, one question where there is a Bode plot of a transfer function $G(s)$, and some questions about the Bode plot. So far so good. However, part b) of the ...
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Poles and Zeros of a DiscreteTimeModelFunction with delay in Wolfram Mathematica

help me please, I have a problem with this TransferFunctionModel, When I want to obtain the poles from the Discrete Model Wolfram gives me an error, what am I doing wrong? Could it be the delay of the ...
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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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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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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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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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