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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Relating transfer functions with step responses

Relate the transfer function to its' corresponding step response. First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...
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Determine impulse response given input and output: which ROC?

Let's suppose I have to find the impulse response of a discrete time LTI system given a specified input and its output through the system. I think I'm going to get the $\mathcal Z$-transform of input-...
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90 views

How to show that this filter is a HP filter

i got a system with transfer function given by: $$H(\omega)=1-e^{-j\omega}$$ I already plot it, and that seems to be a periodic function with $H(0)=0$, $H(\pi)=2$, , is that enough to show that this ...
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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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Transfer function given as z-Domain fraction: gain calculation

I am stuck on a question regarding transfer functions. I have the answer and have attempted the question but am having trouble solving it. Q: Given the transfer function of a digital filter is (5z-5)/...
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Hidden zero in system equation $H(z)$

An FIR linear phase filter has unit sample response $h[n]$ that is real with $h[n]=0$ for $n < 0$ and $n > 7$. If $h[0]=1$ and the system function has a zero at $z=0.4e^{j\pi/3}$ and a zero at $...
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Determining the Filter Coefficients of an FIR Filter

I need to find the filter coefficients of an FIR filter that will block sinusoids of frequency $200\ \rm Hz$ if the sinusoid is sampled at $1.2\ \rm kHz$. I feel like this is a fairly simple problem,...
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Meaning and unit of frequency in Laplace (Fourier) transform

Imagine transfer function obtained by Laplace transform, for example: $G(s) = \dfrac{1}{s+1}$ Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider ...
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Transfer function and difference equations: why does $H(z)$ numerator polynomial not correspond to $Y(z)$?

For a discrete time LTI system, I understand that from a difference equation description of the system in the form $$ \sum\limits_{k=0}^N{a_k y[n-k]}=\sum\limits_{k=0}^M{b_k x[n-k]} $$ I can ...
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Given a causal LTI system with a transfer function, determine if the system is an all-pass filter

We are given a transfer function of a causal LTI system and must determine if it is an all-pass filter: $$ H(z) = \frac{1 + 4z^{-2}}{4 - z^{-2}} $$ To the best of my recollection to determine if a ...
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Forecasting with ARMA models, from a filter point of view

ARMA models are afaik just filters with transfer function $ {MA(z) \over AR(z)} \equiv {FIR(z) \over IIR(z)} $ . However forecasters of stock prices, market trends ... seem to be mainly ...
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Transfer Function from input to node [closed]

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node:
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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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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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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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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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Linear Predictive Coding for general signals

I have a signal that's monotonic and roughly linear and have been looking at using Linear Predictive Coding to encode information and compress my signal. I guess my first general question is if this ...
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Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $ 0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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596 views

Does the frequency response assume the zero input response to be 0?

I'm a bit confused about the frequency response and the state of a system. Is it simply the ratio of the output of the zero state response to the input of the zero state response? Or does it include ...
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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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Stability of transfer function

Now K(s) is obviously the negative feedback loop which is ${H(s) \over 1+H(s)G(s)}$ When I substitute ${H(s) = {1 \over s-2}}$ I get K(s) = ${ 1 \over s-2 +G(s) }$ For the system to be stable I ...
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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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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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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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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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Practical implementation of IIR/biquad filters following non-textbook transfer function of real-wold analog filter

I am trying to program a DSP filter to study prototypes of loudspeaker filters, which will be implemented as passive analog circuits in the final speaker system. This process involves simulation of ...
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358 views

Why I don't get the right PSD

I need to model a noise with a given PSD. To do this, I am starting from a white gaussian noise (WGN) and feed with the WGN a transfer function, which will act like a filter. In fact,it's easy to ...
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833 views

real refractive index from Kramers Kronig relation

I have a measurement of the complex part of the refractive index $k$ (where the refractive index is $m = n + i\,k$) measured at a nonlinear grid of wavelengths or frequencies that span several orders ...
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(How to ask a Homework Question): Define poles by using proportional controller

Given is a process with the transfer function $$G(s) = \frac{s - 1}{s^2 + 3s + 2}$$ I want to create a controller so that the poles of the controlled system are $$p_{1,2} = -4 \pm i$$ Is it ...
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How can I compute the inverse digital of a nonrational transfer function?

My $G(s)=1-e^{-s/\tau}$, $\tau$ is very small, say of order $10^{-4}$. I need to compute a $H(z)$ (a digital filter) such that $H(z)$ has the inverse response of $G(s)$. Is ok even if $G(z)$ has the ...
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Difference between natural response and forced response?

Reference Second post on EdaBoard.com Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time. Natural response ...
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Transfer function between voltage and decibel output for in-ear headphones

What would be a decent formula for approximating the connection between voltage and decibel output for a typical set of unpowered in-ear headphones? I'm generating sine waves from the computer: an ...
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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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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 intuition

What is the meaning of the transfer function of a filter? Please explain intuitively with an example if possible.
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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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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 realize Poles and zeros at infinity??especially through transfer function?

I have a question regarding the poles and zeros at infinity I often read here in DSP SE and also in some textbooks about poles and zeros at infinity This question also answers somehow (but not in ...
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Realization of a filter based on its transfer function

How can we check whether the filter is realizable given its transfer function and What are the parameters the realization depends on? Here is an example: Show that a filter with transfer function $H(...
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Is any time-domain vector stored on a digital machine always intrinsically causal? [closed]

Reading up on causality, I understand the mathematical definition, in so far as that a causal system, is one where the output depends only on the current time, and possibly the past time, but never ...
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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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Is it impossible to determine the inverse Z-transform without any other information?

Suppose I give you this as my transfer function $H(z)$: $$ H(z) = \frac{1} { 1 - az^{-1}}$$ With no other information given, is it even possible to determine the inverse Z-transform? The reason I'...
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Chebyshev poles into transfer function

I have obtained a set of three poles for a third order Chebyshev filter as shown below: $$p_k=\rm -0.2471+0.9660j,\quad -0.2471-0.9660j, \quad -0.4942.$$ However I am unsure of how to actually ...
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transfer function of wiener filter

I am trying to understand the function of a Wiener filter. I get that the Wiener filter minimizes the mean square error between the estimated random process and the desired process. Does this mean ...
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Output of a system given it's transfer function and input (beginner)

I have an exercise that gives me the transfer function of a system $$H(s) = \frac{3s^2+27}{s^4+8s^3 + 16s^2} $$ and an input $$x(t) = \frac13 cos(3t) $$ An ask's what is the output I don't whant ...
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Block diagram transfer function of a line

What is the transfer function of a line, can i ignore it? After simplification i got the diagram: I don't know what to do with the empty feedback
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Fill matlab "ellip" function through transfer function magnitude response

The matlab "ellip" function can be used to design the unquantised coefficient set. From matlab website: $ [b,a]=ellip(n,Rp,Rs,Wp) , $ n: order of filter Wp: normalized passband edge ...
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710 views

Determine the system function H(s) of a system and find out the differential equation

I have created the following system for practice purposes. From this system I want to determine the system function H(s). In the picture I have worked with auxiliary (dummy) variables, which should ...
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bode plot, zero at 0Hz

I'm learning to draw magnitude bode plots from transfer functions: $$ H(s) = \frac{sRC}{sRC+1} $$ So I can see that I have a zero at s = 0, which corresponds to 0 Hz. I know this will add a +20dB/...
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Pole Zero plot given a Transfer function

I've been looking at how to plot zeros/poles based on a transfer function. I found a couple of Tutorials online. In the first youtube tutorial, the author brilliantly explains how to plot the zeros/...

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