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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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Poles of the transfer function in Z Transform

Given that: $H(z)$ has 4 poles maximum. $H(z)$ has a pole at $z_1=a+bi$ Given that the impulse response $h[n]$ is: Symmetric: $h[n] = h[-n]$ Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$ How we can ...
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FIR Impulse response & transfer function

I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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Sound equalization : assumptions around the use of the transfer functions. Are they correct?

I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check. 1/ I'm ...
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How do I plot the square of the amplitude response?

I have calculated the transfer function of an FIR filter $$ y[n] = x[n] + α · x[n − R] $$ This is what I have $$ H(z) = 1 + αz^{-R} $$ Now I should plot the square of the amplitude response. So I ...
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Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$

Consider the following causal IIR transfer function: $$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$ Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?

For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
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275 views

Impulse response of a causal system from transfer function in z-domain

The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$ I need to find the impulse response h[n] of a causal system with x[n] as unit impulse. I have tried to find the impulse response by the following ...
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Why use transfer functions than differential equations?

I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths. Why we use ...
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137 views

Audio transfer function modelling with pink noise + signal

I'm trying to model a transfer function for a noisy audio system, specifically to measure delayed system response. Before I can confidently apply control, I need to verify that I can exert control ...
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Natural frequencies of a transfer function

I have been told in the university that the natural frequencies (also called $\textit{eigenfrequencies}$) are the poles of the transfer function, however, Matlab compute them as the modulus of the ...
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Poles and zeros in time domain of analogs filters

I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
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536 views

Distinguishing FIR and IIR from difference equation

Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$ I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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45 views

Evauating response to $x(n) = \sin{2\pi\frac{1}{4}n}$ given the system function

Let the input signal $x(n) = \sin{2\pi\frac{1}{4}n}$ go in to the system described by: $$y(n) - y(n-1)+\frac{3}{16}y(n-2) =x(n).$$ What is the output signal? I've calculated the system function $H(...
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Phase function of filter

I have a filter with the transfer function $$H(z) = 1 - 2z^{-2} + z^{-4}.$$ The task is to find the phase function $\theta (\omega).$ My attempt is to start by expressing the frequency response \...
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How do I convert a two-pole two-zero transfer function from the s-domain to the z-domain?

I'm trying to convert the following IIR transfer function from the s-domain to the z-domain: $$ H(s) = \displaystyle\frac{\frac{s^2}{\omega_z^2} + 2\zeta_z\frac s\omega_z + 1}{\frac{s^2}{\omega_p^2} + ...
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Confused about applying Routh Hurwitz to $s^2 +s + k$

I have a closed loop transfer function $$G_{\rm cl}(s) = \frac{k}{s^{2} + s + k}$$ I am trying to find the critical gain of the system. From using the Routh Hurwitz criterion I get a $k = 0$.
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Does “improper” imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
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Output eqaution of a repeater?

Assume we have a signal repeater, a simple repeater that amplifies the signal then transmits it as is. Does the output power of the repeater is dependent on the received signal at the repeater ? for ...
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What is the transfer function of this system y(n) =2y(n-1)?

What is the transfer function of this system y(n) =2y(n-1)? Here there is no input dependence. If you give one output sample, all the future output samples are determined by multiplying with 2.
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How to differentiate a time domain signal in the complex transfer function?

I have an input-output data set where the input is current and the output velocity. I am interested in the transfer function from current to acceleration though. So suppose: $H(s) = \frac{I(s)}{V(s)}$ ...
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Where does this star came from? [EDIT - Detailed Question]

First of all, it's a rare topic in google, so I can't find intuitive explanation about step-invariant, so I don't understand actually what it is, except to solve zero order hold transfer function. In ...
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Marginal Stability based on Poles

We know that a discrete-time system with a (Z-transform) transfer function that has a pole of magnitude 1 (i.e. $|z|=1$ is a pole of the transfer function) is marginally stable if the pole at $z=1$ is ...
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Can someone explain waveshaping to me?

Can someone explain waveshaping to me? I only know it shapes waveshapes by passing through some functions, but I don't yet understand e.g. what the plots (such as the following in Melda Production ...
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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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What does G(1) = 1 say about a system?

This is a line from a paper I've been reading: The static gain of the closed loop system must be $1$ ($G(1) = 1$) [...] First of all: I know what gain is, but isn't gain dependent upon frequency? ...
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84 views

Approximate the change in perceived gain from applying transfer function to audio signal

I have an audio signal that I am applying an analogue transfer function $H(s)$ to. I would like to approximate the change in gain ($\Delta \text{ Gain}$) as perceived by the listener for an arbitrary ...
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Real-time implementation of cascaded all-pass filters from given transfer function

I am working on real-time implementation of spring reverb based on scientific paper called Parametric Spring Reverberation Effect by Välimäki, Vesa; Parker, Julian; Abel, Jonathan S. One block of ...
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269 views

Transfer function of a frequency shifting system

There is a system which shifts frequencies of input by -Fc such that: Y(S) = X(S).H(S) But X(S) has value zero from 0 to Fc. I am confused on how the product of X(S) and H(S) becomes a positive ...
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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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Compensating effects of a system with a known transfer function

Suppose we have a system which we want to know the exact transient times. In ideal case, we can extract the transient times, but in practice it will be affected by another system with a known transfer ...
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Determine filter given transfer function [closed]

I am given $$H(z) = 1 + \frac{\alpha}{1-\alpha z^{-1}}$$ where alpha is between $0$ and $1$. This is apparently is a low-pass filter with cutoff frequency $f_c$. How can I see that? And how can I ...
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Calculating Transfer Functions From Harmonic Distortion Percentage

Hi I am working on emulating a piece of analog audio equipment and would like to be able to create a transfer function based on the measured percentages of harmonic distortion. I know that harmonic ...
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When inverting a transfer function, solving for the input using the output does the causality status change

suppose $y(n)=ax(n-1)+bx(n-2)+\dots$ ($y$ is the output and $x$ the input). What happens if I want to solve $x(n)$ from $y(n)$? Z transform: $$Y(z)=G(z)X(z)\tag{1}$$ then $$X(z)=\frac{1}{G(z)...
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What is the difference equation or system function of this system?

I am having trouble figuring out what the difference equation or the system function for this system is? Here ''R'' represents the unit delay. The fact that the delay is not part of the feedback loop ...
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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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376 views

Consider an ideal low pass filter $H(\omega)$, and the input to this filter is the periodic square wave $x(t)$. Find the output $y(t)$

The solution to the problem is $$y(t) = 5 + \frac{20}{\pi} \sin(\pi t) + \frac{20}{3\pi} \sin(3 \pi t) $$ and to get that the solution says to find the Fourier series expansion of $x(t)$ and I am ...
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What are poles and zeroes (with respect to the inputs and outputs of a system)?

I get it, about poles and zeroes, when we talk in terms of the transfer function. But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the ...
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Determine proper coefficients for the transfer function

The problem says that we have the information (actually a .mat file that contains the data) of 1 pixel from an IR camera from an object with 26° of temperature. Because of the noise, the output is ...
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How can I translate what I have learnt in Transfer Functions to differential equations?

I have gone through the entirety of K. Ogata's Modern Control Engineering, and I do not understand how can I translate all the transfer function models into differential equations? For example, how ...
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343 views

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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Solve for transfer function coefficients embedded in a non-linear system

Given a complex input signal $x$ and real input signal $v$, a 4th order (for simplicity) transfer function $H(z)$ is first applied to $v$ to obtain $w$, which in the time domain is represented by the ...
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How to check if the poles of transfer function are stable?

$$H(z)=\frac{az}{[z-(b+ja)][z-(b-ja)]}$$ The two poles are looking like this: $z_{\inf, 1}=b+ja, z_{\inf, 2}=b-ja$ I know they must be inside the unit circle: $|z_{\inf,i}|<1$ So I replace the ...
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236 views

Convolution with an impulse response does not give the same result as the frequency response

Context I am trying to design a linear-phase FIR filter with the following frequency and phase responses: Designing the filter Given its characteristics (peak filter at 1kHz with 9dB gain and Q=7), ...
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79 views

Correct transfer function with 1st order IIR filter

What diffreneces it makes in magnitude and/or phase response when using $$H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}}$$ by adding $b_2=0$, $a_2=0$ instead of $$H(z) = \...
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82 views

Generic response of an IIR filter from its transfer function

How can I derive the general response of an IIR filter from its transfer function? I know that: $$H(z)=\frac{1}{1+\sum\limits_{m=1}^N{a_m z^{-m}}}$$ Thus: $$Y(z)=X(z)H(z)=\frac{X(z)}{1+\sum\limits_{...
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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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176 views

1st order filter output

Two 1st order filters : ...
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687 views

What is $H_2$ and $H_{\infty}$ control? [closed]

I can create a Linear Quadratic Gaussian Integral(LQGI) controller very easy by using GNU Octave. LQGI is in the area of Optimal Control Theory. But there is something called Robust Control Theory. ...
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Could someone please explain how to get frequency response of a given Bode Plot?

Having trouble with bode plots. I understand that the is to be converted to $dB$ but after that I'm stuck. Could someone please show me how this graph gives a frequency response of $10/1+jw10$
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Design discrete controller for zero steady state error

I have the following system where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ...