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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Optimal estimation of FIR coefficients

In estimation theory by Kay (p. 92), he found the FIR coefficient having the input and the noisy output (least-squares). Using the Cramer-Rao bound, he claims that the best performance should appear ...
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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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Limitations in Backing Out a Transfer Function

Suppose you have an LTI system for which the (complex) frequency response $H(j\omega)$ has been measured in some frequency window $[\omega_1,\omega_2]$. Now imagine that you want to provide an input $...
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What real object could be modeled by this transfer function? [closed]

What object from real world could be modeled by this transfer function? What could parameters b, p1 and p2 stand for?
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How is time or sampling rate accounted for in this model?

A basic model of coupled strings (eg. piano) is provided here as: The principle is that it has two identical string simulations each formed by a delay line and LPF. The outputs of these are summed at ...
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Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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Doubt on inversion of the dynamics

I am studying control system and I have encountered the topic of the inversion of the dynamics. So I have seen that the ideal situation would be $C(s)=P(s)^{-1}$ but there are some problem with ...
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How to Determine if FIR has a Linear_Phase Response w/o Matlab

Given the FIR transfer function: h(z) = $ .36 + .384z^{-1} + .1608z^{-2} +.9712z^{-3} + .352z^{-4} + .18z^{-5} - .2z^{-6} $ How do you determine if this transfer function has a linear - phase ...
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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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How can I obtain the response signal for this question?

In particular I am having trouble with 6b). From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. ...
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Steady-State Output from Transfer Function

The progress I have made is as follows: $\sin(t)$ is our signal therefore $\omega = 1 = 2\pi f$ and $f$ = $\frac{1}{2 \pi}$ Also, $f_s$ = 10Hz therefore T = $\frac{1}{f_s}$ = 0.1s $H(z) = \frac{z}{...
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Lead compensator vs lag compensator?

I already know that lag compensator acts like PI controller and improves steady state and lead compensator acts like PD controller improves transient state but how they achieve their goal? Despite ...
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Magnitude and phase response and cut-off frequency of a moving average filter

The frequency response of a typical moving average filter of length $N$ is given by $H(\omega)=\frac{1}{N}\frac{\sin(\omega N/2) e^{-j \omega ((N-1)/2)}}{\sin(\omega/2)}$. Firstly, isn't the cut off ...
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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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A signal $g(t)$ is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0

I am solving a question, where a signal g(t) is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0. I understand that since for this filter the ...
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Finding the impulse response of a system

I have the following transfer function. $$ H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$ I'm trying to find the impulse response of the system. ...
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Are MATLAB function zp2tf() and tf2zp() are complementary or not?

I was under impression that given, pole, zero and gain the transfer function (filter coefficients b and a) is fixed. Therefore, ...
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How would I calculate the DC Gain for a Chebyshev Type 2 filter?

I'm currently working on an implementation of a Chebyshev Type 2 filter but the gain is all over the place when playing around with the order and ripple. I haven't found anything online but (as far as ...
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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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Taking transfer function out of real heating system

I have some king of heating system: heater (that I can control current for final power control) and a thermocouple (for measuring the temperature). I also have a device that can record temperatures ...
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Closed Loop AGC

Interested to develop an AGC for the RF RX chain below. Using the Matlab code as a reference have developed an open loop AGC. Equations as well as block diagram are provided below. Wondered how can ...
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Determining the transfer function from discrete signals

I have measurements of a discrete in- and output signals, and I want to find the transfer function of the system. Is there a good method for finding the transfer function of an LTI system from ...
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Two different answers while doing Inverse Z-transform

Given, $$X(z) = \frac{z}{3z^2 - 4z + 1}$$ Question 1 I need to calculate inverse z-transform for ROC $|z|>1$ When I try to calculate inverse $z$-transform using partial fraction of $X(z)$ and ...
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Inverting Sensor Transfer Functions?

When you see software packages that read in data from sensing equipment, does the software do something to inverse the transfer function? Correct me if I'm wrong in my understanding, but this is how ...
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Calculate transfer function of two parallel transfer functions in a feedback loop

I have rational transfer functions: $$H_1(z) = \frac{ b_0 + b_1z^{-1} + b_2z^{-2} }{a_0 + a_1z^{-1} + a_2z^{-2}}$$ $$H_2(z) = \frac{ q_0 + q_1z^{-1} + q_2z^{-2} }{p_0 + p_1z^{-1} + p_2z^{-2}}$$ And ...
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Step response of third-order continuous-time transfer function

I have a transfer function of the form: $$H(s) = \frac{b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}{s^3 + b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}$$ If it matters, $a=b=2$. Is anyone aware of ...
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Vary poles/zeros of digital IIR filter

Many applications that produce sound, such as software synthesizers, are able to apply a filter that varies with time, such as applying a low pass filter that varies with an LFO. I currently have a ...
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Second Order Transfer Function : Imaginary component in $R$?

I have been looking at the following transfer function: $$ H(z) = \tfrac12 - \tfrac12 z^{-2} $$ Given the usual method for finding $\theta$ and $R$ in the complex plane, I calculate that $\theta = \...
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Compensating the Group Delay of an Analog Filter using DSP

I am having a problem in my current project where I need to measure different biological signals (like ECG) simultaneously. As the instrumentation hardware is developed by different people over time, ...
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Basic Questions on Wiener Filtering

I read a lot about Wiener Filters (focusing on discrete time case). I understand the math, but I am quite disconnected from the real life assumptions behind using such a filter. Unfortunately ...
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Powers of $z$ in a discrete transfer function

I have been working with discrete-time systems and I am not yet able to understand the reason behind using powers of $z^{-1}$ in transfer functions. I get that $z^{-1}$ means a delay, but when we ...
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Similarity or Relation between Walsh Hadamard Transform and Slant Transform

Is there any relation between Walsh Hadamard Transform and Slant Transform? Or is there any common property or similarity?
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Missing delay in heavyside step function

I found the following task that was inspired by an example in the book A. V. Oppenheim and R. W. Schafer, "Discrete-Time Signal Processing", 3rd Edition, 2014. Task: Consider the 2nd-order IIR ...
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Cascade filter realization equivalence? [closed]

Given $$H(z) = \frac{11 +4.6z^{-1} -26z^{-2}-3.75z^{-3}}{1-z^{-1}-8.75z^{-2}}$$ I'd like to know whether this realization: Is equivalent to this one? In short, is the direct form realization ...
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Inverse Fourier of Two-Pole Transfer Function

I would appreciate if someone could walk me through this derivation. I have a transfer function in the frequency domain, which has two poles $$\tilde{H}(\omega) = \Big(\frac{1}{1 + i \omega \tau_1}\...
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What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]

In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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Output of an LTI system given its transfer function and input

Given the transfer function $$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$ and the input $$v_i(t) = 0.1 \sin(100t)$$ find the output, $v_o(t)$. My approach was to use $v_o(t) = \mathcal{L^{-1}}\left\{T(...
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Transfer Function definition

To find the transfer function of a channel we say that it is $$ H(s) = \frac{y(s)}{x(s)}|x(s)=0 for <0 $$ Why we do not define it like $$ h(t) = \frac{y(t)}{x(t)} $$
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Cost function for LTI system identification

I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions. The general approach ...
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Linear Combiner Based LMS Transfer Function

I am currently working on narrowband beamforming and looking to compute the transfer function for a linear combiner based LMS. While doing a quick search I have found the following article which ...
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Z domain transfer function to difference equation

I want to convert this transfer function: $$\ \frac{2\cdot(z-0.5)\cdot(z-0.6)}{z-1}$$ to a difference equation, but I have no idea how. Can someone help me? Thanks, Arjon
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System Response Terminology

If I have a system specified by $$P(D)y(t)=Q(D)x(t)$$ and I specify initial conditions $y(0^-)=a, \ y'(0^-)=b,\ x(0^-)=c$ does the term $x(0^-)=c$ correspond to the zero state response or zero ...
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Calculating impulse response from transfer function

Given the difference equation as 𝑦[𝑛]=5𝑥[𝑛]+5𝑦[𝑛−2] and 𝑥[𝑛]=cos(𝜋𝑛). I would like to obtain the transfer function h[n]. How is that possible manually and on Matlab? Manually it should be ...
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Determine phase response from pole-zero plot

I know how to determine the frequency response from the pole-zero diagram given the following formula: $\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
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Low pass filter transfer function

I am calculating the transfer function of a low pass RC filter and I have gotten $\frac{1}{1+jωRC}$ which is correct. But somehow it seems $ωRC = \frac {ω}{ω_0}$ that refers to the cutoff freqency ...
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Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
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Region of convergence for discrete system

I am confused by two questions on the region of convergence (ROC) when applying the $Z$-transform. Consider a discrete-time linear system $$x[n+1] = Ax[n]+Bu[n], \qquad y[n]=Cx[n]+D$$ whose transfer ...
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What is the zero in this transfer function?

What is the zero for the following transfer function, $-1/2$ or $-2$? $$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$ This appears to give a zero of $-1/2$. I can transform this into the standard form ...
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Poles and zeros representation in s-plane

We have a filter (or a system) that has two poles at $f_{p1} = f_{p2} = 20$ GHz and one zero at $f_{z1} = 15$ GHz. Let's assume the gain is $K = 1$. Then how do you mark these poles and zero in the ...
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Transfer function from poles and zeros

If we know that a filter (or a system) has two poles at 20 GHz and one zero at 15 GHz, then how do you write the transfer function $H(s)$ for such a system? I am wondering why sometimes the poles and ...