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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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 ...
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Determine filter type using recurrence relation
Given the recurrence relation:
$y[n] = x[n] + 0.5y[n-1]$
I want to determine the filter type (i.e. LPF, HPF etc.)
I try to use Z transform, and get that the the transfer function is
$H(z) = \frac{2z}{...
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Transfer function estimation of a noisy system
Overall description
I am trying to estimate a filtering system’s transfer function, given its input and output.
This system takes $x$ as input . This signal is low pass filtered and added to a WGN by ...
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Reducing noise on several Transfer Function measurements
INTRODUCTION
I want to obtain the transfer function of certain system (a ground "path", in this case) using an impact hammer for the excitation and one accelerometer (measuring vertical direction ...
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How do I find the transfer function in the frequency domain?
I was doing some exercises with transfer functions, they were always under the form of $H(z)$ and $H(e^{jw})$ for the frequency response. Today I have found one with $H(f)$. I would like to ask if my ...
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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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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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Get the discrete-time poles and zeros from continuous-time poles and zeros
How do you implement the following function:
$$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$
where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
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Identification of a transfer function
Can you obtain a transfer function in frequency domain with a bode plot form given by this function:
$$ S=k1 \sqrt{1+\frac{k2}{f}} $$
I did not managed it because actually in the lowest part of ...
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Transfer function: from poles and zeros to polynomial coefficients
I understand how this transfer function was solved except I don't know how to get the 0.87.
Any help would be appreciated.
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How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?
Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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Calculating an output of a system (Z- transform question)
I have a following question to answer:
An LTI system is described by its impulse response h[n]. For input x[n] it gives output y[n].
$$h[n] = u(n) - u(n-N) $$
$$x[n] = u(n) - u(n-M)$$
I want to ...
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Recursive filter with repeated poles
This post follows this previous resolved post where I was trying to find the inverse Z-transform of a more simple filter output (that I used as an example to get the methodology). The present filter ...
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222 views
Trivial and non-trivial zeros
I am new to DSP, and I'm self studying. Could someone please explain to me what do we mean by trivial and non-trivial zeros?
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Transfer function of a nonhomogeneous difference equation
Consider the following difference equation:
$y_k=\alpha y_{k-1}+\beta x_k$
The transfer function for this is given by:
$\displaystyle\frac{Y(z)}{X(z)}=\frac{\beta}{1-\alpha z^{-1}} = \frac{\beta}{...
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131 views
Why is interpolation a time varying system
I was reading about interpolation (Interpolation and Decimation of Digital Signals - A tutorial Review, Ronald E. Crochiere) and found that Interpolation filter is a time varying system. Can someone ...
