Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.
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Phase response of S11/S22 parameter for an RF attenuator? [closed]
I am new into the RF measurements. I was measuring the S11/S22 (reflection) parameters of an RF attenuator (with different attenuation levels, e.g., 10 dB) via a vector network analyzer from Rhode &...
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1answer
25 views
What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)
I'm using reference from here and here.
This is Laplace transfer function of DC Control Speed System:
$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$
Where,
$\omega$ is the motor angular ...
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0answers
15 views
Controllable Canonical Form
the transfer function of my causal filter is $G(z)=\dfrac{1}{(1+\dfrac{1}{2}z^{-1})}$, $z$ being the formal z-transform. The parameters in the controllable canonical form are therefore $a_0=1$, $a_1=0$...
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37 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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2answers
38 views
Impulse response when input to a system is differentiated, and its applicability to find response to general inputs
I will first give a short explanation of what I am asking, and then give a more comprehensive context.
If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$,
,
we ...
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1answer
33 views
Finding the transfer function of a discrete signal described by two equations
A discrete time system is described by the following system of equations.
$$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$
$$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$
Find the systen function and then find the ...
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2answers
63 views
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
...
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1answer
61 views
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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1answer
49 views
Is there a way to obtain the transfer function from a bode plot on Python? (I know that it is possible on Matlab)
Quite simply, I have a bode plot obtained from a source signal.
Now I wish to obtain the transfer function.
I know it is possible with Matlab: http://www.mathworks.com/help/ident/examples/frequency-...
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1answer
34 views
Transfer function of open loop system
Suppose i have the system equation
$Y(s) = G(s)X(s)+ 3T(s)$
Then what is the transfer function of the system?
I know that the transfer function is $Y(s)/X(s)$, but i can't get that expression.
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13 views
Are eigenvalues of A poles of H(z)? [duplicate]
So I got this discrete LTI system of which the transfer function is defined by H(z).
Given the state space model: x[k+1] = A x[k] + B u[k] and y[k = C x[k] + D u[k]
the Z-transform can be written ...
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35 views
Comparison of different methods to calculate transfer functions
I have input and output data (x and y), the signal I am interested in is on y but it is noisy. The noise is coherent and also recorded by x. I am trying to remove the noise using a transfer function (...
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1answer
36 views
transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?
From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
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0answers
23 views
How to compare the similarity of 2 transfer functions
I'm working on a power systems where I have 2 linearized transfer functions. The first transfer function corresponds to the no-load case and the second transfer function corresponds to the full-load ...
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1answer
43 views
Estimate a microphone's transfer function
I am trying to compare the transfer functions of k different microphones and need some advice on my current approach. As of now, I have attempted the following:
Play a pink noise test tone $(X)$ ...
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1answer
63 views
Absolutely summable signals
Given an absolutely summable signal $x[n]$, the $z$-transform $X^z(z)$ is rational with a pole at $z=0.5$.
Given the following the statements:
$x[n]$ has a finite support in the time domain.
$x[n]$ ...
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1answer
34 views
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$$\mathbb{R}$
How we can ...
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1answer
68 views
FIR Impulse response & transfer function
I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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0answers
22 views
Sound equalization : assumptions around the use of the transfer functions. Are they correct?
I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check.
1/ I'm ...
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1answer
54 views
How do I plot the square of the amplitude response?
I have calculated the transfer function of an FIR filter
$$
y[n] = x[n] + α · x[n − R]
$$
This is what I have
$$
H(z) = 1 + αz^{-R}
$$
Now I should plot the square of the amplitude response. So I ...
2
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1answer
50 views
Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$
Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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0answers
34 views
How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?
For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
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1answer
103 views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$
I need to find the impulse response h[n] of a causal system with x[n] as unit impulse.
I have tried to find the impulse response by the following ...
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3answers
98 views
Why use transfer functions than differential equations?
I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths.
Why we use ...
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1answer
65 views
Audio transfer function modelling with pink noise + signal
I'm trying to model a transfer function for a noisy audio system, specifically to measure delayed system response. Before I can confidently apply control, I need to verify that I can exert control ...
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1answer
61 views
Natural frequencies of a transfer function
I have been told in the university that the natural frequencies (also called $\textit{eigenfrequencies}$) are the poles of the transfer function, however, Matlab compute them as the modulus of the ...
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1answer
55 views
Poles and zeros in time domain of analogs filters
I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
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0answers
95 views
How to find transfer function of a logarithmic or power function?
I'm dealing with logarithmic system $\log_{10}(y(t)) = m \log_{10}(x(t)) + b$, and I need to find the transfer function, $Y(s)/X(s).$
What is the Laplace transformation of $\log_{10}(f(t))$?
What I ...
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3answers
110 views
Distinguishing FIR and IIR from difference equation
Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$
I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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1answer
40 views
Evauating response to $x(n) = \sin{2\pi\frac{1}{4}n}$ given the system function
Let the input signal $x(n) = \sin{2\pi\frac{1}{4}n}$ go in to the system described by: $$y(n) - y(n-1)+\frac{3}{16}y(n-2) =x(n).$$
What is the output signal?
I've calculated the system function $H(...
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votes
2answers
194 views
Phase function of filter
I have a filter with the transfer function
$$H(z) = 1 - 2z^{-2} + z^{-4}.$$ The task is to find the phase function $\theta (\omega).$
My attempt is to start by expressing the frequency response
\...
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0answers
51 views
How do I convert a two-pole two-zero transfer function from the s-domain to the z-domain?
I'm trying to convert the following IIR transfer function from the s-domain to the z-domain:
$$
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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1answer
33 views
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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1answer
191 views
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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1answer
21 views
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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0answers
43 views
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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1answer
52 views
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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1answer
95 views
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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1answer
377 views
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 ...
3
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1answer
177 views
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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1answer
68 views
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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2answers
167 views
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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2answers
66 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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69 views
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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3answers
124 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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0answers
47 views
Transfer function between two signals\ fiter design from frequency response
If I have a training data with two signals (PPG1 and PPG2 from different locations) and want to see, how different they are of what is their transfer function I can apply MATLAB's function ...
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2answers
1k views
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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1answer
41 views
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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1answer
60 views
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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37 views
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 ...
