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 frequency response of a filter defined as a Z-domain transfer function
I am software engineer studying DSP on my own. I came across this question in a graduate textbook and am not sure how to proceed.
...
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Why is a feedback loop not represented by the least order transfer function?
I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(Z)C(z)}$.
$H(z) = h$ and $C(z) = \frac{K}{z-\alpha}$.
If I manually calculate the transfer function, I get:
$L(z) = ...
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Digital control: Exercise solution
Can you help me (show me how) to solve the following exercise?
For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
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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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Can I determine a system's $z$-domain transfer function from its pole-zero plot?
Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
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57 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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1answer
59 views
Determine the type of filter from the transfer function
i got that system $x_n \to x_n-x_{n-1}$, so $h_n=[.....,0,1,-1,0,...]$, with $h_0=1$ and $h_1=-1$, so the transfer function given by:
$$\sum_{i=-\infty}^{\infty} h_ne^{-jwn} = ...
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If exponentials are eigenfunctions, where does the transient term come from?
Here you can see that the transfer function applied to a cosine input will give you a sinusoid and a transient term:
$$
x(t) = \underbrace{(x(0) + x'(0))(2 e^{-t} - e^{-2t}) + \frac{2}{5} e^{-t} - ...
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50 views
Find the frequency response if i have the magnitude response?
if i have the transfer function of magnitude response is there a method that i could calculate the frequency response?
For example the transfer function of the magnitude response is:
$ 3db \pm ...
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42 views
Z-domain transfer function question
For the difference equation below:
$y(k)=1/2{x(k)+x(k-1)}$
How i can find he z-domain transfer function?
Thanks.
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Derive minimum phase from magnitude
With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
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82 views
Use Butterworth and Chebychev filters
I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters.
I'm developing in C++ with Qt, and I'm looking for algorithms ...
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59 views
Algorithm to estimate coherence when measuring a transfer function with a swept sine
I use a swept sine to measure a transfer function, multiplying the reponse by the in phase and quadrature excitation to get a complex response at each frequency. Can you suggest an enhancement to this ...
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286 views
How do optical illusions work (photo mosaic) from a signal processing perspective?
Hello fellow investigators
I have two question about optical illusions
1) A photo mosaic is something like this:
What are the signal processing principles behind our eye merging the many tiny ...
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1answer
318 views
Amplitude vs Frequency Response
Consider the simple first-order low pass filter, described by
$\tau \frac{d \mathcal{O}}{dt} + \mathcal{O}(t)=\mathcal{I}(t)$
Considered as a linear system (ie $\mathcal{L} \mathcal{O} = ...
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How to estimate a transfer function from a magnitude-only frequency response?
Given an arbitrary frequency response, what signal processing methods might exist that could guess, estimate or determine a transfer function (pole and zero constellation) which gives a "reasonably ...
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What do we know about the transfer function away from its zeros?
So lets say I have a transfer function for an FIR filter $H(z) = (z-a)...(z-n)$ where $a,...,n$ are points along the unit circle. But what about other points along the unit circle that correspond to ...
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How to deal with a negative pole (unstable) in the pre-filter of a control system?
So while answering how to design a PI controller for a first order time delayed system (Question Here )
Here is the closed loop equation to a control system:
$$
G_C(s) = ...
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641 views
Anti-causal systems
If Anti-causal systems are defined as those whose output depends solely upon future inputs.(Is this definition correct as I understand)
So i see that $y[n] = x[n+2]$ ; is anticausal system
How is a ...
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1answer
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How to find frequency response, stability, and causality of a linear system?
I have the following transfer function:
$$H(s)=\frac{s}{(s+1)(s+2)}$$
How can I find the gain and phase response of the above system? I know the first step has something to do with substituting $s = ...
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What is the relation between the PSDs of filter input and output called? $R_Y = |H|^2R_X$
If a wide-sense stationary signal X is fed to an LTI filter with the transfer function H, the power spectral density (PSD) of the output Y can be expressed as:
$R_Y(f) = |H(f)|^2R_X(f)$
where $R_X$ ...
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Are there alternatives to the bilinear transform?
When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
