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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How to estimate multidimensional linear response function from measured input and output signals?
Problem definition:
I measure N sources of noise $x_i$ and one output signal $y$ which contains real signal $y_0$ plus noise from all these sources $x_i$ transformed by linear response functions $h_i$ ...
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What does it mean for a transfer function to have multiple sets of zeros in the numerator?
I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
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Amplitude-and phasefunctions for a system
I am studying a course in signalanalysis and have run into som trouble with a exercise.
I am to dimension the circuit below in such a way that the DC-amplification is 1 and that the frequencies $\...
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Phase Response of $N$-th order Digital All-Pass Filter
I am having trouble reconciling my derivation of the phase response of an N-th order all-pass filter with those I am finding in the literature, and I figured someone here could help me.
Real Version:
...
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Why is state-space representation more numerically stable than zeros-poles representation?
Matlab documentation says things like:
For high order filters, the state-space form is the most numerically accurate, followed by the zero-pole-gain form. The transfer function coefficient form is ...
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how to calculate $H_{lp} = z(1- H_{hp}) $ , given coefficients for $H_{hp}$?
Given a high pass transfer fn of the form
$H_{hp}=a_{1}*z^0 +a_{2}*z^{-1} + ... a_{n}*z^{-n}$
Is it possible to calculate a causal low pass filter using
$H_{lp} = z*(1-H_{hp})$ ?
attempting
$H_{...
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Transfer functions for Scipy and Matlab's Butterworth filter don't seem to match theory
The squared transfer function for a Butterworth filter of order $n$ should be
$$
|H(f)|^2 = \frac{1}{1+\left(\frac{f}{f_c}\right)^{2n}}
$$
where $f_c$ is the cut-off frequency. (Here's one of many ...
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Filter a signal with a complex dB SPL filter
I've been tasked with filtering a sound with a filter that looks something like this.
I don't have any real DSP training, so I'm not sure if my attempt at tackling this is correct. I can filter ...
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Definition of frequency response
I studied various signal processing materials for a long time, and I have a question.
Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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Zeros and poles from transfer function
I have a transfer function
$$ H(z) = \frac{Y(z)}{X(z)} = 1 - 0.5z^{-1} \text{.}$$
I'm interested in zeros and poles.
I know I need to adjust the function to
$$ H(z) = \frac{\prod_i(z-n_i)}{\prod_i(z-...
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Difference equation to FIR filter coefficients
I have a difference equation
$$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$
According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ...
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Finding transfer function from bode plot
Given a bode diagram
From the figure, I see that when $\omega = 100 \text{ rad/s}$ the magnitude response starting to go down and when $\omega = 1000 \text{ rad/s}$ the slope become higher. Then
$$H(...
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A system having impulse response $ h(t)=u(t) $ stable or not?
I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess)
I proceeded as$$ \int_{-\...
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Trying to plot frequency response of a filter Transfer Function in MATLAB, it looks wrong
I have the transfer function below which is for a IIR filter and trying to plot its frequency response for omega<pi. r=0.99 and theta=pi/3:
Here is my attempt at implementing it in MATLAB:
...
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I tried two approaches and gained the different conclusions of judging the stability of the transfer function of the system
We want to judge whether the system is stable or not.
Given the below transfer function.
$$ H\left( z \right) =\frac{\left( 1+2 z^{-1} \right) }{\left( 2+z^{-1} \right) } $$
$$ H\left( z \right) ...
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Seemingly no division operation is done of the diagram of the transfer function
Given the below system.
$$ y\left[n \right] =2 x\left[n \right] -x\left[n -1\right] +0.5 y\left[n -2 \right] $$
We'll find out the transfer function of it.
So, easiely using z-transform,
$$ Y(z) ...
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Identification of a transfer function
Can you obtain a transfer function in frequency domain with a bode plot form given by this function:
$$ S=k_1 \sqrt{1+\frac{k_2}{f}} $$
I did not managed it because actually in the lowest part of ...
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how to take a second order transfer function without any zeros and represent it using two first order transfer functions
does anybody know how to take a second order transfer function with no zeros (no s terms in the numerator):
$$ g(s) = K\frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2} $$
and represent it using ...
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Real Data Complex Transfer Function using H0, H1, H2 Estimators
BACKGROUND:
This question is attempting to consolidate material discussed in two previous topics. These are:
Understanding the H1 and H2 estimators @Pontus S
Frequency-domain deconvolution: "...
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Coupled system instability
Suppose there are two linear devices (containing some multi-physics but the details don't matter here), and these devices are given to us as two black boxes that can be studied experimentally. Black ...
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Stabilizing an unstable system and removing oscillations from step response
I have a system with the transfer function given in this MATLAB code
...
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Developing Lead Compensator to Decrease Settle Time
This is a follow up to this question.
I've approximated the transfer function for a system to be H = zpk([0.012 -1.05 18],[-0.22 -0.22 -45 -1000],10000);. My goal ...
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Get the transfer function when using the "designfilt" command in MATLAB
To put things into perspective, I initially had these four graphs in MATLAB, whose data were sampled with a rate of 10 samples/sec :-
I wanted to remove some of the spikes on the blue graphs, so I ...
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Tuning a PID Controller
I have the following transfer function
$$10000 \cdot\frac{(s-0.012)(s+1.05)(s-18)}{(s+0.22)^2(s+45)(s+1000)}$$
For which I am trying to tune a PID controller for. I'm using the pidTuner in MATLAB to ...
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Adding noise to frequency response
I have the dynamics of a 2nd order system, mass-spring-damper for example, in the transfer-function format.
For the analysis that I am doing, I am calculating the frequency response of the system by ...
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Creating Bode Plot from Experimental Data
I have a blackbox system in which I can input a function and obtain the output signal (in MATLAB). I'm attempting to reconstruct a Bode diagram and have had success with the Magnitude plot, however, I'...
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Get the discrete-time poles and zeros from continuous-time poles and zeros
How do you implement the following function:
$$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$
where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
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How to find H(z) from just zeros and poles
I have a system with a DC gain of 8, poles at z = +- j/2 and zeroes at e^+-j5, I need to find the H(z).
I have tried this but not sure if it is right.
$$
H(z) = G_o * z^{-1} \frac{(z-z_0)(z-z_1)}{(z-...
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Amplitude spectrum (transfer function) of signal?
I have one question related to finding amplitude spectrum (transfer function) of signal knowing that output signal is time derivative of input signal. I have the answer graph but I don't understand ...
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Transfer function estimation from frequency response
Let's assume that we know that we are dealing with a SISO second order system for which we have the frequency response (magnitude and phase for a known frequency range ω). What methods would people ...
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How do I get a faster system response?
I have this model in simulink (the graph is my output):
The step input has amplitude 0.5 m/s, and it steps up after 0.1 seconds. The gain $K_p=5$.
The saturation block is to keep the voltage between -...
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What is the transfer function of this block diagram
I and my friend have different answer for this block diagram
Mine:
$$y[n] = -\frac23x[n] + x[n-1] -\frac12[n-2]$$
Hence
$$H(z) = \frac{1}{-\frac23 + z^{-1} -\frac12z^{-2}}$$
My friend:
$$q[n]=x[n]-...
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Transfer function with blackbox modelling is too slow compared to real expectation
I collected this data from a robot that drives with its wheels up. The blue curve is the voltage and that is my input. The orange curve is the wheel velocity and that is my output.
I want to create a ...
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What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)
I'm using reference from here and here.
This is Laplace transfer function of DC Control Speed System:
$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$
Where,
$\omega$ is the motor angular ...
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how to find frequency response of microphone
hello I want to find the frequency response of a microphone. I give the input signal to my speaker and it produces a specific SPL with specific frequency. on the other side, I read the microphone ...
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Additive disturbance in block diagram representation
Drawing the open loop block diagram between valve and pump is straightforward (please see illustration). But why should $v$ be an additional disturbance in this system (please see solution)?
$v$ is ...
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From transfer function to differential equation
I have the below detailed solution (boxed in blue) that I don't understand completely:
I can reconstitute the differential equation from:
$$ (1+Ts) X(s) = K_v U(s) $$
$$ x(t) + T\dot x(t) = K_v u(t) $...
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Is this system causal or not?
My efforts of solving this question are below.
I came to a conclusion that this system is causal, since:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
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Why eigen values and poles of a system are equivalent?
In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides.
When the model is ...
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Gradient of transfer function (z-transform) with respect to coefficients/parameters?
my problem is perhaps very simple but I just can not find the answer, even though this is used (though not explained) in several books:
What is $\frac{\partial G (z, \theta)}{\partial \theta}$ when $G$...
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For a discrete LTI system, does "bounded memory" imply "rational transfer function?"
Every LTI system with a $\mathcal Z$-domain transfer function that is a rational function - aka a quotient of two polynomials in $z$ - can be implemented using a bounded amount of memory.
Is the ...
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Why the transfer function is equal to the output in this case
In this description of transfer functions on the z-plane (image linked), I'm confused by equation 1.49, which says that $H(f)=v_{out}(f)$ when $v_{in}(f)= 1 * e^{j 2 \pi (f/f_s)}$. (For another matter ...
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Part 2: Root Locus, Transfer Functions and Unit Step Response?
I'm continuing my question referenced here: Part 1 Question / Problem Description
Say I have a new Root Locus shown below
Consider the generic feedback loop, and the transfer function $G(s)$ shown by ...
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Root Locus, Transfer Functions and Unit Step Response?
Consider the generic feedback loop, and the transfer function $G(s)$ shown by the following root locus plot.
Where $\mathbf{x}$ denotes the open-loop poles and $\square$ denotes the closed loop poles....
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How to handle cross products in feedback loop?
I'm trying to simplify the following block diagram from
to the following block diagram
However, h(t), H(s) in time domain, has a cross product in it (gyroscopic torque). How can I represent the ...
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Ending points of the root locus
Let $$D(s) + KN(s) = 0 \tag{1}$$where $D(s)$ and $N(s)$ are polynomials of $s \in \mathbb{C}$ such that $\text{Deg}(D) = n, \ \text{Deg}(N) = m$ and $n\ge m$. The root locus method tells us how the ...
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How to plot magnitude response using $\tt freqz$ in MATLAB if I have a transfer function without a denominator
So I have the transfer function:
$$H[z] = 1 + \sqrt{2}z^{-1} + z^{-2} $$
And I have to evaluate $H(e^{j\omega})$ for $\omega= 0, \pi/4, \pi/4 \ldots$
I have done the calculations manually using ...
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Can we choose a sampling frequency to remove unwanted noise at a specific frequency?
I am studying for my exam in signal processing. In one of the old exam papers I am told to find a sampling frequency, which will remove 80 Hz noise. The filter the exam question is based around has an ...
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Converting Audacity Filter Curve EQ into transfer function and applying it to a signal via python
First of I am very new to Signal Processing and to python in general. I am trying to write a script where I would feed a voice recording into it, internally apply an eq and have the modified signal ...
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What is the relation between input and output PSDs given system transfer function $H(s)$
If I have the system transfer function $H(s)$ in the complex frequency domain, how would I relate the input/output power spectral densities?
I have come across the relation $P_{out}(f) = |H(f)|^2P_{in}...
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