Questions tagged [transfer-function]
Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.
435
questions
0
votes
0
answers
24
views
2
votes
1
answer
101
views
Impulse response of IIR low-pass filter
(Disclaimer. I have started doing some DSP. The last time I worked with this was in the eigthies. And I wasn't much of a specialist then, either.)
Is the impulse response different for IIR and FIR ...
- 45
0
votes
0
answers
25
views
Find transfer function from frequency and phase response [duplicate]
Given a desired frequency and phase response, is it possible to find a transfer function that matches/approximates both the frequency and phase response? Basically once you have a Bode plot, invert it ...
- 111
0
votes
1
answer
31
views
Calculate the Gain of a fixed-point filter
As the title already says, I would like to know how to calculate the Gain and Phase of a given fixed-point filter at a given frequency.
What I've achieved so far:
Let's say for example that I have a ...
- 25
1
vote
1
answer
57
views
Matlab: How to design digital equivalent for a lowpass Bessel filter (Thiran filter)?
In the process of applying a lowpass Bessel filter to my signal, I realized that besself function does not support the design of digital Bessel filters and the bilinear function can be used to convert ...
- 53
5
votes
0
answers
71
views
Alternative derivation for a Thiran filter
Following this reasoning (link on ee.se) I'm trying to derive the transfer function for a Thiran filter, but I get stuck. I know of the original paper, I just thought I'd go this way. This is what I'm ...
- 1,393
0
votes
1
answer
47
views
Normalize Bessel filter
I am applying a low pass filter to my signal and I should make sure the transfer function of my filter is one. How can I normalize my filter?
I am learning about filters and I appreciate any help.
<...
- 53
0
votes
0
answers
42
views
L1-norm of a stable, proper but not strictly proper transfer function
in the literature I find the statement, that the L-norms exist for every strictly proper and stable transfer function. I ask myself, if the L1-norm also exists for a transfer function, that has as ...
- 1
0
votes
1
answer
32
views
How do I calculate offset functions of these circuts? (Matlab results vs analytical results vary)
I am trying to calculate offset functions of these circuts but, the offsets results I got from matlab vary from those I calculated in python(analitically).
So I have three circuts, and after each ...
1
vote
2
answers
45
views
Scipy tf2zpk doesn't return zeros
I have the following transfer function:
$$H(z) =\frac{\alpha z}{(z-(1-\alpha))}$$
I'd like to find zeros and poles of it by scipy.signal.tf2zpk:
...
- 59
1
vote
1
answer
32
views
Simulated Room Transfer Function
I need help obtaining a simulated transfer function in a simulated room. I have created image sources for first and second order reflections, and am assuming a point source for my source. I have the ...
- 13
1
vote
0
answers
64
views
What is the difference between sending pulses and modulating waves?
If you look for amplitude, frequency, phase modulation, you typically get some picture saying you have a wave and you modulate the corresponding parameter (amplitude, frequency, phase). On the other ...
- 31
0
votes
1
answer
45
views
How to design fir filter from transfer function
Transfer function is this equation in frequency domain:
$$G(f) = \frac{1}{4\pi d} e^{i2 \pi d f/c}$$
or Hankel function
d : constant (distance),
c : 340
We may think we know complex number of ...
- 81
0
votes
1
answer
83
views
What is the transform of δ(5t)?
So my question is here: How to transform the function $\delta(5t)$?
I know that this function when is transformed on Fourier it will be $1$, but the $\delta(5t)$ is going to be and this $1$ or ...
- 23
1
vote
1
answer
59
views
Phase of DTFT transform of impulse response
I am approaching to the study of FIR systems. In particular, I was analyzing the graphs of amplitude and phase of the transfer function, when I had some trouble understanding how the phase behaves. ...
- 57
0
votes
0
answers
96
views
Discrepancy in frequency response of biquad filter (in Python)
I have written a simple biquad filter class but when I check its frequency response, I get different results with different methods. If I check it "empirically" (by taking the FFT of its ...
1
vote
0
answers
67
views
Error in the computation of PSF?
I am in trouble computing a PSF of an optical system in optical turbulence.
Background
The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
- 61
4
votes
1
answer
169
views
How accurate is the dominant poles approximation in higher order control systems?
From what I have learnt from control systems classes, the dominant poles of a system are those that can be used to analyze a higher order system in terms of the formulas of a 2nd order system. I took ...
- 143
0
votes
1
answer
60
views
Find Transfer Function and Appropriate Coefficients of the Transfer Functions from Pole Zero Plot
I got a Transfer function problem and I am confused in finding a solid solution step. Below is the problem description:
1st and 2nd order discrete-time filters with different pole-zero locations shall ...
- 101
0
votes
1
answer
69
views
Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab
I have been given an input and output signal.
input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1)
output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n).
or
x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
1
vote
1
answer
59
views
Measure Frequency-Response of Sensor using a Signalsource and Reference-Sensor
Cheers, I want to measure the frequency response of an acceleration sensor.
I have:
A signal source (device similar to a loudspeaker that shakes the acceleration sensor), of which I do NOT know the ...
- 111
2
votes
1
answer
86
views
Recursive equation Of Euler's Backward PID With Derivative Filter
I'm doing the implementation of the PID with derivative filter using the Euler's backward method, but I got stuck in this part since I have z in the denominator of most terms.
I didn't realize yet how ...
- 21
0
votes
0
answers
19
views
How to find response of step function in matlab and plot transfer function?
I have an transfer function:
$$\frac{Y(s)}{F(s)} = \frac{s^2+2s+3}{s^4+6s^3+13s^2+12s+9}$$
How can I find $Y(s)$ response of step function if $f(t)=\sin(5t)$ in MATLAB. And how can I plot the transfer ...
0
votes
1
answer
50
views
Is there a simple way to express this DTFT in polar form?
Consider the discrete-time system
$$
H(z) = a_0 + a_1 z^{-1} + a_2 z^{-2}
$$
To compute the DTFT, let $z = e^{j\omega}$ such that
$$
H(e^{j\omega}) = e^{-j\omega} \left(a_0 e^{j\omega} + a_1 + a_2e^{-...
- 219
0
votes
1
answer
96
views
Calculating numerator and denominator polynomials of a transfer function
I was reading this passage in a Doctoral Thesis about Adaptive cancellation.
Using MATLAB, if i were to write a simple code, it would look something like this.
...
1
vote
3
answers
36
views
How can you see from the transfer function of a system that it has feed forward/feedback elements?
Furthermore, how can you see from the pole/zero plot if the system has feed forward/feedback elements?
- 11
0
votes
0
answers
49
views
Is it allowable to place a zero to cancel out a complex pole?
Consider the following transfer function :
$$
T(s)=\frac{4}{s^{2}+2s+4}
$$
I wish to design a lead-lag compensator satisfying a set of requirements. What matters for now is the process done to meet ...
- 165
2
votes
1
answer
87
views
How to design a Controller that would adjust the steady-state error of a system?
I have a simple model (input-plant-output) with a transfer function :
$$
T(s)=\frac{4}{s^{2}+2s+4}
$$
The goal of this problem is to design a system such that it has the following specification for a ...
- 165
0
votes
1
answer
158
views
Difference equation from a transfer function of a low pass filter
I need to get the difference equation from this transfer function:
$H(z) = g \frac{1+a_1}{1+a_1z^-1}$
My math skills are too many years old, but I remember I need to get the Y(output) on one side and ...
- 103
0
votes
0
answers
34
views
Bode plot of transfer function with vs without feedback
I am looking at some old exams. Particularly, one question where there is a Bode plot of a transfer function $G(s)$, and some questions about the Bode plot. So far so good. However, part b) of the ...
- 101
0
votes
0
answers
20
views
Poles and Zeros of a DiscreteTimeModelFunction with delay in Wolfram Mathematica
help me please, I have a problem with this TransferFunctionModel, When I want to obtain the poles from the Discrete Model Wolfram gives me an error, what am I doing wrong? Could it be the delay of the ...
3
votes
1
answer
64
views
Confusion about analog filters
I'm mixed about the concepts of analog filters, so I hope someone can explain me, or point to information, to unentangle the ideas.
I know there are filters (analog) as Chevyshev, Butterworth, ...
- 131
1
vote
2
answers
63
views
How can we obtain the input signal in Python given the output signal and transfer function?
I have the following transfer function
$$ H(s) = \frac{R}{sRC + 1} $$
where $V$ is the output and $I$ is the input. We can write
$$ V(s) = I(s) H(s) $$
or
$$ V( j \omega ) = I(j \omega) H(j \omega) $$...
- 131
2
votes
0
answers
26
views
Help with setting up transfer function correct format
I have a transfer function as:
H(s) = R / (sRC + 1)
V is the output and I is the input so we can write:
V(s) = I(s)*H(s)
Now the thing is that, I want to obtain I(t) for the given V(t). So I write:
I(...
- 131
1
vote
2
answers
92
views
How can I use an irrational transfer function to convolve a signal?
I have the irrational transfer function
$$H(s)=\mathrm{e}^{-a\sqrt{s}}$$
With the inverse Laplace transform
$$
h(t) = \frac{a\,\mathrm{e^{-a^2/(4t)}}}{2\sqrt{\pi}~t^{3/2}}
$$
For $a > 0$
How can I ...
- 73
2
votes
0
answers
45
views
Mismatch between the frequency response of a transfer function and bode plot
I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)):
<...
- 53
3
votes
0
answers
37
views
Derivation of Strehl ratio
I am in trouble proving the following fact:
The Strehl ratio is the ratio of the volume of the aberrated OTF (optical transfer function) and the ideal OTF, i.e.
\begin{align}
\mathcal{S}=\frac{\int\...
- 61
0
votes
1
answer
56
views
State-space model and/or TF for a $K$-th order linear system given the signal sequence
The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential:
\begin{equation}
x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k}
{\underbrace{e^{\{(- \...
- 69
1
vote
2
answers
55
views
Digital IIR LPF Difference Equation from Transfer Function
I want a digital IIR filter with f0=225kHz and fs=53.125GHz. I can come up with the transfer function and plot it using Matlab. ...
- 13
0
votes
1
answer
58
views
Realize the given system in cascade form of 2nd order section in signal flow graph representation(with complex exponents)?
I know how to solve cascade form for normal case, but I don't know how to solve cascade form if I get complex exponentials. How do I solve this? Can you provide me 1 solved example or some hint or ...
- 31
0
votes
1
answer
130
views
Z domain Transfer function to magnitude
How would one go about calculating the Magnitude of...
$\mathcal{Z}$-transform = $$\frac{1}{1-z^{-2}}$$
I understand that z can be replaced with $${exp}^{j\omega}$$ and I am aware of the identities $${...
- 3
0
votes
1
answer
36
views
Determine transfer function based on a diagram with ai coefficients given
From a diagram with input $x(n)$ a summer and three feedback delay taps I get the difference equation...
$$y(n) = x(n)+a_1y(n-1)+a_2y(n-2)+a_3y(n-3)$$
Then I am given values for ai coefficients.
Case1:...
- 3
1
vote
1
answer
65
views
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 $h_i$ ...
0
votes
1
answer
23
views
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 ...
- 163
4
votes
1
answer
72
views
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:
...
- 580
1
vote
1
answer
38
views
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 $\...
- 53
1
vote
1
answer
122
views
Meaning of term in notch filter coefficient
I have a discrete implementation of a notch/bandstop filter that allows me to specify the stop band frequency, the width of the notch and the attenuation of the stop band frequency. I've been tasked ...
- 35
0
votes
1
answer
39
views
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_{...
1
vote
2
answers
371
views
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 ...
- 113
7
votes
1
answer
74
views
Who first coined "Direct Form I" and "Direct Form II"?
I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
- 36.1k