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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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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1answer
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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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1answer
55 views
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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1answer
27 views
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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1answer
30 views
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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1answer
65 views
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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1answer
52 views
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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1answer
51 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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1answer
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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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1answer
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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 ...
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1answer
72 views
Linear Predictive Coding for general signals
I have a signal that's monotonic and roughly linear and have been looking at using Linear Predictive Coding to encode information and compress my signal. I guess my first general question is if this ...
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1answer
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MIT exercise 6.003 HW2 - Concept of system initially at rest
I am following the MIT open course you can find here. My question is about one of the exercises given as homework in the latter and more specifically I think I am missing something on the concept of "...
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Why I don't get the right PSD
I need to model a noise with a given PSD. To do this, I am starting from a white gaussian noise (WGN) and feed with the WGN a transfer function, which will act like a filter. In fact,it's easy to ...
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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
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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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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
57 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
40 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
101 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
82 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
208 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
40 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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1answer
60 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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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
56 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
126 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
44 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$$\mathbb{R}$
How we can ...
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1answer
106 views
FIR Impulse response & transfer function
I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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Sound equalization : assumptions around the use of the transfer functions. Are they correct?
I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check.
1/ I'm ...
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1answer
65 views
How do I plot the square of the amplitude response?
I have calculated the transfer function of an FIR filter
$$
y[n] = x[n] + α · x[n − R]
$$
This is what I have
$$
H(z) = 1 + αz^{-R}
$$
Now I should plot the square of the amplitude response. So I ...
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1answer
57 views
Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$
Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?
For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
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1answer
186 views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$
I need to find the impulse response h[n] of a causal system with x[n] as unit impulse.
I have tried to find the impulse response by the following ...
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3answers
161 views
Why use transfer functions than differential equations?
I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths.
Why we use ...
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1answer
100 views
Audio transfer function modelling with pink noise + signal
I'm trying to model a transfer function for a noisy audio system, specifically to measure delayed system response. Before I can confidently apply control, I need to verify that I can exert control ...
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1answer
63 views
Natural frequencies of a transfer function
I have been told in the university that the natural frequencies (also called $\textit{eigenfrequencies}$) are the poles of the transfer function, however, Matlab compute them as the modulus of the ...
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1answer
65 views
Poles and zeros in time domain of analogs filters
I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
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145 views
How to find transfer function of a logarithmic or power function?
I'm dealing with logarithmic system $\log_{10}(y(t)) = m \log_{10}(x(t)) + b$, and I need to find the transfer function, $Y(s)/X(s).$
What is the Laplace transformation of $\log_{10}(f(t))$?
What I ...
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3answers
278 views
Distinguishing FIR and IIR from difference equation
Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$
I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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1answer
44 views
Evauating response to $x(n) = \sin{2\pi\frac{1}{4}n}$ given the system function
Let the input signal $x(n) = \sin{2\pi\frac{1}{4}n}$ go in to the system described by: $$y(n) - y(n-1)+\frac{3}{16}y(n-2) =x(n).$$
What is the output signal?
I've calculated the system function $H(...
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2answers
212 views
Phase function of filter
I have a filter with the transfer function
$$H(z) = 1 - 2z^{-2} + z^{-4}.$$ The task is to find the phase function $\theta (\omega).$
My attempt is to start by expressing the frequency response
\...
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0answers
66 views
How do I convert a two-pole two-zero transfer function from the s-domain to the z-domain?
I'm trying to convert the following IIR transfer function from the s-domain to the z-domain:
$$
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
36 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
448 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
26 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 ...
