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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Z domain transfer function to difference equation
I want to convert this transfer function: $$\ \frac{2\cdot(z-0.5)\cdot(z-0.6)}{z-1}$$ to a difference equation, but I have no idea how.
Can someone help me?
Thanks,
Arjon
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System Response Terminology
If I have a system specified by
$$P(D)y(t)=Q(D)x(t)$$
and I specify initial conditions $y(0^-)=a, \ y'(0^-)=b,\ x(0^-)=c$ does the term $x(0^-)=c$ correspond to the zero state response or zero ...
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Calculating impulse response from transfer function
Given the difference equation as 𝑦[𝑛]=5𝑥[𝑛]+5𝑦[𝑛−2] and 𝑥[𝑛]=cos(𝜋𝑛).
I would like to obtain the transfer function h[n]. How is that possible manually and on Matlab?
Manually it should be ...
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Determine phase response from pole-zero plot
I know how to determine the frequency response from the pole-zero diagram given the following formula:
$\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
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Low pass filter transfer function
I am calculating the transfer function of a low pass RC filter and I have gotten $\frac{1}{1+jωRC}$ which is correct. But somehow it seems $ωRC = \frac {ω}{ω_0}$ that refers to the cutoff freqency ...
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Take a wavelet function as a transfer funtion
Is there anyone having the experience of taking the wavelet funtion as a transfer function?
That is:
if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
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Region of convergence for discrete system
I am confused by two questions on the region of convergence (ROC) when applying the $Z$-transform.
Consider a discrete-time linear system $$x[n+1] = Ax[n]+Bu[n], \qquad y[n]=Cx[n]+D$$ whose transfer ...
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What is the zero in this transfer function?
What is the zero for the following transfer function, $-1/2$ or $-2$?
$$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$
This appears to give a zero of $-1/2$.
I can transform this into the standard form ...
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Poles and zeros representation in s-plane
We have a filter (or a system) that has two poles at $f_{p1} = f_{p2} = 20$ GHz and one zero at $f_{z1} = 15$ GHz. Let's assume the gain is $K = 1$. Then how do you mark these poles and zero in the ...
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Transfer function from poles and zeros
If we know that a filter (or a system) has two poles at 20 GHz and one zero at 15 GHz, then how do you write the transfer function $H(s)$ for such a system?
I am wondering why sometimes the poles and ...
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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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0answers
37 views
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
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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
54 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
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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
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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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1answer
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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
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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
83 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
51 views
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
94 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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0answers
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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
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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
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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
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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
92 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
317 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
68 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
63 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
152 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
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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$$\mathbb{R}$
How we can ...
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1answer
160 views
FIR Impulse response & transfer function
I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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Sound equalization : assumptions around the use of the transfer functions. Are they correct?
I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check.
1/ I'm ...
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1answer
67 views
How do I plot the square of the amplitude response?
I have calculated the transfer function of an FIR filter
$$
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)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?
For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
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1answer
242 views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$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
217 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
119 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 ...
