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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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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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What is the formula to convert from continuous-time transfer function to 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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How does works the transfer functions in the “cookbook formulae for audio EQ”?

To try to understand the audio filtering, I'm working with those two documents : Introdution to digital filters with audio applications Cookbook formulae for audio equalizer biquad filter ...
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Relationship of frequency response $H(\omega)$ to actual cycles per second

As a part of a signal processing course we were instructed to construct a filter that dampens the frequency $\pi/3$. I was succesful, but being a music geek, I began to wonder. The response curve of $|...
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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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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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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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LTI system insensitive to vertical shift

I have a biological signal which I want to model with $y_k=\alpha y_{k-1}+\beta u_k$. Here's what the original signal (grey) and the model (red) may look like. Params $\alpha, \beta$ and $y_0$ were ...
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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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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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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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MIMO Phase response

In the SISO case a Bode plot collects the frequency and phase response. In the MIMO case a Bode plot exists for each input/output combination which, however, neglects coupling. But with the help of ...
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Likelihood / Error of a Zero Input Sequence

How can I measure how well a known system describes an unknown sequence? In my work I need to evaluate how likely a particular observation sequence is given any parameterization of an LTI system. The ...
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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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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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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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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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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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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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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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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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Comparison of different methods to calculate transfer functions

I have input and output data (x and y), the signal I am interested in is on y but it is noisy. The noise is coherent and also recorded by x. I am trying to remove the noise using a transfer function (...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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What is the transfer function of this system y(n) =2y(n-1)?

What is the transfer function of this system y(n) =2y(n-1)? Here there is no input dependence. If you give one output sample, all the future output samples are determined by multiplying with 2.
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How to differentiate a time domain signal in the complex transfer function?

I have an input-output data set where the input is current and the output velocity. I am interested in the transfer function from current to acceleration though. So suppose: $H(s) = \frac{I(s)}{V(s)}$ ...