Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [transfer-function]

Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.

25
votes
2answers
4k views

Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
15
votes
3answers
24k views

How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
15
votes
1answer
1k views

How to deal with a negative pole (unstable) in the pre-filter of a control system?

So while answering how to design a PI controller for a first order time delayed system (Question Here ) Here is the closed loop equation to a control system: $$ G_C(s) = \frac{\frac{K}{T}(1-sT)(s)...
10
votes
3answers
8k views

How to estimate a transfer function from a magnitude-only frequency response?

Given an arbitrary frequency response, what signal processing methods might exist that could guess, estimate or determine a transfer function (pole and zero constellation) which gives a "reasonably ...
7
votes
2answers
11k views

What is the relation between the PSDs of filter input and output called? $R_Y = |H|^2R_X$

If a wide-sense stationary signal $X$ is fed to an LTI filter with the transfer function $H$, the power spectral density (PSD) of the output $Y$ can be expressed as: $$R_Y(f) = \left|H(f)\right|^2R_X(...
7
votes
1answer
2k views

Converting mel spectrogram to spectrogram

I have a set of songs for which I extracted the STFT (Short-Time Fourier Transform) and used the magnitude spectrum $|S|$ to calculate the mel spectrogram by using a mel filterbank matrix $M$, so $X=\...
7
votes
4answers
368 views

Does instability make an otherwise LTI system nonlinear (or time-variant)?

I am spinning this question off from the question from johnny. Matt L. and I have had directly opposite conclusions to johnny's question. I want to decouple the question from issues of causality and ...
6
votes
1answer
206 views

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 ...
6
votes
1answer
9k views

How to find frequency response, stability, and causality of a linear system?

I have the following transfer function: $$H(s)=\frac{s}{(s+1)(s+2)}$$ How can I find the gain and phase response of the above system? I know the first step has something to do with substituting $s = ...
5
votes
1answer
4k views

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 ...
5
votes
1answer
299 views

Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
5
votes
1answer
2k views

Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
5
votes
2answers
550 views

Understanding $\mathcal Z$-transforms and pole locations

I am trying to gain a better understanding of pole locations in the $z$-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the $\mathcal Z$-...
5
votes
1answer
697 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 ...
5
votes
2answers
2k views

Inverse system in Simulink

I have the following inverse system $$G(s)= s^2 + 2s + 3$$ How do I implement it in Simulink? Note that the transfer function is only accepted if and only if the order of the numerator is less than ...
4
votes
2answers
770 views

Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...
4
votes
2answers
262 views

Can I determine a system's $z$-domain transfer function from its pole-zero plot?

Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
4
votes
3answers
3k views

Anti-causal systems

If Anti-causal systems are defined as those whose output depends solely upon future inputs.(Is this definition correct as I understand) So i see that $y[n] = x[n+2]$ ; is anticausal system How is a ...
4
votes
2answers
3k views

Estimate the transfer function of an unknown system?

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
4
votes
2answers
61 views

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 ...
4
votes
2answers
84 views

Why does this transfer function has a second zero

I'm learning about $\mathcal Z$-transforms in DSP and I have a transfer function of the following form: $$H(z)=\frac{2-3z^{-1}}{1-1.6z^{-1}+0.8z^{-2}}$$ When I calculate zeros and poles of this ...
4
votes
2answers
1k views

Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
4
votes
2answers
2k views

derivative filter transfer function

In many of the papers it is said that the derivative filter transfer function is given by: $$H(z) = \dfrac{1}{8T}\left(-z^{-2} - 2z^{-1} + 2z + z^{2}\right)$$ But no one gave the detailed information ...
4
votes
2answers
3k views

How to find poles of transfer function by looking at the step response?

How to find poles of transfer function by looking at the step response? Given a step response graph like such: How would I find the sketch for its poles on the complex plane? The only thing I can ...
4
votes
2answers
909 views

How to establish transfer function of a speaker?

I'm working on a signal processing project about vocal system, and I'm trying to use controlling theories to solve the problem. I need to get the transfer function, $H(s)$, of a speaker, from ...
4
votes
1answer
4k views

Transfer function determination from input and output data

I have some input and output data that I believe adequately includes excitation of the important dynamics of a system. I know it is at most a 4th-order transfer function. How can I identify the ...
4
votes
1answer
4k views

Applying a filter on an audio signal with Python

Let's say I have a filter described by its transfer function: $$ H(\omega) = \frac{1}{1 + j\frac{\omega}{\omega_0}} $$ And I want to apply this filter to an audio signal (a .wav file) using Python. ...
4
votes
3answers
401 views

How do optical anti-aliasing filters work from a frequency domain perspective?

To prevent aliasing caused by the finite number of pixels on a sensor, a blurring filter is commonly used. How does that work from a frequency domain perspective? What is the transfer function of such ...
4
votes
1answer
1k views

Measuring the open loop transfer function in closed loop: what's the better approach?

Considering the closed loop system; $C$,$G$, and $H$ all linear and stable transfer functions, If I chose to excite $\bf r$ and measure $\bf e$, I get the Sensitivity Function, $S$ $$S=\frac{1}{1+CGH}...
4
votes
1answer
149 views

How can the order of a transfer function be derived from its equivalent state space representation?

Suppose I have a discrete state space model: \begin{align} \theta[k+1] &= A \theta[k] + B u[k]\\ y[k] &= C \theta[k] \end{align} I know that the equivalent transfer function can be found by ...
4
votes
2answers
752 views

Transfer function estimation from logarithmic sweep frequency response data

I have complex frequency response data (of an analog system) in the range of 100 Hz to 100 GHz, and it is sampled in frequency with logarithmic spacing. I would like to be able to turn this into a ...
4
votes
1answer
702 views

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 ...
4
votes
7answers
14k views

Why more poles than zeroes?

I read that an "improper system" "has more zeros than poles; it is not causal, cannot be implemented, has a strictly proper inverse and has infinite high-frequency gain." Does causality fail due to ...
4
votes
0answers
426 views

Attempting to use the trapezoidal rule to form a difference equation representing a circuit

I have a differential equation that has been proven to be correct. The transfer function obtained by Laplace domain analysis and Matlab freqs match up and all is well. The problem is somewhere in ...
4
votes
0answers
193 views

Digital control: Exercise solution

Can you help me (show me how) to solve the following exercise? For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
3
votes
3answers
3k views

What is the relationship between poles and system stability?

I see two notions that describe the relationship between poles and system stability. But they are not the same from my understanding The system is BIBO stable if and only if all the poles are in the ...
3
votes
3answers
2k views

Digital filters with more zeros than poles

I am having trouble wrapping my head around digital filters with different orders of numerator and denominator. Let me know if any of these points is wrong: All (digital or analog) transfer ...
3
votes
2answers
3k views

Finding the frequency response of a filter defined as a Z-domain transfer function

I am software engineer studying DSP on my own. I came across this question in a graduate textbook and am not sure how to proceed. ...
3
votes
2answers
3k views

How to compute the impulse response from a transfer function

Say I have a transfer function, for example: $$H(z)=\frac{1}{1+0.1z^{-30}}$$ How can I compute the impulse response? (This is just an example, the important thing is that it is in closed symbolic ...
3
votes
2answers
498 views

What is the general form of a transfer function

I repeatedly see two representations of the general transfer function in the literature. The first is the following which is factorization of the numerator and denominator polynomials: $$\textbf{G}(s)...
3
votes
2answers
3k views

Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
3
votes
5answers
2k views

What is the transfer function of a moving average?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
3
votes
1answer
2k views

Poles and zeros of a transfer function

What are the poles and zeros of this transfer function (in $z$): $$H(z)=z+2+z^{-1}$$ and how would you approach the resolution of such problem? Personally, I would write $$H(z)=\displaystyle\frac{...
3
votes
2answers
125 views

What do we know about the transfer function away from its zeros?

So lets say I have a transfer function for an FIR filter $H(z) = (z-a)...(z-n)$ where $a,...,n$ are points along the unit circle. But what about other points along the unit circle that correspond to ...
3
votes
1answer
323 views

Can someone explain waveshaping to me?

Can someone explain waveshaping to me? I only know it shapes waveshapes by passing through some functions, but I don't yet understand e.g. what the plots (such as the following in Melda Production ...
3
votes
2answers
469 views

Control design: under what conditions can closed-loop poles be placed arbitrarily?

Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
3
votes
1answer
170 views

Find state space model from transfer function

Let's suppose we have: G(s) = (s+1)/(s^2-2s+1) how can we find the state space representation of the transfer function: x_dot = x2 x2_dot = 2*x2-x1+u where u is an arbitrary input. I am very new ...
3
votes
1answer
492 views

Bandpass general equation to difference equation

I know this is a very basic question and I am coming out from a quarter of DSP. I want to create a function in Java which can taken in two parameters, either ...
3
votes
2answers
648 views

Response of a system to a step function (heaviside)

I'd like to compute the response to a step function of a electrical/thermal system. Generally I can "easily" compute the transfer function $H$: $$H(\omega) = \frac{V_{out}(\omega)}{V_{in}(\omega)}$$ ...
3
votes
1answer
107 views

Build discrete IIR from a transfer function which is not in terms of $s$

Firstly I should state that my maths knowledge is limited. I'm currently designing an acoustics modelling application which uses a rectilinear FDTD grid for modelling pressure variations - but I've ...