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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5k 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 $A(s)$ ...
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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? ...
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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)...
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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 ...
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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=\...
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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(...
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1answer
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Digital filter coefficients from low-pass to high-pass

Given I have coefficients a0, a1, a2, b1, and b2, defining the difference equation for a digital filter as: ...
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What Is the Transfer Function of a Moving Average (FIR Filter)?

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 ...
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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 ...
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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 ...
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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 ...
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Basic Questions on Wiener Filtering

I read a lot about Wiener Filters (focusing on discrete time case). I understand the math, but I am quite disconnected from the real life assumptions behind using such a filter. Unfortunately ...
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1answer
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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 ...
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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 ...
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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 ...
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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 = ...
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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{...
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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 ...
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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 ...
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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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Transform Function with Non Linearity

I'm a newbie to Signal Processing - my apologies if this question is too obvious (I'm a financial trader trying to use DSP techniques). For a linear filter: $y[n] = (1-p) x[n]+p y[n-1]$ we can the ...
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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 $\mathcal Z$-...
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how to find frequency response of microphone

hello I want to find the frequency response of a microphone. I give the input signal to my speaker and it produces a specific SPL with specific frequency. on the other side, I read the microphone ...
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1answer
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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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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 ...
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1answer
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Unstable plant transfer function identification

I would like to find the transfer function of an unknown unstable SISO plant. If it was a stable plant, I would input a sine sweep and measure the frequency response at the output; but I cannot do ...
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1answer
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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. ...
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1answer
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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 ...
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Uncountable Set of Poles?

It is easy to define an (ideal) LTI system that would have an infinite number of poles - for instance, if the transfer function is $$ H(z)=\frac{1}{\cos(z)-1} $$ However, this would only define a ...
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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 ...
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3answers
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Is this system causal or not?

My efforts of solving this question are below. I came to a conclusion that this system is causal, since: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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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 ...
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2answers
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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?
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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
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1answer
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Transfer function with blackbox modelling is too slow compared to real expectation

I collected this data from a robot that drives with its wheels up. The blue curve is the voltage and that is my input. The orange curve is the wheel velocity and that is my output. I want to create a ...
4
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1answer
286 views

How do I get a faster system response?

I have this model in simulink (the graph is my output): The step input has amplitude 0.5 m/s, and it steps up after 0.1 seconds. The gain $K_p=5$. The saturation block is to keep the voltage between -...
4
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1answer
382 views

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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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
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1answer
474 views

Deconvolution Using Response to an Heavy Side

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU): I would like to get the "...
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2answers
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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 ...
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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
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1answer
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Finding the Transfer Function of a Multiplicative Distortion in MATLAB

I have the frequency response of two signals shown above. One is uncontaminated, and the other is the same signal contaminated by a multiplicative distortion with two poles and two zeros. I need to ...
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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
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2answers
988 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 $H$: $$H(\omega) = \frac{V_{out}(\omega)}{V_{in}(\omega)}$$ ...
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1answer
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Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
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1answer
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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
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3answers
675 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 ...
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1answer
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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}...
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1answer
152 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
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2answers
954 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 ...

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