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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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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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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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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How frequency response related to a transfer function

Can anyone explain how frequency response related to a transfer function?
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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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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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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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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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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 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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Use Butterworth and Chebychev filters

I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters. I'm developing in C++ with Qt, and I'm looking for algorithms ...
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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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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 ...
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Output of a system given it's transfer function and input (beginner)

I have an exercise that gives me the transfer function of a system $$H(s) = \frac{3s^2+27}{s^4+8s^3 + 16s^2} $$ and an input $$x(t) = \frac13 cos(3t) $$ An ask's what is the output I don't whant ...
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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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determining type of filter given its pole zero plot

How can I classify a filter given its pole-zero map. For example I've got my zero's located at $\pm j$ and my poles located at $\pm\frac{1}{2}j$.
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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 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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Determining the Filter Coefficients of an FIR Filter

I need to find the filter coefficients of an FIR filter that will block sinusoids of frequency $200\ \rm Hz$ if the sinusoid is sampled at $1.2\ \rm kHz$. I feel like this is a fairly simple problem,...
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Why does this transfer function estimation not work? System identification

Goal: I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses. Method: I begun first with creating the ...
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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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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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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 ...
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Calculation frequency response of digital filter with known structure

Short question What are main stages (steps) of calculation frequency response of digital filter by their structure? Detailed question Let suppose that there is discrete FIR filter with known ...
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Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $ 0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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Relating transfer functions with step responses

Relate the transfer function to its' corresponding step response. First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...
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transfer function of wiener filter

I am trying to understand the function of a Wiener filter. I get that the Wiener filter minimizes the mean square error between the estimated random process and the desired process. Does this mean ...
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Transfer function of double exponential smoothing?

Double exponential smoothing a.k.a. Holt-Winters smoothing tracks level and trend of a time series in coupled IIRs: $\qquad$ In: $Y_t$, t = 0 1 2 ... $\qquad$ State: $L_t, T_t \quad$ -- level and ...
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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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Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler integral ...
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Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
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How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
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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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How to invert FFT these magnitude equations to get FIR filters?

I need filter designs that will reproduce or approximate each of the following: 1) ${\rm magnitude} = e^{-cf^{2}}$ 2) ${\rm magnitude} = e^{-\frac{a+b\sqrt{gf}}{df}}$ Where: $a$, $b$, $c$, $d$ and $...
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Can I use Fourier transforms instead of Laplace transforms (analyzing RC circuit)?

I don't study electrical engineering or something related but I was assigned a problem on transfer functions, impulse responses, and in general, everything related to this post. (Specifically, I'm ...
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How to find analytic description of filtered signal

I am looking for an exact analytic description of a filtered signal. I have an electronic circuit whose input is a monoexponential decay. First (1) the signal gets filtered by a simple RC-Lowpass. ...
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Convolution with an impulse response does not give the same result as the frequency response

Context I am trying to design a linear-phase FIR filter with the following frequency and phase responses: Designing the filter Given its characteristics (peak filter at 1kHz with 9dB gain and Q=7), ...