Signal Processing Stack Exchange
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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.

Transfer functions are commonly used in the analysis of systems such as single-input single-output filters, typically within the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear, time-invariant systems (LTI), as covered in this article.

Source: 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 $A(s)$ we substitute $$z =…
Phonon
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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? Secondly, the theory says that a system is stable when…
Val
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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)} { s^3 + (\frac{1}{T} + a - KK_p)s^2 +…
CyberMen
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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 good" approximation (for some given estimation…
hotpaw2
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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: y[n] = a0 * x[n] + a1 * x[n - 1] + a2 * x[n - 2] - b1 * y[n - 1] - b2 * y[n - 2] Which defines a low-pass filter with particular cutoff…
user2649681
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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 $X=\log(M\times |S|)$. I want to know is there any…
user76170
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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: $$R_Y(f) = \left|H(f)\right|^2R_X(f)$$ where $R_X$ denotes the PSD of $X$. Does…
user42
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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 disposal). One of the post processing used is a…
Sclrx
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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 converse true? That is, are there any LTI systems that…
Mike Battaglia
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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 other goofy stuff. So we have a simple…
robert bristow-johnson
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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 instant signal change? I try to make up a…
Val
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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 textbooks are just laying out the formulas without…
Cowboy Trader
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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 magnitude response and the phase response. I am…
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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 write Transfer Function as $H(z) =…
uday
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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 represented using State Space approach, the eigen values…
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