# 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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### Impulse response of IIR low-pass filter

(Disclaimer. I have started doing some DSP. The last time I worked with this was in the eigthies. And I wasn't much of a specialist then, either.) Is the impulse response different for IIR and FIR ...
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### Find transfer function from frequency and phase response [duplicate]

Given a desired frequency and phase response, is it possible to find a transfer function that matches/approximates both the frequency and phase response? Basically once you have a Bode plot, invert it ...
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### Calculate the Gain of a fixed-point filter

As the title already says, I would like to know how to calculate the Gain and Phase of a given fixed-point filter at a given frequency. What I've achieved so far: Let's say for example that I have a ...
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1 vote
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### Matlab: How to design digital equivalent for a lowpass Bessel filter (Thiran filter)?

In the process of applying a lowpass Bessel filter to my signal, I realized that besself function does not support the design of digital Bessel filters and the bilinear function can be used to convert ...
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### Alternative derivation for a Thiran filter

Following this reasoning (link on ee.se) I'm trying to derive the transfer function for a Thiran filter, but I get stuck. I know of the original paper, I just thought I'd go this way. This is what I'm ...
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### Normalize Bessel filter

I am applying a low pass filter to my signal and I should make sure the transfer function of my filter is one. How can I normalize my filter? I am learning about filters and I appreciate any help. <...
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### L1-norm of a stable, proper but not strictly proper transfer function

in the literature I find the statement, that the L-norms exist for every strictly proper and stable transfer function. I ask myself, if the L1-norm also exists for a transfer function, that has as ...
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### How do I calculate offset functions of these circuts? (Matlab results vs analytical results vary)

I am trying to calculate offset functions of these circuts but, the offsets results I got from matlab vary from those I calculated in python(analitically). So I have three circuts, and after each ...
1 vote
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### Scipy tf2zpk doesn't return zeros

I have the following transfer function: $$H(z) =\frac{\alpha z}{(z-(1-\alpha))}$$ I'd like to find zeros and poles of it by scipy.signal.tf2zpk: ...
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1 vote
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### Simulated Room Transfer Function

I need help obtaining a simulated transfer function in a simulated room. I have created image sources for first and second order reflections, and am assuming a point source for my source. I have the ...
1 vote
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### What is the difference between sending pulses and modulating waves?

If you look for amplitude, frequency, phase modulation, you typically get some picture saying you have a wave and you modulate the corresponding parameter (amplitude, frequency, phase). On the other ...
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### How to design fir filter from transfer function

Transfer function is this equation in frequency domain: $$G(f) = \frac{1}{4\pi d} e^{i2 \pi d f/c}$$ or Hankel function d : constant (distance), c : 340 We may think we know complex number of ...
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### What is the transform of δ(5t)?

So my question is here: How to transform the function $\delta(5t)$? I know that this function when is transformed on Fourier it will be $1$, but the $\delta(5t)$ is going to be and this $1$ or ...
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### Phase of DTFT transform of impulse response

I am approaching to the study of FIR systems. In particular, I was analyzing the graphs of amplitude and phase of the transfer function, when I had some trouble understanding how the phase behaves. ...
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### Discrepancy in frequency response of biquad filter (in Python)

I have written a simple biquad filter class but when I check its frequency response, I get different results with different methods. If I check it "empirically" (by taking the FFT of its ...
1 vote
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### Error in the computation of PSF?

I am in trouble computing a PSF of an optical system in optical turbulence. Background The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
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### How accurate is the dominant poles approximation in higher order control systems?

From what I have learnt from control systems classes, the dominant poles of a system are those that can be used to analyze a higher order system in terms of the formulas of a 2nd order system. I took ...
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### Find Transfer Function and Appropriate Coefficients of the Transfer Functions from Pole Zero Plot

I got a Transfer function problem and I am confused in finding a solid solution step. Below is the problem description: 1st and 2nd order discrete-time filters with different pole-zero locations shall ...
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### Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab

I have been given an input and output signal. input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1) output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n). or x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
1 vote
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### Measure Frequency-Response of Sensor using a Signalsource and Reference-Sensor

Cheers, I want to measure the frequency response of an acceleration sensor. I have: A signal source (device similar to a loudspeaker that shakes the acceleration sensor), of which I do NOT know the ...
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### Recursive equation Of Euler's Backward PID With Derivative Filter

I'm doing the implementation of the PID with derivative filter using the Euler's backward method, but I got stuck in this part since I have z in the denominator of most terms. I didn't realize yet how ...
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### How to find response of step function in matlab and plot transfer function?

I have an transfer function: $$\frac{Y(s)}{F(s)} = \frac{s^2+2s+3}{s^4+6s^3+13s^2+12s+9}$$ How can I find $Y(s)$ response of step function if $f(t)=\sin(5t)$ in MATLAB. And how can I plot the transfer ...
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### Determine transfer function based on a diagram with ai coefficients given

From a diagram with input $x(n)$ a summer and three feedback delay taps I get the difference equation... $$y(n) = x(n)+a_1y(n-1)+a_2y(n-2)+a_3y(n-3)$$ Then I am given values for ai coefficients. Case1:...
1 vote
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### How to estimate multidimensional linear response function from measured input and output signals?

Problem definition: I measure N sources of noise $x_i$ and one output signal $y$ which contains real signal $y_0$ plus noise from all these sources $x_i$ transformed by linear response functions $h_i$ ...
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### What does it mean for a transfer function to have multiple sets of zeros in the numerator?

I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
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### Phase Response of $N$-th order Digital All-Pass Filter

I am having trouble reconciling my derivation of the phase response of an N-th order all-pass filter with those I am finding in the literature, and I figured someone here could help me. Real Version: ...
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### Transfer functions for Scipy and Matlab's Butterworth filter don't seem to match theory

The squared transfer function for a Butterworth filter of order $n$ should be $$|H(f)|^2 = \frac{1}{1+\left(\frac{f}{f_c}\right)^{2n}}$$ where $f_c$ is the cut-off frequency. (Here's one of many ...
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