# 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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### 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 ...
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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 ...
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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: Y(s)/F(s) = (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 function? Thank ...
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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:...
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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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### Who first coined "Direct Form I" and "Direct Form II"?

I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
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### Filter a signal with a complex dB SPL filter

I've been tasked with filtering a sound with a filter that looks something like this. I don't have any real DSP training, so I'm not sure if my attempt at tackling this is correct. I can filter ...
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### Definition of frequency response

I studied various signal processing materials for a long time, and I have a question. Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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### Seemingly no division operation is done of the diagram of the transfer function

Given the below system. $$y\left[n \right] =2 x\left[n \right] -x\left[n -1\right] +0.5 y\left[n -2 \right]$$ We'll find out the transfer function of it. So, easiely using z-transform,  Y(z) ...
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### Filter odd or even harmonics with notch or inverse notch filter

Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ...
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### Real Data Complex Transfer Function using H0, H1, H2 Estimators

BACKGROUND: This question is attempting to consolidate material discussed in two previous topics. These are: Understanding the H1 and H2 estimators @Pontus S Frequency-domain deconvolution: "...
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### Coupled system instability

Suppose there are two linear devices (containing some multi-physics but the details don't matter here), and these devices are given to us as two black boxes that can be studied experimentally. Black ...
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### Stabilizing an unstable system and removing oscillations from step response

I have a system with the transfer function given in this MATLAB code ...