Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.

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How can the order of a transfer function be derived from its equivalent state space representation?

Suppose I have a discrete state space model: $\begin{eqnarray*} \theta[n+1] &=& A \theta[n] + B U[n]\\ Y[n] &=& C \theta[n] \end{eqnarray*}$ I know that the equivalent transfer ...
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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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Matlab's invfreqs won't fit at low frequencies

I'm wondering of anyone can explain why invfreqs() is unable to fit a polynomial to the data in the image below. The red line is the measured frequency response of an analog system. I should mention ...
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What am I doing wrong?-Bode plots to get transfer function

I've noticed a couple of similar questions which haven't been answered such as: derivation of Transfer Function from bode plot Anyway, I thought I would ask since it hasn't been answered. So as I ...
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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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Deconvolution using response to an Heaviside

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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Spectral Factorization of Magnitude Squared IIR

Taking an IIR: $$ H(z) = \frac {A(z)} {B(z)} = \frac {\sum_{n=0}^{N} a_nz^{-n}} {\sum_{m=0}^{M} a_mz^{-m}} \qquad z=e^{iw} $$ The magnitude squared of the numerator $A(z)$ (the maths of the ...
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derivation of Transfer Function from bode plot

I have some data from a device described in frequency domain (an accelerometer (second-order oscillator) plus a low-pass filter (in cascade)). I sketched the bode plot in Matlab. I must find their ...
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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 does the impulse response determine the transfer function of a system? [closed]

why does it describe the transfer function.. How come? Especially for LTI systems. I thinking about the theory about how come an impulse input can provide information about a complete system.. As it ...
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26 views

Phase plot in Bode Diagrams

I'm studying the transfer function of an aircraft that relates the pitch angle, $\theta$, with the horizontal stabilizer angle, $\delta$. $$ H(s) = \dfrac{\theta (s)}{\delta (s)}$$ I have computed ...
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31 views

Forecasting with ARMA models, from a filter point of view

ARMA models are afaik just filters with transfer function $ {MA(z) \over AR(z)} \equiv {FIR(z) \over IIR(z)} $ . However forecasters of stock prices, market trends ... seem to be mainly ...
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input output read/write frequency

I am trying to identify a system based on input/output response and thereby estimate a transfer function. I generated a frequency sweep function in Mathematica which gives me the discrete values of a ...
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45 views

Convert low pass continuous time filter design to bandpass, discrete time

I am trying to convert the continuous time transfer function of a second order lowpass Butterworth filter is given by: To a bandpass fourth order bandpass digital filter, I first apply the mapping ...
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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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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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80 views

Transfer function block diagram

Can any one help with the $y[n]$ and $x[n]$ relationship in this block diagram, I just keep have a $t[n]$ in my answer that I can't get rid off. On my best try I got to $y[n] = ...
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286 views

How to compute magnitude and phase response from transfer function in Z-domain?

I have a transfer function $$H(z)=\frac{1+1.2z^{-1}+0.8z^{z^-2}}{1-0.9z^{-1}}$$ from which I'm supposed to sketch the magnitude and phase response. I know that you can transform $z=e^{j\omega}$ to get ...
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Transformation of coordinate set

I have a problem in which i have a video that was taken from the side of the subject, something like this and i need to transform the coordinates of the subject to be as if the photo was taken from ...
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104 views

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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54 views

What is the transfer function $H_{xy}$ of this flow graph?

I am trying to get transfer function $H_{xy}$ from this graph. I managed to get the other one but I am struggling with this one. Any help or guidance? Thank you
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82 views

How to find transfer function looking bode plot

I have some Bode plot (only in amplitude) as these: Now, I must to find their transfer functions, in particular the exact value of their zeros and poles. It is clear that their are a low pass ...
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115 views

Obtain transfer function from signal flow graph

I have a pretty complex signal flow graph with all the blocks and the branches completely describing an analog filter, in the Laplace complex variable s. The signal $X(s)$ is the input and $Y(s)$ is ...
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44 views

Solving simple transfer function

I was hoping that you can help me understand how to find poles and zeros in this transfer function. $$ H(s)=\frac{1}{(s-s_{\alpha1})(s-s_{\alpha2})} $$ I know that this function does not have any ...
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Bode Plots and Unit Step Response

You can probably tell I'm pretty new to this; I'm trying solve this problem and this is what I think I need to do; multiply the transfer function by $ \frac {1} {s} $, then take the inverse laplace ...
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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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For a standard second order transfer function, what is the equivalent time domain significance of $\zeta>0.707$?

In frequency domain $\zeta>0.707$ implies no resonant peak in frequency response. But I am unable to correlate what is the exact time domain effect of this? If $\zeta=0.707$ acts like an ...
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499 views

How to compute transfer function (Frequency Response Function) from experimental data

I have a set of data, in the freqeuncy domain, corresponding to a structural test. I have amplitude, phase and frequency for both the measured output and the input signal (accelerations are measured ...
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71 views

How to find roll-off from its transfer function equation?

I want to find roll-off (unit dB/decade) of highpass filter $H(z) = 1 - a \cdot z^{-1}$. I derived magnitude response to be $1+a^2 - 2a\cdot \cos(\omega)$ To find out roll-off factor from above ...
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Why is my discretized transfer function unstable when my discretized state-space model is stable?

I am working with a 30-state, 14-input linear model that is described by a state-space model: model_state_space = ss(A, B, C, D); The model is extremely slow (it ...
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301 views

Biquad Filter Transfer Function Frequency Response

$H(z) = G\cdot\displaystyle\frac{2b_0\left(1-z^{-2}\right)}{1-2a_1z^{-1}-2a_2z^{-2}} + 1$ I have a data sheet with the above transfer function, I need to calculate its frequency response in code. I ...
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Symmetry of Walsh matrix

Walsh matrix is abtained by sorting the rows of Hadamard matrix by number of sign changes (1st row had 0 changes, 2nd has 1 change of sign etc). Walsh matrix is symmetric. Meaning the sorting the ...
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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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Gonzalez question solution

If I have the histogram of an input image as Gaussian probability density function of the form: $$P_r(r)=\dfrac{1}{\sqrt{2\pi}\sigma}e^{-\dfrac{(r-\mu)^2}{2\sigma^2}} $$ where: $\mu$ and $\sigma$ ...
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Equivalence of FFT and PSD based output based on the Frequency Response Function

Correct me please if I am wrong... I have just started working in the domain of signal processing using the Fourier Transform ($\mathbf{FFT}$) and Power Spectral Density ($\mathbf{PSD}$). I am trying ...
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Hardware Transfer Function Estimation

Suppose you have the ability to inject any arbitrary waveform into a piece of analog rf hardware and collect and digitize the output for analysis. If you wanted to characterize/estimate the transfer ...
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154 views

Lorentzian signal fit

A plot showing two S21 peaks through a resonator is given below: As you can see, the first resonance peak occurs at 4.43GHz. The fit applied to this peak is given below. $$y = A - 10 \log_{10} ...
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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 ...
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Stability of transfer function

Now K(s) is obviously the negative feedback loop which is ${H(s) \over 1+H(s)G(s)}$ When I substitute ${H(s) = {1 \over s-2}}$ I get K(s) = ${ 1 \over s-2 +G(s) }$ For the system to be stable ...
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Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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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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Block diagram transfer function of a line

What is the transfer function of a line, can i ignore it? After simplification i got the diagram: I don't know what to do with the empty feedback
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IIR filter SOS and Direct Forms doubt

I have below doubts, so confusing! As I don't want to assume from what I read, I am asking for help here! Are Second Order Sections another name for biQuads ? If I have 2 single pole transfer ...
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Given input and output time series, obtaining filter design

Say I have 5 minutes of input and output audio. One method I know is to do FFT on windows from input and output. Then divide FFT output into bins and find average energy in various bands for all the ...
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259 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
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Describing a time delay at a maximum for maxima and minima but tends to 0 elsewhere

I have two force-time signals obtained from a couple of force plates, corresponding to input/output signals for some system. Plotting the two together one of the first things I noticed was a time ...
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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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Obtaining an expression for the transfer function when using FFT

Say I have two signals, a(t) and b(t) where the former is the input and the latter in the output. These signals are both recorded by sampling at every 0.01s. The Fast Fourier Transform was applied to ...
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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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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 ...