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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Periodicity of transfer function of FIR filter proof (Parks and Burrus, Digital Filter Design)

In Digital Filter Design by Parks and Burrus, p. 19. The transfer function of an FIR filter is given by the $\mathcal Z$-transform of $h(n)$ as: $$H(z)=\sum_{n=0}^{N-1}h(n)z^{-n}$$ (where $h$ is ...
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Power/Amplitude Response of a system

I am currently looking over filters and understand the frequency response of a system, e.g. a low-pass filter. However I am confused by the 'Power/Amplitude response' of a system as detailed in my ...
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Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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Inverse $\mathcal Z$-transform of rational functions

What will be inverse $\mathcal Z$-transform for this function: $$H(z) = \frac{\left(1+\beta z^{-1}\right)\left(1+\beta z\right)}{\left(1+\alpha z^{-1}\right)\left(1+\alpha z\right)}$$
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How to plot magnitude and phase response by hand if I have the Transfer Function?

I have the transfer function of the system, which is: $$H(z) = \frac{1-z^{-1}}{5(1+2z^{-1})}$$ How do I sketch the magnitude and phase response? I'm sorry for the bad formatting, it's my first time ...
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Behaviour of the poles in transfer function $H(s)$, given system properties

If a linear system is causal and its impulse response is an energy signal. What's the behaviour of the poles of $s$-domain transfer function $H(s)$?
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Transfer function sinusoidal response

Why does the phase shift between the input and the output of a transfer function vary with the frequency of the input sinusoid?
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How to eliminate audio device transfer function from recording?

I'm working on a project which requires analysis of filter transfer function of vocal tract. The vocal tract is excited by a source signal that is a frequency sweep. The source signal is provided ...
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Asymptotic bode plots

I am really struggling to see how the lecturer took this transfer function and produced the bode plot that I have in my notebook. It is not the plotting so much that is confusing, I just don't ...
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How to use deconv() instead of roots() on MATLAB to find roots to a polynomial [closed]

I recently read that for polynomials of degree 5 or more, when executed with the roots() command on MATLAB produces an error. The documentation said as follows: As a substitute, using the deconv() in-...
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Inverse $\mathcal Z$-transform of system with an 8th order pole

Can I find the inverse $\mathcal Z$-transform of this transfer function: $$H(z)=\frac{1}{1-\alpha z^{-8}}$$ in a way other than contour integration and finding the residues of the 8 poles? If so, how?
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Transfer function from experimental time domain data

I have two sets of time domain data. One is the input to a system and the other is its corresponding output, both measured at the same sampling frequency. How to calculate the system's transfer ...
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Parameter identification for PI controller

I have a PI temperature controller being used in experiments, which I am also trying to simulate. However, using the proportional gain and integral time as used in the experiments gives different ...
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Calculating the product of discrete transfer functions

I'm trying to construct a higher order IIR from a biquad cascade, I know this is generally frowned upon, but it's necessary as the coefficients will be embedded into a larger formula used in a FDTD ...
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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 ...
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Determining type of filter given its equation

Given a general filter equation, how can one tell the type of filter that the same equation represents? Meaning how can I know if the filter is Low/High/Band Pass etc...? For example, the following ...
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DFT/FFT Transfer function

I want play and record a sine sweep. When i have both signals the recorded one and the send one i can create a Transferfunction. That is what i know so far. $$ H_0 = \frac{OUT}{IN} = \frac{Y}{X} $$ ...
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Question regarding transfer functions and prerequsities for finding the real impulse response

The transfer function of a system is given by: $$\large H(s) = \huge \frac{V_{out}(s)}{V_{in}(s)}$$ In digital domain the principle is of course the same, just replace laplace transform with z-...
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Response of a system to a step function (heaviside)

I'd like to compute the response to a step function of a electrical/thermal system. Generally I can "easily" compute the transfer function $H$: $$H(\omega) = \frac{V_{out}(\omega)}{V_{in}(\omega)}$$ ...
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What is the transfer function of this block diagram

I and my friend have different answer for this block diagram Mine: $$y[n] = -\frac23x[n] + x[n-1] -\frac12[n-2]$$ Hence $$H(z) = \frac{1}{-\frac23 + z^{-1} -\frac12z^{-2}}$$ My friend: $$q[n]=x[n]-...
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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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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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Calculating frequency and damping ratio from transfer function given eigenvalues

I have the following standard transfer function for a damped linear oscillator: $$G(s) = \dfrac{\omega_0^2}{s^2 + 2\zeta\omega_0s + \omega_0^2}$$ Now I have two eigen values at locations $-100 \pm ...
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Finding minimum-phase/allpass of transfer function

I am trying to find the minimum-phase system of the transfer function $H(z) = \frac{2 + 3.125z^{-2}}{1-0.9z^{-1}+0.81z^{-2}}$. I know I need to find and remove the allpass (basically reflect the two ...
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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{align} \theta[k+1] &= A \theta[k] + B u[k]\\ y[k] &= C \theta[k] \end{align} I know that the equivalent transfer function can be found by ...
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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: https://dsp.stackexchange.com/questions/24381/derivation-of-transfer-function-from-bode-plot Anyway, I thought I would ...
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756 views

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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338 views

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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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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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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343 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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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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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 to ...
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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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571 views

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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695 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] = 2t[n]-x[n-1]-y[n-2]+x[...
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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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824 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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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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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 filter ...
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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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956 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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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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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 '...