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

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DTFT and Inverse DTFT Homework Problem

I'm trying to solve this signals homework problem: So for part a, since multiplication in the time domain is convolution in the frequency domain, I just used a DTFT table, found the DTFT for $\left(...
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Bandpass general equation to difference equation

I know this is a very basic question and I am coming out from a quarter of DSP. I want to create a function in Java which can taken in two parameters, either ...
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Proof of transfer function factorization $\frac{b_0}{a_0} \frac{\prod_{k=1}^M (1-c_kz^{-1})}{\prod_{k=1}^N(1-d_kz^{-1})}$

This is from Oppenheim's Discrete-Time Signal Processing, but the book doesn't seem to describe how the factorization is done. The transfer function: $$H(z)=\frac{Y(z)}{X(z)} = \frac{\sum_{k=0}^M ...
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System identification/ Filter estimation to mimic frequency equalizer of audio with Scipy

At the current problem I'm working on, I have two signals: One "original" signal that contains audio (voice). The second signal is the same audio file but edited with a frequency equalizer, for ...
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59 views

Amplitude transfer function

Given a LTI-system $$y[n]=x[n]-2x[n-1]+y[n-1]- \frac{8}{9}y[n-2]$$ The transfer function $H(z)$ is: $$H(z) = \frac{1-2z^{-1}}{1-z^{-1}+ \frac{8}{9} z^{-2}} $$ How do I calculate the amplitude ...
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Measuring the open loop transfer function in closed loop: what's the better approach?

Considering the closed loop system; $C$,$G$, and $H$ all linear and stable transfer functions, If I chose to excite $\bf r$ and measure $\bf e$, I get the Sensitivity Function, $S$ $$S=\frac{1}{1+...
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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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Combined low pass and notch filter design

I designed low pass filter with cut-off frequency $5\textrm{ Hz}$ and notch filter with notch frequency of $50\textrm{ Hz}$ and the corresponding MATLAB code is shown below. ...
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25 views

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 transfrom

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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54 views

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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25 views

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() ...
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A 2 input 1 output model with time delay

What assumptions should be taken into consideration if I need to build a 2 by 1 black box process model on Matlab where the inputs samples I have are sampled each minute to result eventually after 1 ...
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43 views

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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38 views

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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Input/output for buck-boost converter controller implemented with FPGA

I'm not sure if this question is appropriate for DSP as I'm new to StackExchange, but I think it could be related. I am trying to implement a voltage controller for a buck-boost converter using FPGA. ...
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How to calculate the step response and transfer function

The output system is: $x(t)$ -->(S)--> $y(t) = \int_{-\infty}^{t}x(\tau) d\tau$ I am still not sure whether my work is correct, please some one advise me. I know that a step response is the ...
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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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What are the figures of merit/ performance measurements I can use for deconvolution?

I'm currently performing deconvolution on a bunch of 2D slices of fluorescent beads using MATLAB. Now I want to measure the performance of different deconvolution methods on the filtering of the PSF(...
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101 views

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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80 views

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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125 views

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[...
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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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36 views

Effect of sampling frequency on DFT?

I don't get it. I have the following form of the DFT: $$ Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1 $$ But this assumes that the sampling ...
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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: $\begin{eqnarray*} \theta[k+1] &=& A \theta[k] + B u[k]\\ y[k] &=& C \theta[k] \end{eqnarray*}$ 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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82 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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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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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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45 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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76 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 ...