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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How to differentiate a time domain signal in the complex transfer function?

I have an input-output data set where the input is current and the output velocity. I am interested in the transfer function from current to acceleration though. So suppose: $H(s) = \frac{I(s)}{V(s)}$ ...
624 views

Where does this star came from? [EDIT - Detailed Question]

First of all, it's a rare topic in google, so I can't find intuitive explanation about step-invariant, so I don't understand actually what it is, except to solve zero order hold transfer function. In ...
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Marginal Stability based on Poles

We know that a discrete-time system with a (Z-transform) transfer function that has a pole of magnitude 1 (i.e. $|z|=1$ is a pole of the transfer function) is marginally stable if the pole at $z=1$ is ...
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What are poles and zeroes (with respect to the inputs and outputs of a system)?

I get it, about poles and zeroes, when we talk in terms of the transfer function. But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the ...
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Find transfer function given impulse

I am given the following discrete time transfer function : $$G_d(z^{-1})=z^{-d}\frac{b_0+b_1z^{-1}}{1+a_1z^{-1}}$$ which has the following impulse response $$g_d[n]=\{0,1,-0.1,-0.05,...\}$$ How can I ...
519 views

A question regarding z transform and its magnitude response

My teacher of signals and systems gave us a review problem as following: given a DT rightsided LTI system with transfer function $$\frac{1-a^*z}{z-a}, \left | a \right |<1$$ show that the system'...
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FIR Filter - Transfer Function

I am dealing with the transfer function of an FIR filter: $$H(z) = (1-0.5z^{-1})(1-2z^{-1})$$ I am having trouble determining which type of Linear-phase FIR filter it is, Type 1-4. I believe it ...
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How to find analytic description of filtered signal

I am looking for an exact analytic description of a filtered signal. I have an electronic circuit whose input is a monoexponential decay. First (1) the signal gets filtered by a simple RC-Lowpass. ...
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Find the difference equation and draw the simulation diagram

Calculate the difference equation and then draw the simulation diagram of the below transfer function. $$H(z) = \frac{Y(z)}{X(z)} = \frac{0.4142 + 0.4142z^{-1}}{1.4142 - 0.5858z^{-1}}$$ I ...
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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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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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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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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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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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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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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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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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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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A question about the meaning of pole in time domain

Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as: $$H(s) = \frac{1}{s - (-1-j)}$$ So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good. Now ...
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How do optical illusions work (photo mosaic) from a signal processing perspective?

Hello fellow investigators I have two question about optical illusions 1) A photo mosaic is something like this: What are the signal processing principles behind our eye merging the many tiny ...
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Difference equation to FIR filter coefficients

I have a difference equation $$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$ According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ...
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Is there a simpler way to calculate the amplitude response of the following filter

I would like to calculate the amplitude response $|H(z)|$, $z=e^{j\omega}$, of the following filter: $$H(z)=\frac{\frac{b}{2}+z^{-2}}{2+bz^{-2}}$$ and I would like to avoid using Euler's formula and ...
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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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Distinguishing FIR and IIR from difference equation

Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$ I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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Difference equation from a transfer function of a low pass filter

I need to get the difference equation from this transfer function: $H(z) = g \frac{1+a_1}{1+a_1z^-1}$ My math skills are too many years old, but I remember I need to get the Y(output) on one side and ...
I have rational transfer functions: $$H_1(z) = \frac{ b_0 + b_1z^{-1} + b_2z^{-2} }{a_0 + a_1z^{-1} + a_2z^{-2}}$$ $$H_2(z) = \frac{ q_0 + q_1z^{-1} + q_2z^{-2} }{p_0 + p_1z^{-1} + p_2z^{-2}}$$ And ...
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]-...