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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1answer
261 views

Convolution with an impulse response does not give the same result as the frequency response

Context I am trying to design a linear-phase FIR filter with the following frequency and phase responses: Designing the filter Given its characteristics (peak filter at 1kHz with 9dB gain and Q=7), ...
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80 views

Correct transfer function with 1st order IIR filter

What diffreneces it makes in magnitude and/or phase response when using $$H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}}$$ by adding $b_2=0$, $a_2=0$ instead of $$H(z) = \...
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83 views

Generic response of an IIR filter from its transfer function

How can I derive the general response of an IIR filter from its transfer function? I know that: $$H(z)=\frac{1}{1+\sum\limits_{m=1}^N{a_m z^{-m}}}$$ Thus: $$Y(z)=X(z)H(z)=\frac{X(z)}{1+\sum\limits_{...
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Transfer function and difference equations: why does $H(z)$ numerator polynomial not correspond to $Y(z)$?

For a discrete time LTI system, I understand that from a difference equation description of the system in the form $$ \sum\limits_{k=0}^N{a_k y[n-k]}=\sum\limits_{k=0}^M{b_k x[n-k]} $$ I can ...
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186 views

1st order filter output

Two 1st order filters : ...
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1answer
795 views

What is $H_2$ and $H_{\infty}$ control? [closed]

I can create a Linear Quadratic Gaussian Integral(LQGI) controller very easy by using GNU Octave. LQGI is in the area of Optimal Control Theory. But there is something called Robust Control Theory. ...
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2answers
674 views

Could someone please explain how to get frequency response of a given Bode Plot?

Having trouble with bode plots. I understand that the is to be converted to $dB$ but after that I'm stuck. Could someone please show me how this graph gives a frequency response of $10/1+jw10$
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365 views

Design discrete controller for zero steady state error

I have the following system where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero? I know that this ...
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1answer
94 views

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 ...
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835 views

How to find out the transfer function of a FIR filter?

$$h[n]=\begin{cases}a^n & \text{if } 0 \le n < N \\ 0 & \text{otherwise}\end{cases}$$ And for which values of $a$ the filter is stable I know that the transfer function will be $$H(z)=\...
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1k views

Determine impulse response given input and output: which ROC?

Let's suppose I have to find the impulse response of a discrete time LTI system given a specified input and its output through the system. I think I'm going to get the $\mathcal Z$-transform of input-...
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What is the transfer function of a moving average?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
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222 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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Applying a filter on an audio signal with Python

Let's say I have a filter described by its transfer function: $$ H(\omega) = \frac{1}{1 + j\frac{\omega}{\omega_0}} $$ And I want to apply this filter to an audio signal (a .wav file) using Python. ...
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2k views

Poles and zeros of a transfer function

What are the poles and zeros of this transfer function (in $z$): $$H(z)=z+2+z^{-1}$$ and how would you approach the resolution of such problem? Personally, I would write $$H(z)=\displaystyle\frac{...
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How can I find the transfer function from this Bode diagram?

I've been given this bode diagram : I've been asked to find the transfer function only by using the bode diagram. It's the first time I'm doing this so here's what I thought. The starting value is ...
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First derivative analog filter

I'm reading about fault detection via signal processing in time domain. One possibility is to check that first derivative of the signal is in some predefined bounds. The text says that to obtain the ...
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1answer
536 views

Estimate transfer function from Bode curve

I have measured the magnitude response Y_mag(f) and phase response Y_phase(f) of an unknown physical system. Is it possible to ...
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1answer
1k views

Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
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1answer
386 views

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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1answer
269 views

Given a causal LTI system with a transfer function, determine if the system is an all-pass filter

We are given a transfer function of a causal LTI system and must determine if it is an all-pass filter: $$ H(z) = \frac{1 + 4z^{-2}}{4 - z^{-2}} $$ To the best of my recollection to determine if a ...
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943 views

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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1answer
61 views

(How to ask a Homework Question): Define poles by using proportional controller

Given is a process with the transfer function $$G(s) = \frac{s - 1}{s^2 + 3s + 2}$$ I want to create a controller so that the poles of the controlled system are $$p_{1,2} = -4 \pm i$$ Is it ...
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820 views

Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...
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353 views

Finding DC gain of a signal

I have a gray scale image produced by an optical photon simulation and I am trying to find the DC gain of the image using Matlab. For that, I simulate a slant edge image in the simulation where N ...
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123 views

Why is the dB plot of a signal usually non-positive?

Almost every decibel plot of a signal is usually below 0. Why is this the case? I recently just plotted a transfer function with a very high decibel plot above 0.
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220 views

Simplify equation of single pole IIR transfer function

Example - Consider the causal stable IIR transfer function $$ H(z)=\frac{K}{1-\alpha z^{-1}}, \quad 0 < \lvert \alpha\rvert 1 $$ where $K$ and $\alpha$ are real constants Its square-...
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319 views

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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2answers
491 views

Control design: under what conditions can closed-loop poles be placed arbitrarily?

Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
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1answer
331 views

What is the frequency response function for the Bode Plot pictured here?

I've forgotten how to get the frequency response function out of a Bode Plot. The phase component of $H(j\omega) = e^{j\pi/2}$, right? But I am having trouble finding $|H(j\omega)|$. How would I get ...
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Why do we assume zero mean noise in sensor data?

I am reading a paper on measuring respiratory patterns from video data. In defining the model, the authors formulate the problem mathematically as: $x_i(t)=h_i(t) \ast g(t) + n_i(t) $ Where $n_i(t)...
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8k views

determining type of filter given its pole zero plot

How can I classify a filter given its pole-zero map. For example I've got my zero's located at $\pm j$ and my poles located at $\pm\frac{1}{2}j$.
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1answer
338 views

Does the frequency response assume the zero input response to be 0?

I'm a bit confused about the frequency response and the state of a system. Is it simply the ratio of the output of the zero state response to the input of the zero state response? Or does it include ...
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1answer
185 views

Find state space model from transfer function

Let's suppose we have: G(s) = (s+1)/(s^2-2s+1) how can we find the state space representation of the transfer function: x_dot = x2 x2_dot = 2*x2-x1+u where u is an arbitrary input. I am very new ...
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210 views

How to calculate the impulse response from the transmission function of an optical device?

Let $f(x,y)$ be the electric field in complex representation processed by an optical device described by a transmission function $t(x,y)$ such as: $$ f'(x,y)=f(x,y)t(x,y) $$ Where $f'$ is the output ...
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194 views

Gain at given frequency from $z$-plane zero-pole plot. Two methods gives different results

I have two zeros at $z=-1$ and two complex conjugate poles at $z=A\cos\theta\pm jA\sin\theta$ This gives me the next transfer function $$H(z)=\frac{1+2z^{-1}+z^{-2}}{1-2A\cos\theta z^{-1}+A^2z^{-2}}$...
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1answer
86 views

Basic transfer function question

Why is the transfer function from node 2 to 3 $H_{23}=\frac{z^{-1}}{1+az^{-1}}$? I don't understand the $z^{-1}$ in the numerator.
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How to plot magnitude response using freqz in matlab if I have a transfer function without a denominator

So I have the transfer function: $$H[z] = 1 + \sqrt{2}z^{-1} + z^{-2} $$ And I have to evaluate $H(e^{j\omega})$ for $\omega= 0, \pi/4, \pi/4 \ldots$ I have done the calculations manually using ...
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Why does this transfer function has a second zero

I'm learning about $\mathcal Z$-transforms in DSP and I have a transfer function of the following form: $$H(z)=\frac{2-3z^{-1}}{1-1.6z^{-1}+0.8z^{-2}}$$ When I calculate zeros and poles of this ...
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1answer
366 views

Force an unstable IIR filter to be stable by forcing a nonlinearity in the digital block diagram

I am modeling an analog filter with digital software and have reduced the model to a 4th order FIR filter in discrete space with transfer function $$ H(z) = \frac{b_0 + b_1 z^{-1} + b_2 z^{-2} + b_3 ...
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1answer
311 views

Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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1answer
636 views

How do I identify a notch filter given the transfer function?

I am studying for an exam, and a problem that my professor gave produces a transfer function that looks like the following: $$H(z)=\frac{z^2-j}{z^2-\frac{1}{4}j} = \frac{\left(z-e^{j\frac{\pi}{4}}\...
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Difference between transfer function and frequency response? [duplicate]

AFAIK both represent the ratio of the output response $Y(j\omega)$ to the input excitation $X(j\omega)$: $$H(j\omega)=\frac{Y(j\omega)}{X(j\omega)}$$ Are there any difference?
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1answer
489 views

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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Deriving the transfer functions of a heating system

I'm tying to develop a model for a heated system that consists of a small steel block (~25 sq. in.) with a heating element embedded in it. The block acts as a sort of hot-plate that is used to deform ...
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1answer
195 views

Chebyshev poles into transfer function

I have obtained a set of three poles for a third order Chebyshev filter as shown below: $$p_k=\rm -0.2471+0.9660j,\quad -0.2471-0.9660j, \quad -0.4942.$$ However I am unsure of how to actually ...
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1answer
207 views

For a discrete LTI system, does “bounded memory” imply “rational transfer function?”

Every LTI system with a $\mathcal Z$-domain transfer function that is a rational function - aka a quotient of two polynomials in $z$ - can be implemented using a bounded amount of memory. Is the ...
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1answer
122 views

Converting transfer function that is a sum of unusual rational polynomials to finite difference equation

I have the following rather exotic transfer function: $$ H(z) = cz^{-m} + \frac{b_0 z^{-1} + b_1z^{-2} + \dots + b_{2m}z^{-2m}}{1 + a z^{-1}} + \frac{q_0 z^{-1} + q_1z^{-2} + \dots + q_{2m}z^{-2m}}{1 ...
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1answer
181 views

How do I test stability of a MIMO system?

Let's say I have a system similar to two interconnected IIR filters described like this: \begin{align} x_1(t)&=a_{11} x_1(t-1)+a_{12} x_1(t-2) +a_{13} x_2(t-1) + a_{14} x_2(t-2)+y_1(t)\\ x_2(t)&...
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961 views

How to establish transfer function of a speaker?

I'm working on a signal processing project about vocal system, and I'm trying to use controlling theories to solve the problem. I need to get the transfer function, $H(s)$, of a speaker, from ...