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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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Missing delay in heavyside step function

I found the following task that was inspired by an example in the book A. V. Oppenheim and R. W. Schafer, "Discrete-Time Signal Processing", 3rd Edition, 2014. Task: Consider the 2nd-order IIR ...
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How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?

Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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Cascade filter realization equivalence? [closed]

Given $$H(z) = \frac{11 +4.6z^{-1} -26z^{-2}-3.75z^{-3}}{1-z^{-1}-8.75z^{-2}}$$ I'd like to know whether this realization: Is equivalent to this one? In short, is the direct form realization ...
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Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
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Z domain transfer function to difference equation

I want to convert this transfer function: $$\ \frac{2\cdot(z-0.5)\cdot(z-0.6)}{z-1}$$ to a difference equation, but I have no idea how. Can someone help me? Thanks, Arjon
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Why I don't get the right PSD

I need to model a noise with a given PSD. To do this, I am starting from a white gaussian noise (WGN) and feed with the WGN a transfer function, which will act like a filter. In fact,it's easy to ...
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Inverse Fourier of Two-Pole Transfer Function

I would appreciate if someone could walk me through this derivation. I have a transfer function in the frequency domain, which has two poles $$\tilde{H}(\omega) = \Big(\frac{1}{1 + i \omega \tau_1}\...
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transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?

From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
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What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]

In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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Is there a way to obtain the transfer function from a bode plot on Python? (I know that it is possible on Matlab)

Quite simply, I have a bode plot obtained from a source signal. Now I wish to obtain the transfer function. I know it is possible with Matlab: http://www.mathworks.com/help/ident/examples/frequency-...
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Output of an LTI system given its transfer function and input

Given the transfer function $$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$ and the input $$v_i(t) = 0.1 \sin(100t)$$ find the output, $v_o(t)$. My approach was to use $v_o(t) = \mathcal{L^{-1}}\left\{T(...
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Consider an ideal low pass filter $H(\omega)$, and the input to this filter is the periodic square wave $x(t)$. Find the output $y(t)$

The solution to the problem is $$y(t) = 5 + \frac{20}{\pi} \sin(\pi t) + \frac{20}{3\pi} \sin(3 \pi t) $$ and to get that the solution says to find the Fourier series expansion of $x(t)$ and I am ...
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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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Transfer Function definition

To find the transfer function of a channel we say that it is $$ H(s) = \frac{y(s)}{x(s)}|x(s)=0 for <0 $$ Why we do not define it like $$ h(t) = \frac{y(t)}{x(t)} $$
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Cost function for LTI system identification

I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions. The general approach ...
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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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Linear Combiner Based LMS Transfer Function

I am currently working on narrowband beamforming and looking to compute the transfer function for a linear combiner based LMS. While doing a quick search I have found the following article which ...
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System Response Terminology

If I have a system specified by $$P(D)y(t)=Q(D)x(t)$$ and I specify initial conditions $y(0^-)=a, \ y'(0^-)=b,\ x(0^-)=c$ does the term $x(0^-)=c$ correspond to the zero state response or zero ...
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Transfer function from poles and zeros

If we know that a filter (or a system) has two poles at 20 GHz and one zero at 15 GHz, then how do you write the transfer function $H(s)$ for such a system? I am wondering why sometimes the poles and ...
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Get the discrete-time poles and zeros from continuous-time poles and zeros

How do you implement the following function: $$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$ where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
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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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Calculating impulse response from transfer function

Given the difference equation as 𝑦[𝑛]=5𝑥[𝑛]+5𝑦[𝑛−2] and 𝑥[𝑛]=cos(𝜋𝑛). I would like to obtain the transfer function h[n]. How is that possible manually and on Matlab? Manually it should be ...
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Determine phase response from pole-zero plot

I know how to determine the frequency response from the pole-zero diagram given the following formula: $\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
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Low pass filter transfer function

I am calculating the transfer function of a low pass RC filter and I have gotten $\frac{1}{1+jωRC}$ which is correct. But somehow it seems $ωRC = \frac {ω}{ω_0}$ that refers to the cutoff freqency ...
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Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
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Region of convergence for discrete system

I am confused by two questions on the region of convergence (ROC) when applying the $Z$-transform. Consider a discrete-time linear system $$x[n+1] = Ax[n]+Bu[n], \qquad y[n]=Cx[n]+D$$ whose transfer ...
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What is the zero in this transfer function?

What is the zero for the following transfer function, $-1/2$ or $-2$? $$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$ This appears to give a zero of $-1/2$. I can transform this into the standard form ...
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Poles and zeros representation in s-plane

We have a filter (or a system) that has two poles at $f_{p1} = f_{p2} = 20$ GHz and one zero at $f_{z1} = 15$ GHz. Let's assume the gain is $K = 1$. Then how do you mark these poles and zero in the ...
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Determine filter type using recurrence relation

Given the recurrence relation: $y[n] = x[n] + 0.5y[n-1]$ I want to determine the filter type (i.e. LPF, HPF etc.) I try to use Z transform, and get that the the transfer function is $H(z) = \frac{2z}{...
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Transfer function estimation of a noisy system

Overall description I am trying to estimate a filtering system’s transfer function, given its input and output. This system takes $x$ as input . This signal is low pass filtered and added to a WGN by ...
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How do I find the transfer function in the frequency domain?

I was doing some exercises with transfer functions, they were always under the form of $H(z)$ and $H(e^{jw})$ for the frequency response. Today I have found one with $H(f)$. I would like to ask if my ...
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Reducing noise on several Transfer Function measurements

INTRODUCTION I want to obtain the transfer function of certain system (a ground "path", in this case) using an impact hammer for the excitation and one accelerometer (measuring vertical direction ...
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Hidden zero in system equation $H(z)$

An FIR linear phase filter has unit sample response $h[n]$ that is real with $h[n]=0$ for $n < 0$ and $n > 7$. If $h[0]=1$ and the system function has a zero at $z=0.4e^{j\pi/3}$ and a zero at $...
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How to find poles of transfer function by looking at the step response?

How to find poles of transfer function by looking at the step response? Given a step response graph like such: How would I find the sketch for its poles on the complex plane? The only thing I can ...
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Practical implementation of IIR/biquad filters following non-textbook transfer function of real-wold analog filter

I am trying to program a DSP filter to study prototypes of loudspeaker filters, which will be implemented as passive analog circuits in the final speaker system. This process involves simulation of ...
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Identification of a transfer function

Can you obtain a transfer function in frequency domain with a bode plot form given by this function: $$ S=k1 \sqrt{1+\frac{k2}{f}} $$ I did not managed it because actually in the lowest part of ...
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Transfer function: from poles and zeros to polynomial coefficients

I understand how this transfer function was solved except I don't know how to get the 0.87. Any help would be appreciated.
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Recursive filter with repeated poles

This post follows this previous resolved post where I was trying to find the inverse Z-transform of a more simple filter output (that I used as an example to get the methodology). The present filter ...
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Calculating an output of a system (Z- transform question)

I have a following question to answer: An LTI system is described by its impulse response h[n]. For input x[n] it gives output y[n]. $$h[n] = u(n) - u(n-N) $$ $$x[n] = u(n) - u(n-M)$$ I want to ...
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108 views

Trivial and non-trivial zeros

I am new to DSP, and I'm self studying. Could someone please explain to me what do we mean by trivial and non-trivial zeros?
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Transfer function of a nonhomogeneous difference equation

Consider the following difference equation: $y_k=\alpha y_{k-1}+\beta x_k$ The transfer function for this is given by: $\displaystyle\frac{Y(z)}{X(z)}=\frac{\beta}{1-\alpha z^{-1}} = \frac{\beta}{...
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Why is interpolation a time varying system

I was reading about interpolation (Interpolation and Decimation of Digital Signals - A tutorial Review, Ronald E. Crochiere) and found that Interpolation filter is a time varying system. Can someone ...
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Linear Predictive Coding for general signals

I have a signal that's monotonic and roughly linear and have been looking at using Linear Predictive Coding to encode information and compress my signal. I guess my first general question is if this ...
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MIT exercise 6.003 HW2 - Concept of system initially at rest

I am following the MIT open course you can find here. My question is about one of the exercises given as homework in the latter and more specifically I think I am missing something on the concept of "...
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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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How do I plot the square of the amplitude response?

I have calculated the transfer function of an FIR filter $$ y[n] = x[n] + α · x[n − R] $$ This is what I have $$ H(z) = 1 + αz^{-R} $$ Now I should plot the square of the amplitude response. So I ...
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Anti-causal systems

If Anti-causal systems are defined as those whose output depends solely upon future inputs.(Is this definition correct as I understand) So i see that $y[n] = x[n+2]$ ; is anticausal system How is a ...
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Phase response of S11/S22 parameter for an RF attenuator? [closed]

I am new into the RF measurements. I was measuring the S11/S22 (reflection) parameters of an RF attenuator (with different attenuation levels, e.g., 10 dB) via a vector network analyzer from Rhode &...
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What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)

I'm using reference from here and here. This is Laplace transfer function of DC Control Speed System: $$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$ Where, $\omega$ is the motor angular ...