**221 transfer-function questions.**

I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths.
Why we use ...

Let the input signal $x(n) = \sin{2\pi\frac{1}{4}n}$ go in to the system described by: $$y(n) - y(n-1)+\frac{3}{16}y(n-2) =x(n).$$
What is the output signal?
I've calculated the system function $H(...

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

I have the following inverse system
$$G(s)= s^2 + 2s + 3$$
How do I implement it in Simulink? Note that the transfer function is only accepted if and only if the order of the numerator is less than ...

I'm trying to model a transfer function for a noisy audio system, specifically to measure delayed system response. Before I can confidently apply control, I need to verify that I can exert control ...

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 ...

Please help me in solving the following problem:
Find the pulse transfer function and weighting sequence of the system described by the following difference equation: $$y[k+2]+ y[k+1]+(0.89)y[k]=r[...

I have been told in the university that the natural frequencies (also called $\textit{eigenfrequencies}$) are the poles of the transfer function, however, Matlab compute them as the modulus of the ...

I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...

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 ...

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 ...

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. ...

I'm dealing with logarithmic system $\log_{10}(y(t)) = m \log_{10}(x(t)) + b$, and I need to find the transfer function, $Y(s)/X(s).$
What is the Laplace transformation of $\log_{10}(f(t))$?
What I ...

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 ...

I have an audio signal that I am applying an analogue transfer function $H(s)$ to. I would like to approximate the change in gain ($\Delta \text{ Gain}$) as perceived by the listener for an arbitrary ...

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 ...

I have a filter with the transfer function
$$H(z) = 1 - 2z^{-2} + z^{-4}.$$ The task is to find the phase function $\theta (\omega).$
My attempt is to start by expressing the frequency response
\...

I have a closed loop transfer function
$$G_{\rm cl}(s) = \frac{k}{s^{2} + s + k}$$
I am trying to find the critical gain of the system. From using the Routh Hurwitz criterion I get a $k = 0$.

I'm trying to convert the following IIR transfer function from the s-domain to the z-domain:
$$
H(s) = \displaystyle\frac{\frac{s^2}{\omega_z^2} + 2\zeta_z\frac s\omega_z + 1}{\frac{s^2}{\omega_p^2} + ...

This answer and the comments in it made me wonder whether the following statement is true:
If a transfer function is improper, then that system cannot be causal and stable at the same time.
I had ...

Assume we have a signal repeater, a simple repeater that amplifies the signal then transmits it as is.
Does the output power of the repeater is dependent on the received signal at the repeater ?
for ...

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 ...

What is the transfer function of this system y(n) =2y(n-1)? Here there is no input dependence. If you give one output sample, all the future output samples are determined by multiplying with 2.

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:
$H(s) = \frac{I(s)}{V(s)}$
...

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 ...

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 ...

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), ...

Can someone explain waveshaping to me?
I only know it shapes waveshapes by passing through some functions, but I don't yet understand e.g. what the plots (such as the following in Melda Production ...

I have a system through which I can pass a signal to get a response. For example, I can pass a sinusoid through and see how the system responds to it. I want to find a transfer function for this ...

$G(z) = \frac{1-p}{z-p}$
If the value of p satisfies $ 0 \leq p < 1$ there are no oscillations
in the transient response.
Question: Why is that $\uparrow$ true? I know roughly what a ...

This is a line from a paper I've been reading:
The static gain of the closed loop system must be $1$ ($G(1) = 1$) [...]
First of all: I know what gain is, but isn't gain dependent upon frequency? ...

I am working on real-time implementation of spring reverb based on scientific paper called Parametric Spring Reverberation Effect by VÃ¤limÃ¤ki, Vesa; Parker, Julian; Abel, Jonathan S.
One block of ...

I need to find the filter coefficients of an FIR filter that will block sinusoids of frequency $200\ \rm Hz$ if the sinusoid is sampled at $1.2\ \rm kHz$.
I feel like this is a fairly simple problem,...

There is a system which shifts frequencies of input by -Fc such that:
Y(S) = X(S).H(S)
But X(S) has value zero from 0 to Fc. I am confused on how the product of X(S) and H(S) becomes a positive ...

If I have a training data with two signals (PPG1 and PPG2 from different locations) and want to see, how different they are of what is their transfer function I can apply MATLAB's function ...

Suppose we have a system which we want to know the exact transient times. In ideal case, we can extract the transient times, but in practice it will be affected by another system with a known transfer ...

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 ...

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 ...

I am given $$H(z) = 1 + \frac{\alpha}{1-\alpha z^{-1}}$$ where alpha is between $0$ and $1$. This is apparently is a low-pass filter with cutoff frequency $f_c$.
How can I see that? And how can I ...

Hi I am working on emulating a piece of analog audio equipment and would like to be able to create a transfer function based on the measured percentages of harmonic distortion.
I know that harmonic ...

suppose $y(n)=ax(n-1)+bx(n-2)+\dots$ ($y$ is the output and $x$ the input). What happens if I want to solve $x(n)$ from $y(n)$?
Z transform: $$Y(z)=G(z)X(z)\tag{1}$$
then $$X(z)=\frac{1}{G(z)...

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 ...

I am having trouble figuring out what the difference equation or the system function for this system is? Here ''R'' represents the unit delay. The fact that the delay is not part of the feedback loop ...

Relate the transfer function to its' corresponding step response.
First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...

The problem says that we have the information (actually a .mat file that contains the data) of 1 pixel from an IR camera from an object with 26Â° of temperature. Because of the noise, the output is ...

I have gone through the entirety of K. Ogata's Modern Control Engineering, and I do not understand how can I translate all the transfer function models into differential equations? For example, how ...

To prevent aliasing caused by the finite number of pixels on a sensor, a blurring filter is commonly used. How does that work from a frequency domain perspective? What is the transfer function of such ...

[Can someone help me with this problema please much appreciate it, Ive have reached a solution of g(s)= 1s/2s+3s-k

- filters
- z-transform
- frequency-response
- control-systems
- discrete-signals
- laplace-transform
- matlab
- filter-design
- fourier-transform
- infinite-impulse-response
- linear-systems
- homework
- impulse-response
- poles-zeros
- signal-analysis
- frequency-spectrum
- system-identification
- state-space
- stability
- noise
- frequency
- image-processing
- fft
- audio
- convolution

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