**228 transfer-function questions.**

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 ...

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 ...

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 ...

I'm working on a power systems where I have 2 linearized transfer functions. The first transfer function corresponds to the no-load case and the second transfer function corresponds to the full-load ...

I am trying to compare the transfer functions of k different microphones and need some advice on my current approach. As of now, I have attempted the following:
Play a pink noise test tone $(X)$ ...

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 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 ...

The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$
I need to find the impulse response h[n] of a causal system with x[n] as unit impulse.
I have tried to find the impulse response by the following ...

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 ...

Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles?
...

Given an absolutely summable signal $x[n]$, the $z$-transform $X^z(z)$ is rational with a pole at $z=0.5$.
Given the following the statements:
$x[n]$ has a finite support in the time domain.
$x[n]$ ...

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen
\begin{equation}
\int_{-\pi}^{\pi}X_R\left(e^{j\theta}\right)\sum_{k=-\infty}^{\infty}\delta(\omega-\theta-2\pi{}k)d\...

I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...

Given that:
$H(z)$ has 4 poles maximum.
$H(z)$ has a pole at $z_1=a+bi$
Given that the impulse response $h[n]$ is:
Symmetric: $h[n] = h[-n]$
Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$
How we can ...

I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check.
1/ I'm ...

For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...

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 ...

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'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 ...

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 ...

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 ...

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 ...

$G(z) = \frac{1-p}{z-p}$
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 Välimäki, 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 ...

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

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