# Questions tagged [laplace-transform]

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### Bode plot phase shift equation when poles and zeros are not at the origin

Let $$H(s)=\frac{s^{n}}{s^{m}}$$ For $n \ne m$ the phase shift between output and input will be $\frac{\pi}{2}(n-m)$. For situations where the poles and zeros are not at the origin, I could find the ...
1 vote
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### Mixer and control systems

A mixer in the time domain usually multiplies 2 signals of the time domain , however what does it do in the Laplace domain?Is there a equivalent block diagram of a mixer in the Laplace domain?The ...
1 vote
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### Simulate Op-Amp low-pass transfer function in Python

I am struggling to simulate the frequency response of a simple op-amp low-pass transfer function in Python. The results I get are not accurate. The transfer function is $H(s)=\frac{1}{1 + s\tau}$, ...
51 views

### I have a transfer function in s domain convert to time domain

I have a transfer function of $\frac{1}{s^2}$ in $s$ domain that represents a $\frac{\text{output}(s)}{\text{input}(s)}$. Say I put a constant DC input as input (s) or just input in time domain that ...
72 views

### Equipment to test my theory on time varying systems

How can I make a linearly time varying system to test my theory? Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
1 vote
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I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$ The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$ This is my ...
52 views

### Derivation of 9 point Laplacian filter

I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
1 vote
79 views

### Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?

Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
1 vote
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### How to separate Transient and Steady-State Expression from Periodic Summation Response?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
1 vote
162 views

### Laplace domain transfer function from system sampled at discrete times

I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is here (PDF page 6, slide marked 11); I'll explain further below. Suppose I have a ...
83 views

### Finding the region of stability of a system

Suppose we have a closed loop system controlled by some microcontroller $K$ First we take the open loop gain which is $\frac{K}{s(s+6)}$.It has 1 pole at the origin and at $s=6$ and 0 zeros. So we ...
1 vote
271 views

### Calculating transfer function of a linear time varying system?

If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
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### Max input of a system given it's transfer function and an assumed step change (beginner)

I have an exercise that gives me the following transfer function $$\frac{0.5}{s+0.5}$$ and an assumed step change in the target of 20 I am asked to calculate the maximum input for the assumed step ...
62 views

1 vote
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### How we determine type of filter with pole(s), zero(s)? [duplicate]

Let's say we have this Laplace transform: $$H_{1}(s)=\frac{1}{(s+1)(s+3)}\;, \; \Re{e} (s)>-1$$ So, we know that there is a poles at $s=-1$ and $s=-3$. With these informations, we found that to be ...
1 vote
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### Name of property of Laplace transform

\begin{align} L[e^{-at}u(t)] &= \frac{1}{s+a}\\ L[\cos(\omega_{o}t)u(t)] &= \frac{s}{s^{2}+\omega^{2}_{o}}\\ L[e^{-at}\cos(\omega_{o}t)u(t)] &= \frac{s+a}{(s+a)^{2}+\omega_{o}^2} \end{...
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### Amplitude ratio is larger than 0.5 on a RC-filter if RC = 1.7684e-03

I have two signals ...
348 views

### Sampling with impulse train

There are many times when the textbooks used by all university students like me make an introduction to the notion of sampling of a continuous-time signal with an impulse train as shown below. Why do ...
1 vote
159 views

### Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
119 views

### Study the stability of $H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. The degree of ...
251 views

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### Step response of a given input and output (Laplace or Fourier)

I am trying to calculate the step response of the following given: Should I use Laplace transform or Fourier transform?
1 vote
56 views

### Filter filters out more than needed

I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
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### The Laplace transform - Steven W. Smith Book - impulse response cancellation method

While studying the Laplace transform using Steven W. Smith Book I found something uncomprehending. In the 32th chapter - The Laplace Transform, page 590, last paragraph describes the cancelling ...
94 views

### What will the output of a system which has no Fourier transform?

Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?
609 views

### Confusions regarding differences between Fourier transform & Laplace transform?

Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard Number 1) Link of question https://electronics.stackexchange.com/questions/...
241 views

### Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions?

Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions $y(t)$?? With output I am meaning that $y(t)$ is such ...
1 vote
Given that the Laplace transform of a continuous-time signal $h(t)$ is $H(s)$, what can a plot of the poles and zeros of $H(s)$ on the $s$-plane tell me about the magnitude response and phase response ...