Questions tagged [continuous-signals]
A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum.
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Is there a software to interactively stretch parts of a signal in the time domain (input as array)
I have a collection of audio signals as well as arrays related to the frequency spectrums of other audio sources. The audio signals are 2D arrays (of floats) as well. I need to interactively stretch ...
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25 views
Inverse Laplace Transform
A system given by $\frac{s-1}{(s+1)(s-2)}$ has to be inverse transformed so that it is anticausal and nonstable. The answer given is $h(t)=-\frac{1}{3}(2e^{-t}+e^{2t})u(-t)$
Why the minus sign at the ...
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Determining Stability of a continuous time system using Laplace Transform
I'm following Oppenheim's book. In exapmles, the laplace transforms of of the following signals
$e^{-t}u(t)$ and $e^{-t-1}u(t+1)$
is given as $\frac{s}{(s+1)}$ and $\frac{e^{-s}}{(s+1)}$ both ...
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EE homework is kicking my behind [migrated]
EE student here, having a hell of a time with some homework. Is this the right place to ask for some help or guidance?
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1answer
44 views
Step response of third-order continuous-time transfer function
I have a transfer function of the form:
$$H(s) = \frac{b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}{s^3 + b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}$$
If it matters, $a=b=2$. Is anyone aware of ...
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51 views
How can the Poles of the Root Locus be negative?
My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...
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46 views
Cross-correlation of filtered random processes
I have a wide-sense-stationary (WSS) process $\{x(t)\}$ and two linear filters with impulse functions $h_1$ and $h_2$.
Let $\delta(\omega)$ be the power spectrum of $\{x(t)\}$ and $$H_1:\omega\...
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23 views
Fourier Transform: interpretation of continuous spectrum at specific frequencies
B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform:
When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
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145 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
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38 views
What is Imaginary in Fourier transform?
How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
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Help regarding property of unit impulse function
We know that using properties of unit impulse function it can be shown that
$$\int_{t_1}^{t_2} x(t) \delta^{(n)}(t-t_0) dt=(-1)^nx^{(n)}(t_0),\quad t_1<t_0<t_2$$ (source: Continuous and ...
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Determining LTI system response to a scale change
We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on.
But my question is what will be the system response for the input $x(-2t)$...
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39 views
How to automatically identify a surge in a periodic signal
Say I have a periodic signal i.e. Sine wave, which sometimes can have spikes that are 100% larger than the peak value. These spikes can be periodic as well. I'm trying to find an algorithm that could ...
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Is Fourier series a sampled version of Fourier transform?
I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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How can I know if these two signal are orthogonal to each other
So the question is to determine if this statement is true or false. The question can be seen below.
I know that two signals are orthogonal if their inner product is equal to 0. I know how this ...
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37 views
How to convolve $u(-t)$ with other signals?
How can I convolve the following
$u(t+1)*u(-t)$
I know that convolution with $u(t)$ gives the integral of a function but what change occurs due to $u(-t)$?
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1answer
42 views
Continuity and its relationship with asymptotic spectral decay
The asymptotic decay of the magnitude of the Fourier transform of a function appears always to be determined by its continuity properties as follows, with examples given in Fig. 1:
Continuous ...
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what is the co-variance of system output cooresponding to a non-iid random variable
Consider the following system.$\DeclareMathOperator{\sign}{sign}$
$$
\begin{aligned}
&\dot{e_1}=c_1e_1+c_2e_2+\eta\\
&\dot{e_2}=c_3e_1+c_4e_2-c_5 \sign(e_1)+a \eta
\end{aligned}
$$
which $\eta$...
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1answer
53 views
analog-to-discrete-to-analog system sampling problem
This is not a homework problem, I am solving practice problems for my exam.
Consider the analog-to-discrete-to-analog system shown in figure 1. The CT signal $x_a(t)$
is sampled at a frequency of $...
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3answers
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Characterization of transfer functions with no local peaks
Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$
Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
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1answer
54 views
Laplace transform of a finite duration signal
Consider the following signal:
$$ x(t) = e^{-2t}[u(t) - u(t-5)] $$
This signal exists only from 0 to 5 time units. Elsewhere, it is zero.
Now, let's find the laplace transform of this signal using ...
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Find LF component of AM signal
I'm trying to figure out how to find the low frequency component of an AM-signal when I have regained the carrier.
So the signal is:
$$U_{AM} = 2[3+0.4cos(2\pi\cdot2\cdot 10^3\cdot t)]\cdot sin(2\pi\...
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Signal Header:Physical Min is not less than Physical Max- after opening EDF file on the viewer
Whenever I open an EDF file on the Case Western Research University's EDF Viewer Application, I get a Scaling Warning-"Signal Header:Physical Min is not less than the Physical Max ". I am reading ...
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45 views
What is the effect on Hilbert transform of signal after multiplication by sinusoid?
Question :
Find Hilbert transform of $[u(t-a)-u(t-b)]\cos2\pi f_{0}t\\\\$ such that $\\0<a<b$
my attempt:
we know Hilbert transform of
$[u(t-a)-u(t-b)]\xrightarrow{\mathcal H} \dfrac{1}{\pi}\...
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1answer
23 views
Continuous time double exponential filtering in state space form?
I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem.
Typically, this model is expressed as a pair ...
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2answers
49 views
How is frequency defined for a periodic signal?
For sinsusoids, frequency is $2\pi/T$, but for general periodic signals, how is frequency defined? Is it $1/T$ or $2\pi/T$?
($T$ is the fundamental period of the signal)
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2answers
57 views
PSD of modulated signal
I know this question has been previously asked just saw it and tried to do myself but reaching an expression which is different from expression of PSD which I remember for modulated signal
Actual ...
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24 views
Low pass representation of Bandpass Random process
Can A WSS random process with non-zero mean be also represented in such form.
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35 views
How to Derive Rayleigh distribution using transformation formula
Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm
e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
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3answers
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Confusion in AC and DC signals
I have certain doubts in the fundamentals of AC and DC signals.
Most of the time, we deal with DC signals in the form of batteries, whose waveform is a constant signal with peak as 1.5v
However, i ...
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2answers
45 views
Independence of Functions of random Variable
Consider I am given two functions of one random variable each for example x=cos(at),y=rect(bt) where a and b are random variables.And I am given Probability density function for a and b then if I am ...
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Notch filtering minimizing artifacts in signal
I have to notch filter the following signal
As you can see it is a signal with really high amplitude.And this causes me a lot of problems. I've designed a bandstop filter (46-55 Hz).The MATLAB code ...
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25 views
Diode demodulation for AM
What is the capacitor and resistance at output of LPF meant for in the document it was mentioned that it is DC blocker I don't get it can't message contain DC value.
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95 views
Is convolution distributive over multiplication?
Is there any formula or expansion for
$$a(t)*[b(t) \cdot c(t)]$$
$$a(t) \cdot[b(t)*c(t)]$$
where $*$ denotes the convolution?
By expansion I mean something like $a(t)\cdot[b(t)+c(t)]=a(t)b(t)+a(t)...
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Envelope detector for AM signals
How or what are the constraints for deciding factors of envelope detector for AM As far as I know that charging time of capacitor should be below 20T where T is periodic time of carrier and ...
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2answers
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Digital Equations problem - The fundamental ones that everyone should know
I think I am looking at conflicting equations from a few sources, or maybe I just dont understand it. But please can someone help me with these fundamental equations that everyone should know
$ \...
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How to find fundamental frequency of two signals?
I am facing difficulty with finding fundamental frequency of signals
I mean by fundamental frequency=(1/Time period)
Correct me if I am wrong
consider two continuous time signals with
Time period ...
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3answers
305 views
How to Prove a System Is Invertible?
what i know is that for a system to be invertibel it should be one-one ,
but I am confused that if i am given a transfer function of a LTI system how can I prove or verify if it is invertible.
...
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1answer
34 views
Peak Detection on ECG signal
I've been working on a ECG signal collected during exercise through my chest mount heart rate monitor. My goal is to accurately detect the location of the R-wave; R-wave is the narrow peak similar to ...
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1answer
76 views
Discrete Kalman filter for a continuous system
The question is related to the implementation of a discrete kalman filter given a description of the system model in continuous time.
I will give an example. Suppose we have a mass, spring and damper ...
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1answer
55 views
Computing response of LTI system in terms of its step response
I have solved a problem, Kindly help me in determing if I solved it correctly.
I will post the question and my own working below.
Problem
My working
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1answer
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Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?
I have been studying signals and systems lately and I have came across the following claim:
The uniform sampling of a periodic continuous-time signal may not be periodic!
Can someone please ...
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1answer
45 views
Conversion from continuous to sampled signal?
I am bit confused regarding sampling as i read different types of statements in different texts
Forexample i have a continous time signal $x=sin(t)$ defined for $t=0:10$
and i want to sample it with ...
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why we use time step only in continuous convolution in MATLAB? But not in discrete convolution?
I am studying convolution from book of alex palamides but i am confused because he uses time step(in this case 0.01) in his code for continuous convolution as shown highlighted in attached photo but ...
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Usefulness of Matched $z$ transform Method
I'm aware that the matched $z$ transform method maps between the continuous $s$ plane and the discrete/digital $z$ plane but my question is - when would this be necessary? Why would we need to convert ...
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1answer
34 views
explanation of Hybrid systems?
I want to study Detailed explanation of hybrid systems?Which incorporate both continuous and discrete time signals & systems?
for example
In which a continuous-time input signal is transformed ...
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2answers
72 views
negative value of signals
can we say there is no sound produced when the amplitude is 0?
if yes what can we say when the amplitude is negative?
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Continuous-time RNN and Shannon sampling theorem
The most-used discrete-time RNN equations used in Deep Learning these days are those of Elman:
I have seen two very different continuous-time version of these, with different justifications. The most ...
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1answer
42 views
Are the error probability of orthogonal signal and on/off signal the same?
I have to write the error probability of orthogonal signal and on/off signal,and now i have finished the error probability of on/off signal,but i don't know how to write the code about error ...
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1answer
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Time Setting of $z$ and Laplace Transforms
I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
