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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questions
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Confusion about systems involving integrals
$$y_1(t)=\int_a^tx(τ)dτ$$
$$y_2(t)=\int_a^bx(t)dt$$
I'm confused about what are the input signals in each of these systems.
To my understanding, in the second case the input signal is $x$ since both ...
-1
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1answer
41 views
Bandwidth and probability of continuous signal
I'm a little bit confused as to how to calculate the bandwidth of a signal. A question has me believing that it is correlated with the probability distribution. I am however not sure of this.
...
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0answers
13 views
convert analog voltage into discrete time signal. show in time domain graph [closed]
Convert the analog voltage E(t) = 5 sin(2*pi*t) mV into a discrete time signal and
show your answer in time domain graph. Specifically, use sample time increments
i)1/8 second
ii)0.75 second
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1answer
37 views
How to convert from Laplace Domain to Time Domain?
I want to convert the following equation from Laplace domain to continuous time domain:
$F(s) = \frac{-2 m k v R}{2 m R s^{2} + m k s + 2 k R}$
m, k, v, R are all constants.
If I can factor or put ...
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0answers
24 views
Are discrete time functions expected to be this inaccurate?
I am attempting to test some discrete time functions against their continuous counterparts and I am surprised by how inaccurate the discrete versions are coming out.
I am modeling the displacement, ...
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1answer
43 views
One more inverse z transform … a bit more complicated [closed]
Thank you for all the help teaching me. I am looking at one more inverse z transform and not understanding what to do with it.
$F(t) = m \cdot a(t)$ (i.e. Force = mass $\times$ acceleration)
$F(s) = ...
0
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1answer
14 views
How to do this inverse Z-transform? Is this correct?
It was explained to me here that I need to do an inverse z-transform on a z-based equation in order to get something I can use. That example was quite simple. But I'm not sure how to do the same ...
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2answers
69 views
What does z^(-1) represent here?
I understand that when you have a Laplace function, you can do a bilinear or forward/backward Euler substitution for $s$ to phrase it in terms of $z^{-1}$. In a typical filter, $z^{-1}$ represents the ...
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2answers
29 views
Period of a continuous signal
So I have
$$x_1=2 \cos(.6\sqrt\pi x+\pi/6)$$ and $$x_2= \sin(1.2\sqrt\pi x-\pi/3)$$ and need to find the period of $(x_1+x_2)^2$.
Let $$a=.6\sqrt\pi x+\pi/6 ~~~\text{and} ~~~ b=1.2\sqrt\pi x-\pi/3$$ ...
1
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2answers
38 views
Even and odd signals
We've studied in signal and systems about odd and even signals. But what is the actual implementation or application of this property?
like for energy and power signals we know If you're using a ...
0
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1answer
47 views
When is a discrete time transfer function unrealizable?
I don't understand why the following makes sense:
Given a second-order mass damper system in continuous time:
$H(s) = \frac{1}{ms^{2}+cs}$
Its inverse $H^{-1}(s)$ is unrealizable as a transfer ...
2
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2answers
73 views
Pulse Doppler Radar: time delay in down conversion
My understanding of Pulse Doppler Radar is the system measures Time Of Flight for the pulse.
My confusion is that during the down conversion process prior to ADC the lowpass filter causes some time ...
1
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2answers
66 views
How do I find the convolution of the following signals? [closed]
$h(t)$ is the inputted to convolve the $x(t)$
The signal written in unit step are:
$x(t) = (5-t)u(t-3) - (5-t)u(t-5)$
$h(t) = 2u(t-1) - 2u(t-3)$
So to convolve I first change the function to:
$h(...
2
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2answers
56 views
LTI system output given input and frequency response
The question I'm trying to understand is as follows: A linear time-invariant continuous-time system has the frequency response function $$H(\omega)=\frac{1}{j\omega+1} $$
Compute the output response $...
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0answers
16 views
Cross location Cross frequency coupling
Let's say there are 2 sensors recording data at some sampling rate. I'd like to know, how to calculate Cross frequency coupling (Phase amplitude coupling, for now) between these 2 channels ?
I have ...
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3answers
94 views
How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?
This result has been used in the second last line of the pic. I don't know why it's true. Both functions are zero for $t$ not equal to $-b/a$. But at $t=-b/a$, a scaling factor $1/|a|$ has been ...
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0answers
21 views
Using unlabeled EEG data for Machine Learning
I am working on a project that is basically a game for motor-paralyzed people.
It should take an EEG signal from FP1 channel of brain and then after processing it should generate command for the game ...
0
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1answer
35 views
Is $y(t) = \cos(t) + x(t)$ a time-invariant system?
Is $y(t) = \cos(t) + x(t)$ a time-invariant system?
$y(t-k) = \cos(t-k) + x(t-k)$
But it isn't equal to $\cos(t) + x(t-k)$
So, would it be time-invariant?
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0answers
15 views
Signal similarity analysis after cross correlation
I have a time series signal and using this as reference, from the main data set extracted possible matching sections using cross correlation technique.(xcorr matlab).Based on with the threshold xcorr ...
1
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1answer
43 views
Fourier Series representation of a signal
Use the defining equation for the Fourier Series coefficients to evaluate the Fourier Series representation of the following signal:
$$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
3
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2answers
125 views
What is the autocorrelation of a Dirac pulse?
What is the autocorrelation of $x(t) = \delta(t)$?
Can you explain to me how to calculate it?
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2answers
60 views
Matlab - Bode plot of Lag Filter + Integrator
I am rather new to Matlab and I just cant make sense of what I see in the bode plot of the continuous and discrete version of the same function. The bode plot of the continuous function looks as ...
0
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1answer
25 views
Bessel filters: linear passband phase characteristic only for low pass filters?
I've found a test (internet) from the contest to signal processing teacher and it has a question (true) or (false).
I cant find any book or paper to argue this statement. Is it really true?
2
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1answer
110 views
Initial Rest Condition for LCCDE causal LTI systems
I am self studying Alan Opennheim's course Signals and Systems. I am a math major and have no background in EE.
I understand that for a LCCDE system to be linear its auxiliary conditions must be 0.
...
2
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0answers
51 views
Fourier series representation of a full wave rectifier output
I am trying to compute the Fourier series representation of a full wave rectifier output.
The equation of the signal is:
$ x_8(t) = | \cos (2 \pi f_o t) $ |
I have tried to find the Fourier series ...
1
vote
1answer
31 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 ...
1
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1answer
27 views
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 ...
0
votes
1answer
67 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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1answer
57 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. ...
1
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2answers
74 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 $$H_1:\omega\...
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2answers
91 views
Fourier Transform: interpretation of continuous spectrum at specific frequencies
B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform:
When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
0
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2answers
199 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
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1answer
43 views
What is Imaginary in Fourier transform?
How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
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2answers
76 views
Help regarding property of unit impulse function
We know that using properties of unit impulse function it can be shown that
$$\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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4answers
108 views
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)$...
0
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1answer
44 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 ...
4
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4answers
761 views
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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3answers
260 views
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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1answer
40 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)$?
2
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1answer
47 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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0answers
31 views
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}
$$
which $\eta$...
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1answer
72 views
analog-to-discrete-to-analog system sampling problem
This is not a homework problem, I am solving practice problems for my exam.
Consider the analog-to-discrete-to-analog system shown in figure 1. The CT signal $x_a(t)$
is sampled at a frequency of $...
2
votes
3answers
48 views
Characterization of transfer functions with no local peaks
Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$
Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
1
vote
1answer
101 views
Laplace transform of a finite duration signal
Consider the following signal:
$$ x(t) = e^{-2t}[u(t) - u(t-5)] $$
This signal exists only from 0 to 5 time units. Elsewhere, it is zero.
Now, let's find the laplace transform of this signal using ...
0
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0answers
23 views
Find LF component of AM signal
I'm trying to figure out how to find the low frequency component of an AM-signal when I have regained the carrier.
So the signal is:
$$U_{AM} = 2[3+0.4cos(2\pi\cdot2\cdot 10^3\cdot t)]\cdot sin(2\pi\...
0
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0answers
24 views
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 ...
1
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1answer
53 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}\...
0
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1answer
35 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 ...
1
vote
2answers
64 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
112 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 ...
