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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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 ...
0
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0answers
15 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
32 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
14 views
In an automotive ECU application for STM32, what ADC modes should I use? [migrated]
I am writing an application for the STM32f407-Discovery board that will use the ADCs present on it. I want to have access to all 17 of the input channels, and I will be using the HAL library to write ...
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0answers
12 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
vote
1answer
42 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:
$$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
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0answers
31 views
Time Domain Behaviour of Thermal Noise
Let's consider the thermal noise (or Johnson–Nyquist noise): It is white noise, that means that its power spectral density does not depend on frequency.
Now my question is: Which is a typical time ...
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votes
2answers
99 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
49 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
19 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
65 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
42 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
27 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
vote
1answer
23 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
57 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 ...
0
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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
vote
2answers
54 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 $$H_1:\omega\...
0
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2answers
37 views
Fourier Transform: interpretation of continuous spectrum at specific frequencies
B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform:
When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
0
votes
2answers
162 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
0
votes
1answer
39 views
What is Imaginary in Fourier transform?
How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
0
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2answers
44 views
Help regarding property of unit impulse function
We know that using properties of unit impulse function it can be shown that
$$\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 ...
0
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4answers
72 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
41 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
votes
4answers
695 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 ...
1
vote
3answers
198 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 ...
0
votes
1answer
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)$?
2
votes
1answer
46 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
29 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}
$$
which $\eta$...
3
votes
1answer
59 views
analog-to-discrete-to-analog system sampling problem
This is not a homework problem, I am solving practice problems for my exam.
Consider the analog-to-discrete-to-analog system shown in figure 1. The CT signal $x_a(t)$
is sampled at a frequency of $...
2
votes
3answers
48 views
Characterization of transfer functions with no local peaks
Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$
Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
1
vote
1answer
77 views
Laplace transform of a finite duration signal
Consider the following signal:
$$ x(t) = e^{-2t}[u(t) - u(t-5)] $$
This signal exists only from 0 to 5 time units. Elsewhere, it is zero.
Now, let's find the laplace transform of this signal using ...
0
votes
0answers
23 views
Find LF component of AM signal
I'm trying to figure out how to find the low frequency component of an AM-signal when I have regained the carrier.
So the signal is:
$$U_{AM} = 2[3+0.4cos(2\pi\cdot2\cdot 10^3\cdot t)]\cdot sin(2\pi\...
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0answers
19 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 ...
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vote
1answer
48 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
votes
1answer
30 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
55 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)
0
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2answers
76 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 ...
0
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0answers
30 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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0answers
51 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 $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm
e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
1
vote
3answers
167 views
Confusion in AC and DC signals
I have certain doubts in the fundamentals of AC and DC signals.
Most of the time, we deal with DC signals in the form of batteries, whose waveform is a constant signal with peak as 1.5v
However, i ...
0
votes
2answers
45 views
Independence of Functions of random Variable
Consider I am given two functions of one random variable each for example x=cos(at),y=rect(bt) where a and b are random variables.And I am given Probability density function for a and b then if I am ...
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0answers
29 views
Notch filtering minimizing artifacts in signal
I have to notch filter the following signal
As you can see it is a signal with really high amplitude.And this causes me a lot of problems. I've designed a bandstop filter (46-55 Hz).The MATLAB code ...
0
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1answer
26 views
Diode demodulation for AM
What is the capacitor and resistance at output of LPF meant for in the document it was mentioned that it is DC blocker I don't get it can't message contain DC value.
1
vote
1answer
205 views
Is convolution distributive over multiplication?
Is there any formula or expansion for
$$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)...
0
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0answers
34 views
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 ...
1
vote
2answers
63 views
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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0answers
53 views
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 ...
4
votes
3answers
406 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.
...
0
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1answer
37 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 ...
1
vote
1answer
110 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 ...
