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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1answer
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Why is this function BIBO stable?
I have a continuous system described as:
$$y(t)=2x(t)+0.5x(t-2)+0.25x(t+2)$$
and I'm trying to understand why the system is stable. I know that a system is unstable when you provide an input and as a ...
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1answer
74 views
Find continuous signal given a condition on its samples
Let $x(t)$ be band-limited with $B = \omega_m$. Sampling gives us $$x(nT_s) = \begin{cases}
1, & n = 0 \\
0, & n \not = 0
\end{cases}$$
And $\omega_s = 2\omega_m = \frac{2\pi}{T_s}$. Find ...
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0answers
71 views
Reconstruct $x(t)$ from $y(t)$ and $z(t)$
Let $x(t)$ be band-limited signal with $X(j\omega) = 0$ for $|\omega|\gt \omega_M$. We use $$s(t) = \sum_{k =-\infty}^{+\infty}(-1)^k\delta(t - \frac{kT}{2})$$ for sampling. So we have $z(t) = x(t)s(t)...
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2answers
48 views
How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?
How to compute transfer function
$$G(s) = \exp \left( - \sqrt{s} \right)$$
in Matlab / Simulink?
I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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0answers
22 views
For an LTI system, the zeos and poles are defined in the z plane. How to add additional poles and zeroes so LTI system is real valued?
The question already has a zero and a pole in the complex plane. It is asking to add additional zero and pole so LTI becomes zero valued.
zeros=-1/2 + 1/2 i , poles = -1/3 -1/3 i .
What I understand ...
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1answer
53 views
Fourier transform of the sampled signal
I want to calculate Fourier transform of the sampled signal in two ways. Let $$s(t) = \sum_{k = -\infty}^{\infty}\delta(t - kT)$$And $z(t) = x(t)s(t)$. So we have $$z(t) = \sum_{k = -\infty}^{\infty}x(...
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0answers
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Output of LTI diagram with this question and is it stable [closed]
the input δ(t) and output of a LTI signal is shown below.
1- is this system casual?
2- is it stable? why?
3- draw the output of the system.
Tnx in advance
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1answer
30 views
Compute output given input, transfer function and initial conditions
The problem statement is
Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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6answers
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What is the first derivative of Dirac delta function?
Could you please help me in a simple way, what is the first derivative of a Dirac delta function?
I found this answer:
The informal answer is a positive Delta function immediately followed by a ...
1
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1answer
37 views
Behaviour of integrator at steady state
I wanted to calculate response of integrator of sinusoidal input at steady state via these two methods as mention in image but these two methods give two different answers at steady state, so where ...
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3answers
73 views
Meaning of sampling frequency?
Say there is a communication system, which can manage sampling frequency up to 4 MHz (given by software). Can the system be able to process signals with maximum frequency more than 2 MHz? Because ...
0
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1answer
31 views
Accelerometer sensor's data analysis [closed]
Here is a sample data that I got from the accelerometer sensor:
The first selected area shows the acceleration of the IMU device to right side and the second shows the movement to left side.
I am ...
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2answers
27 views
Apply Transfer Function in Continuous Domain in Matlab
I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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1answer
44 views
Fourier transform of an integrator filter
I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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1answer
27 views
simulation of lin-log amplification
I struggle with two simple questions.
First. What is the distribution of the signal on the output of the lin-log amplifier if Rayleigh noise is driven to the input of it.
Using an approach with ...
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0answers
32 views
How should I sample the signal $f(t) = \sin(24t)^3\chi_{[0,0.52]}$ on the interval $[0,1.25]$?
I am from an applied math/PDE background and I don't usually deal with proper sampling and signal processing. I just take roughly what seems to be a good number of samples. But I would like to be ...
1
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1answer
27 views
Determining if the system is linear and time invariant
The Fourier transforms of input $x[n]$ and output $y[n]$ of a discrete-time system are related by the following equation: $$Y(e^{j\omega}) + (e^{-j\omega})Y(e^{j\omega})= X(e^{j\omega}) - X^{'}(e^{j\...
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1answer
24 views
Extracting the DC component of a signal, that proportional to the displacement about the y-axis
I’m not sure that I clearly enough reflected the essence of a small problem in the title of the topic, but I’ll try to reveal its essence in the question itself.
https://www.wolframalpha.com/input/......
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0answers
81 views
Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$
Let
$$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$
Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$?
If not, what's the reason for ...
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0answers
22 views
Pre-envelope of an FM signal $s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$ [duplicate]
I want to ask a question about pre-envelope of an FM wave:
$$s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$$
Can someone explain briefly how we calculate the pre-envelope of this signal?
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0answers
23 views
Stability of a signal
I would like to know when I can determine that a system is stable. I've seen Stability of a system but this is very theoretically.
My background is that I've set up a measurement system to detect the ...
0
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2answers
77 views
Autocorrelation function and correlation integral
I am confused by the definition of autocorrelation function. It is originally defined as the expected value
$$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$
where $\langle\...
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vote
3answers
56 views
Time scaling and shifting of delta function
Learning signals and systems.
Solving time scaling and shifting problems.
For the question
$$x(t) = u(2t - 1)$$
First we shift by 1 to the right side and then we do time scaling , i.e divide by 2 ...
1
vote
2answers
44 views
Determining time-invariance of a system
I have a question about determining time-invariance of a linear system. We are given this system and we need to determine if it is time-invariant or not:
$$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$
...
1
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0answers
31 views
How to determine number of observations based on measurement frequency?
So I'm working on a problem where I'm measuring a signal with two different instruments -- one is a low frequency measurement system (1 Hz), and the other is a high frequency measurement system (200 ...
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4answers
80 views
Negative frequency in the Fourier Transform [duplicate]
Why use this instead of a positive frequency? I asked on the math forum but it just wasn't helpful.
I understand the idea of a negative frequency is important in general since many real signals like ...
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2answers
99 views
Question about Hilbert transform
Hilbert transform of a function $g(t)$ which is defined in time domain, would result in another function in time domain. Is there any other transformation like Hilbert that the results be in time ...
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1answer
27 views
Baseline correction for continuous EEG signals
I'm new to the topic so forgive the trivial question.
I am trying to understand data preprocessing for EEG signals. As I understand, after recording continuous EEG signals, they should be band-pass ...
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1answer
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1answer
32 views
Continuous frequency grid to discrete grid
I am designing a controller for a system using several methods, one of which is a discrete method. In the continuous time I am looking at a logarithmically spaced frequency grid in the range $$\omega \...
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0answers
7 views
Using delta MFCC for signal segmentation
Hello I am focused on implementing a method of speech segmentation into syllables based on delta mfcc. After the calculating of delta, I extracted their maximum local and the next step is to determine ...
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0answers
23 views
how to perform frequency convolution?
much has been said about convolution of continuous time signals. But what about frequency convolution?
For instance, consider the function:
$$f(t) = \text{sinc}(t)=\frac{\sin x}{x}$$
I take the ...
4
votes
2answers
89 views
Continuous vs discrete signal energy
I am looking to calculate the signal energy of real, sampled acoustic data. According to this source, the energy of a continuous signal is:
$$\tag{1}\hspace{1cm} E_x = \int_{-\infty}^{+\infty}|x(t)|^...
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2answers
151 views
Cross correlation and cross power spectrum for signal + noise
Quick question about my understanding of cross correlations and cross spectral densities.
Let $C_{ab}$ be the cross correlation between the signals $a$ and $b$, i.e., $C_{ab}(\tau) = \langle a(t)b(t+\...
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2answers
34 views
Where did the k of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$?
Where did the $k$ of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$?
We turn $\omega0$ to be $d\omega$, but $\omega=\omega_0k$, so shouldn’t there be a $k$ in the reverse ...
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2answers
65 views
Is there an easy way to translate a Fourier transform table from angular frequency $\omega$ to Hertz $f$?
I have a table with transform operations, e.g. scaling:
\begin{equation} \tag{0} \label{0} x(at) \iff \frac{1}{a} X(\frac{\omega}{a}) \end{equation}
or frequency shifting:
\begin{equation}\tag{1} ...
1
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0answers
20 views
Difference between these two Continuous Wavelet Transforms?
I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
3
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6answers
403 views
Design a LTI system which returns DC value of the input signal
Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
4
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4answers
365 views
Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?
I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
0
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1answer
49 views
Initial rest condition for the linear constant-coefficient differential equations
Suppose that system has the input/output relation as follows
$$\sum_{k=0}^{N}a_k \frac{d^ky(t)}{dt^k} = \sum_{k=0}^{M}b_k \frac{d^kx(t)}{dt^k}$$
Where $a_k, b_k \in \mathbb{R}$.
Obviously we need ...
0
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1answer
32 views
Sampling rate and number of samples
I am doing an experiment where i have to excite a plate and scan a region on it using a laser signal.
I am acquiring the signal from the laser continuously using an NI daq tool. i then have to divide ...
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2answers
56 views
Unit impulse vs Kronecker delta vs Dirac delta?
Apparently these 3 terms are similar, but what is exactly difference between them and what is exact value of each of them at time zero,1 or infinity?
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2answers
221 views
How can I generate a sine and cosine function using an exponential function?
I have been trying to generate sine and cosine sampled graphs by a given sampling frequency.
...
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1answer
46 views
A check on the definition of the continuous periodogram, and does it assume ergodicity somewhere?
Can someone verify my understanding of what the continuous periodogram is/means, and please tell me if I say something wrong:
As I've learned so far, the power spectral density of a wide-sense ...
0
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2answers
29 views
Understanding Communication Theory Jargon for Statistical Linear Models
Coming from a statistical background, I understand the following formula:
\begin{equation}
y = X\beta + \epsilon
\end{equation}
as a linear regression model, with data input-output pair: $(X,y)$, ...
0
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1answer
17 views
Difference in frequency spectrum of continuous time signal and discrete time signal?
I am studying chapter 4 of book signal processing first
There i came across a concept which says that(what i have understood)the spectrum of continuous time signal has limited number of lines while ...
0
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2answers
59 views
When deriving the power spectral density of stochastic processes, why does taking an expectation allow the $T\rightarrow\infty$ limit to be taken?
I am following the arguments presented in the paper AN-255 Power Spectra Estimation, from Texas Instruments, to learn how to derive the power spectral density for a stationary stochastic process, and ...
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2answers
90 views
Time reversal of input signals in convolution
Let $f(t)$ and $g(t)$ be signals.
I can't figure out what happens to the convolution of $f(t)$ and $g(t)$ if
both $f(t)$ and $g(t)$ are reversed
one of $f(t)$ and $g(t)$ is reversed
I tried the ...
0
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1answer
59 views
“plot” command for continous time signal in matlab?uses interpolation?
We know digital computer cannot deal with continuous time signals directly. But then how MATLAB "plot" command works?
Does that uses interpolation technique to show an apparently continous time ...
0
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2answers
66 views
Signals in real world?especially natural signals?
Do all the signals in real world ,that are of interest in engineering(for measurements or processing)are only continous/analog or there any other alternatives also?
For example birds make voice,...
