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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What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

I'm dealing with bunch of .asc(ascii) files that are the output of continous monitoring of various electronic equipments for certification purposes. We monitor various parameters of the equipments ...
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3 answers
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How do you find the null to null bandwidth for the signal below?

My tutor does not explain it very well. Can someone please explain to me the reasoning and what null to null bandwidth actually is?
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Algorithm to detect down-up-down pattern in time series

I'm trying to write an online algorithm in Python to detect this below Down-Up-Down pattern in time-series. It's not hard to do roughly if I calculate 3 contiguous non-overlapping moving averages, and ...
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Different PI controller implementations and their respective discrete transfer functions

So I need to implement a PI-controller and I found an Implementation of an PID-controller with some background explanation. I adapted the implementation to an PI-controller, implemented it and got the ...
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Transfer function and Laplace domain

If we give a input $x(t)=u(t)$ to a system $\mathcal{S}$ we get an output $y(t) = e^{-t} u(t)$. After we Laplace-transform both the input and the output we get the transfer function $$H(s) = 1-\frac{1}...
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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{...
2 votes
2 answers
62 views

Why do we decompose signals to even and odd

I was learning the decomposition of a signal into one even signal and one odd signal: $$x(t) = x_{e}(t)+x_{o}(t)$$ with $$x_{e}(t) = \frac{1}{2}\cdot [x(t)+x(-t)]$$ and $$x_{o}(t) = \frac{1}{2}\cdot [...
2 votes
2 answers
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How do I determine if the fundamental period $T_{x}$ exists and if so what it is?

I recently came across this $$ x(t) = \cos(6t) + \sin(8t) + e^{j2t} $$ signal that I want to find the fundamental period $T_{0}$ and fundamental frequency $\omega_{0} = 2\pi f_{0} = \frac{2\pi}{T_{0}}$...
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Convolution process confusion

I am currently studying for a test and I have this example: Given the impulse response of a system: $$ h(t) = \left \{ \begin{matrix} 1,& 0 \le t \le1\\ 0, & \mbox{elsewhere} \end{matrix} \...
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Compact books for reviewing signal processing

I am about to start a new engineering job in the fields of signal processing and machine learning. I have a bachelor's degree in electrical engineering, but for the last two years I have been doing a ...
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Condition for these sequences to be stationary correlated (tipp for integration of exponential functions)

I have two sequences $s$ and $r$ defined as : $s = \{s_n\}_{n \in \mathbb{Z}}$ where $s_n(t) = (M_{\beta}^n s)(t) = s(t) e^{int}$ with arbitrary $s \in L^2(\mathbb{R})$ and $\beta > 0$ $r = \{r_n\}...
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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 ...
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1 answer
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Finding a periodic signal knowing its period, mean value and power

I've found an interesting exercise which I have been trying to solve for a couple days, without success. Let $x(t) \in \mathbb{R}$ be a periodic signal with fundamental period $T_0 = \tfrac{1}{4}$, ...
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Inverse Continuous Wavelet Transform off by constant factors

I am implementing a continuous wavelet transform and its inverse using morlet wavelets. When I compute the inverse, the resulting signal is off by some constant factor (but otherwise correct). ...
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Stability analysis of hybrid discrete-continuous systems

I'm trying to derive the overall state-space system model for a hybrid system, in order to plot its eigenvalues. The system is shown as follows: Which is originally from this paper: Modeling and ...
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1 answer
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Inverse continuous wavelet transform output has significant error in magnitude and phase

For the inverse continuous wavelet transform, I am using a for-loop which runs through each frequency. At each frequency, I convolve the corresponding morlet wavelet with the signal at that frequency, ...
1 vote
1 answer
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AWGN continous time channel + colored noise

I'm working on an exercise but I'm stuck at the question where the noise becomes colored, can someone help me ? Let $\{\psi_1(t) = \mathbf{1}\{t \in [0,1)], \psi_2 = \mathbf{1}\{t \in [1,2]\}\}$ be an ...
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How to remove noise from audio and convert the audio to text

This is a video link https://www.youtube.com/watch?v=78YHir50N4o I have used the audio from this video. I am using SpeechRecognition library to transform it to text but because of the noise it is not ...
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mp3 encoding in the frequency domain

Let's start with an arduino signal, which can be periodic over time. When this signal is converted from analog to digital it "turns" into a series of bits. At this point, is this signal in ...
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1 answer
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Bandwidth of a given function

Suppose the signal given is $x(t)=(cos(5t)+e^{-2t})u(t)$ and the goal is to find the bandwidth of this signal. We know the bandwidth, $B$, is just $f_{max}-f_{min}$. Our first step is taking the ...
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Impulse Response Formula

How can you determine the impulse response if you know the output of the system? You should change the input signal with the dirac function with the argument equal to $t$ or $t-\tau$? I have this ...
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how to convert continuous signals into discrete signals / signal power

I've just started learning about continuous and discrete signals. I don't really understand how to convert continuous signals into discrete signals especially since there are no values given.
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Can the Fourier Transform of the unit step be used as a filter?

Using the FT of the step function we have $H(\delta)=\pi\delta(\omega)+\frac{1}{j\omega}$, and it's magnitude is $\infty$ at $\omega=0$ and approaches $0$ as $\omega$ goes to both positive and ...
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What is the magnitude response and phase of this function?

Given the system/filter $H(\omega)=\frac{1}{5-j\omega}$, find $h(t)$, it's magnitude response and phase and identify what type of filter it is. Now clearly given it's form, $h(t)=e^{5t}u(-t)$, but I'm ...
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Determine if the system is linear, time invariant

I have a system described by the following impulse response: $h(t,τ) = g(t-2τ)$ Where $g(t) = e^{-at}u(t)$ I have to determine if the system is linear time invariant causal Then I have to determine ...
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Spectrum of triangular pulse - MATLAB

I am new in matlab.I was given the code for spectrum of rectangular pulse of amplitude 1V and duration 1ms, and now I have to find the spectrum of a triangular pulse of amplitude 1V and duration 1ms ...
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1 answer
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reconstruct the low resolution signal before upsampling

When we upsampling a discrete 1d signal by 2x, we first interleave the signal by 0 and add zero padding, then pass through a low pass filter. low resolution signal [x1, x2, x3, x4] -> interleave 0 ...
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3 votes
1 answer
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Sufficient condition for a system to have memory

This is for a black box system which is not LTI and for which we have no input output expression, but we have some examples of sample inputs and corresponding outputs. I believe in this situation, we ...
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60 views

Fourier Transform: $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$

I'm currently studying Fourier Transforms and do not understand the Fourier Transform of $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$ My solution states that it is $X(\omega)=\frac{2}{2\pi}(-j\pi[\delta_0(...
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How do you prove that the bandwidth of a signal is inversely proportional to the length of the signal?

I am trying to prove the below identity where $f_c(x)=f(cx)$ such that c is a positive number. $F_c(\alpha)=\frac 1 c F(\frac\alpha c)$ F above represents the Fourier transformed $f(x)$. I attempted ...
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Computing Phase Response: do we reform equations to the form $e^{j\phi(\omega)} C(e^{j\omega})$?

I want to understand how we derive the Phase Response. The general formula is $H(e^{j\omega})=|H(e^{j\omega})|e^{j\phi(\omega)}$ Came across an example where: $H(e^{j\omega})=2\cos(\omega)e^{-j\omega}$...
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4 votes
3 answers
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Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions? I had this question when I saw this claim in my textbook: for ...
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What's the value of the integral $\int_{-4}^{4}(\frac{\mathrm{d}}{\mathrm{d} t} \delta(2t))\sin(t)\mathrm{d} t$ ..where $\delta(t)$ is the Dirac delta [closed]

Can it be solved like $$\begin{align}\int_{-4}^{4}\frac{\mathrm{d}}{\mathrm{d} t} \delta(2t)\sin(2t)\mathrm{d}t &=\frac{1}{2} \frac{\mathrm{d} }{\mathrm{d} t}\int_{-4}^{4}\delta(t)\sin(2t)\mathrm{...
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Calculation confusing of conjugate in CT fourier transform

when calculate conjugate of $$X(f)=\int_{-\infty}^{+\infty} x(t)e^{-j2\pi ft}dt ,\tag{1}$$ I can get $$X^*(f)=\int_{-\infty}^{+\infty} x(t)^*e^{j2\pi ft}dt ,\tag{2}$$ so $$F[x^*(t)]=X^*(-f).\tag{3}$$ ...
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Product of Doublet and Arbitrary Function

We know that the product of the delta function and another function samples the latter function. That is, $$ \delta(t-\tau)f(t)=\delta(t-\tau)f(\tau) $$ Does the doublet function retain this same ...
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1 answer
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How to find energy of the signal $S_1(t) = \sqrt{t}$ where $t \in [-1,1]$

What is the energy of the signal $S_1\left( t\right) = \sqrt{t}$ for $ t \in{[-1,1]}$ and $S_1(t) = 0$ otherwise. As all of we of us know, the energy of this signal should be finite. However this ...
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How to determine the impulse response matrix, when zero state response is given

My understanding is that since its zero state response, the system is at rest. But what should I do after that? is there any online material to read about this ? Thank you
1 vote
1 answer
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PSD of Poissonian shot noise

I have a signal $R(t)$ that is DC with shot noise. It has units of events per second. I am trying to understand this signal in a continuous-time picture. In time-domain, I can model it as a series of ...
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1 vote
2 answers
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Proving real and odd function has imaginary and odd Fourier Transform

Cheers, I am trying to prove that a real and odd function/signal has imaginary and odd Fourier Transform. Although it seems fairly easy, I can't find a way to achieve it, and searching online hasn't ...
5 votes
1 answer
141 views

Getting phase response from magnitude. How to develop and solve this Hilbert transform?

I'm trying to generate phase data from magnitude data in a frequency function, assuming the system is minimum phase. Using Hilbert Transform. For instance, having this simple system: $G(s) = s$ $G(j\...
1 vote
1 answer
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how to prove that the convolution between two discrete signals is the discrete signal of convolution between two continuous signals

Like the title. We already know $x[n]$ and $h[n]$ are the discrete time signal of $x(t)$ and $h(t)$ respectively, which are continuous time signals. And also $x(t)*h(t)=y(t)$, $x[n]*h[n]=y[n]$. Prove ...
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Calculate output of exponential signal, given $H(\omega)$

Cheers, I am given the input signal of $x(t) = A \cos(2πft + \frac{\pi}{4})$ which is linear and time invariant, and I am asked to find the output, if I know that, $f = 500hz$ and $|H(f)| = 1, \angle ...
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1 answer
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What is The Fourier Transform Formula for 1/(j*pi*t) Types?

I have old homework and solution of that but i didn't understand actually solution. Because i didn't see continous-time fourier transform formula for that. $g(t)$=$\frac{1}{j\pi*t}$ and it asks ...
2 votes
0 answers
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Ideal low pass filter with cut-off B does not affect a band-limited baseband signal with maximum frequency B

Let $x(t)$ be a band-limited signal with spectrum (fourier transform) lying between -B and +B. Such a signal is not warped by an ideal low-pass filter with cut-off frequency equal or higher than +B. ...
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Why doesn't the magnitude of Fourier Transform change when signal is shifted (i.e when a time shift is introduced)?

I understand that a time shift in the time domain produces a corresponding phase change / phase shift in the frequency domain. But I don't understand why the magnitude is unchanged (I am referring to ...
1 vote
1 answer
56 views

Ft and DTFT of negative frequency

I have a question that might sound silly but if I have a real and even signal x(t) can I define the FT and DTFT of the negative frequency if I can show: $$X(-\omega) = \int_{-\infty}^{\infty} x(-t)e^{...
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Fourier Series of a piecewise function

I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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1 vote
1 answer
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Find fourier transform given the graph of a function

Cheers, I am given the following graph for $x(t)$: and I am asked to find the fourier tranform by using the integral property and knowing that $F(Π(t)) = sinc (\frac{\omega}{2\pi})$ The solution I ...
1 vote
1 answer
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Find the unit-energy for $\mathrm{rect}(t/T)$?

My book says: The width-1 NRZ pulse is $$ \mathrm{rect} (t) = \begin{cases} 1 , \qquad -1/2 \leq t \leq 1/2\\ 0, \qquad \mathrm{otherwise} \tag 1 \end{cases} $$ The unit-energy width-$T$ NRZ pulse ...
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What's the base and height of triangle obtained by FT{$\operatorname{sinc}^2(7\pi t)$}?

I'm a little confused about the $\operatorname{sinc}^2(7\pi t)$ function. How do you know the base and height of the triangle produced in the frequency domain only looking at the $\operatorname{sinc}^...

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