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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How can I solve this [closed]

a) Consider the signal waveform g(t)= g1(t) + g2(t) where g1(t)= C1cos(w1t+θ1) g2(t)= C2cos(w2t+θ2) and w1≠w2 i. Determine the suitable signal size measure for g(t) ii. Find the numerical value of (i) ...
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Sinc function Energy [closed]

I am struggling for days trying to compute the energy of the follow sinc function. Any help appreciated ! Thanks. -(sin(π(t-2)/2))/(π(t-2)/2))
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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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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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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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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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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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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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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
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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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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 ...
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5 votes
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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\...
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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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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 ...
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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 ...
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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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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 ...
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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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What will the output of a system which has no Fourier transform?

Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?
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Confusions regarding differences between Fourier transform & Laplace transform?

Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard Number 1) Link of question https://electronics.stackexchange.com/questions/...
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Graph Plot On Time Shift of Cosine Signal Hanning Function

I am plotting time shift of the Hanning function. I find few plot result that I am not able to understand. Therefore I would like to ask my question here. The given Hanning function is: $$ x(t)={\tt ...
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Is the filter $1/(1-s)$ anti-causal?

The filter with the response function $$ H(s) = \frac{1}{1 - s} $$ Produces a positive phase shift and a negative group delay for all frequencies Is it anti-causal? Is there a way to deduce such ...
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2 votes
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How to design a digital Butterworth bandpass filter?

I am looking into designing a Bandpass Butterworth filter in python, but, I was not sure I am designing my filter correctly. What I have are the following: High cutoff frequency = 200Hz Low cutoff ...
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How to design function for Random Decrement technique in python and implement the function?

I was looking into a technique called Random decrement technique from the following links/articles: How can I use Random Decrement Method to convert a non-stationary signal into a decay function ...
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3 answers
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Doppler shift in signals

I have started doing some reading into the effects of the doppler shift on signals. In particular, radar signals from ships moving relative to a receiver. This might seem weird but I understand why ...
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Fourier transform of $\textrm{sinc}^2(100\pi t)$

I'm confused about a tutorial problem concerning the Fourier transform of the $\textrm{sinc}^2$ function. Specifically, the question involves the Fourier transform of $\textrm{sinc}^2(100\pi t)$, ...
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1 vote
2 answers
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How are pole-zero plots, magnitude response plots, and phase response plots related?

Given that the Laplace transform of a continuous-time signal $h(t)$ is $H(s)$, what can a plot of the poles and zeros of $H(s)$ on the $s$-plane tell me about the magnitude response and phase response ...
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Time Invariance of Continuous Time System

I am trying to check whether the system given by the following input-output relation is LSI or not? $$y(t) = \cos(x(t)-x(0))$$ My work: The given relation: $$y(t) = \cos(x(t)-x(0))$$ If the input ...
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How to create an objective function for Mackey glass time series (using "bayesopt")?

I am optimizing 5 hyperparameters of Mackey-Glass time series and using built-in function "bayesopt" in MATLAB. My Mackey glass time series with fixed parameters shows correct results. ...
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How can we translate this statement into an input signal expression?

I want to make sure if I got this right, the following statement: if the operator enters a unity sloped linearly increasing input then the output must eventually track the input and be at most 0.1 cm ...
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Where is SNR and CNR calculated for LTE?

I read below that SNR and CNR are different and we have difference of post/pre modulation. In context of LTE which modulation do we refer to- Digital Data modulated using QAM/QPSK to IQ, or Baseband ...
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CTFT of $ X(j\omega) $ vs $ X(jf) $

The CTFT of a signal as a function of $ \omega $ and $ f $ is identical: $$ X(j\omega) = \int_{-\infty}^{\infty} x(t) \, e^{-j \omega t} \operatorname{dt} \;\;\;\;\bigg|\;\;\;\; X(j f) = \int_{-\infty}...
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How do we equate the signal energy before and after sampling?

I have a band-limited signal and sample it at sample rate of $f_\mathrm{s}$. By taking the continuous time fourier transform, I will see copies of the same signal at $n\cdot f_\mathrm{s}$ where $n \in ...
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