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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If the system is not time-invariant what should be the difference between $h_k[n]$ and $h_0[n-k]$? Any examples?
I want to understand how convolution is defined for time-variant systems. I know that for linear time-invariant (LTI) systems, we use the standard convolution sum/integral to express the output in ...
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Fourier transform of decaying impulse train
I am working on finding the Fourier transform of the continuous-time signal defined by
$$ x(t) = \sum\limits_{k=0}^{\infty} \alpha^{k} \delta(t-kT) $$
where $|\alpha| < 1$. It is easy to see that ...
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How to extract only one underlying coherent cycle from the signal?
I only want to extract one cycle from the signal.What I tried is:
I subtracted raw signal from gaussian filtered signal(using ...
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Why does an LTI system not change a signal's sample rate?
I am taking a DSP course, and I want to understand the motivation behind a definition:
$x(t)$ is sampled by C/D at time intervals of $T_s$. We get the sampled signal $x[n]$ and it is fed into a ...
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Least Squares Spectral Analysis
For the traditional FFT, the frequency resolution is inversely proportional to the length of the sampled signal. I would like to know how to determine the frequency resolution of least-square methods, ...
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Generate Stationary Signals with Cholesky Decomposition with Random Amplitudes (CDRA) Technique
I am trying to simulate earthquake signals at different positions on a plane at x = 0, 500 m, and 1000 m using Cholesky Decomposition in Python, as described in the book I am following:
$$
f(x_i, t) = ...
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When to pick MUSIC, ESPRIT, GLRT instead of DFT for FMCW AoA?
In the context of FMCW angle of arrival determination and angle resolution, how can one know exactly which method to pick between MUSIC, ESPRIT, GLRT (relies on ratio of density of probabilities under ...
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Fourier transform of a periodic square wave
I'm quite perplexed by the Fourier transform of a periodic signal, such as a square wave.
I fully understand that such a signal can be represented by an aperiodic square pulse convolved with an ...
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What is the best Signals and systems Module Online course/resource/Youtube playlist?
What is the best "Signals and systems" Module Online course/resource/Youtube playlist?
FYI, this request is for a Final Year undergrad following Bachelor's degree in EEE.
I have checked Neso ...
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Bandpass Sampling Conditions Derivation
I’m taking a DSP course, and we covered bandpass sampling (undersampling). I’d like a rigorous derivation of the minimal sampling frequency $f_s$ and the corresponding constraints on the band edges $\...
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Time-invariant system paradox: fixed output at $t=0$, non-constant response?
I'm confused about the relationship between zero initial conditions in linear constant-coefficient differential equations (LCCDEs) and the time-invariance of their associated input-output systems.
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How does a real 1D signal gets turned into an complex electromagnetic wave through an antenna?
For example, imagine a person speaking on a cellphone. A transducer converts air pressure into a voltage signal. This voltage signal should still be a real 1D signal in time.
To transmit this 1D ...
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Usage of Ramping Functionality in interrupts
This is a general technical query to gather ideas regarding the use of ramp functionality on audio signals within interrupts when developing code for DSP processors.
Given that interrupt service ...
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How to calculate the periodic system response of an LTI system?
Given $h (t) = e^{-t} u(t)$, where $u$ denotes the Heaviside step function, find $h_{\text{per}}(t)$, the periodization of $h$ with period $T$.
I found $H(\omega) = \dfrac{1}{1 + j\omega}$, and now I'...
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LTI convolution integral $\int _{-\infty}^{\infty} L\{ x(\tau) \delta(t - \tau)\} \ d\tau$ why $L$ act on $t$ rather than on $\tau$?
In the usual derivation of the LTI convolution formula, we often start with this identity:
$$x(t) = (x*\delta)(t) = \int _{-\infty}^{\infty} x(\tau) \delta(t - \tau) \ d\tau$$
Then for a linear system ...
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