Signal Processing Stack Exchange
Signal Processing Stack Exchange

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.

In case of a continuous signal, the function's domain is an uncountable set. The function itself need not be continuous. To contrast, a discrete time signal has a countable domain, like the natural numbers.

Source: Wikipedia.

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The difference between convolution and cross-correlation from a signal-analysis point of view

I am trying to understand the difference between convolution to cross-correlation. I have read an understood This answer. I also understand the picture below. But, in terms of signal processing, (a field which I know little about..), Given two…
MathBgu
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Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ we substitute $$z =…
Phonon
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How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? Secondly, the theory says that a system is stable when…
Val
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Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or discrete wavelets. In all reality everything on…
John Robertson
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What are advantages of having higher sampling rate of a signal?

Being a non signal processing science student I have limited understanding of the concepts. I have a continuous periodic bearing faulty signal (with time amplitudes) which are sampled at $12\textrm{ kHz}$ and $48\textrm{ kHz}$ frequencies. I have…
Raady
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Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original signal using the same Gaussian. The problem is that…
user1724
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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 negative-going Delta function. Could you please…
Amro Goneim
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Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

I have been studying signals and systems lately and I have came across the following claim: The uniform sampling of a periodic continuous-time signal may not be periodic! Can someone please explain why this statement is true?
a4w
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Why do linear systems show sinusoidal fidelity?

I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine or cos wave then the output only changes the…
Hobyist
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Do discrete-time series always have a continuous-time underlying?

Can one argue that discrete time-series coming from stocks or commodities (prices) are derived from a continuous-time process? One can probably argue that stocks or commodities at any time have a value and therefore a continuous-time price/value…
cifuentesba
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Inconsistency between the units of power spectral density and the definition that people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a continuous signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\infty}_{-\infty} |x(t)|^2\mathrm dt \hspace{1cm}…
teeeeee
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Deriving the Fourier transform of cosine and sine

In this answer, Jim Clay writes: ... use the fact that $\mathcal F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$ ... The expression above is not too different from $\mathcal F\{{\cos(2\pi…
pyler
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Alias frequency Formula

I'm taking a multimedia systems class in my MSc Computer Science, and I'm having some trouble understanding the formula for the alias frequency - this could stem from my misunderstanding of the alias signal. My understanding of an alias signal is…
user1058210
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Fourier Transform Identities

We know the below, $$ \mathscr{F}\big\{x(t)\big\}=X(f) \tag{1} $$ $$ \mathscr{F}\big\{x(-t)\big\}=X(-f) \tag{2} $$ $$ \mathscr{F}\big\{x^*(t)\big\}=X^*(-f) \tag{3} $$ Now, if for some signal $$ x(-t)=x^*(t) \tag{4} $$ Then, is it safe to assume the…
sundar
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For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a definition or if there's a mathematical proof…
Florian Castellane
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