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 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? ...
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$2\pi$ periodicity of discrete-time Fourier transform

In my signals and systems course, we have learned that the discrete-time Fourier transform is $2\pi$ periodic, but the continuous-time Fourier transform is not periodic in general. For reference, we ...
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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 ...
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3D wiggle plot for an analytic signal: Heyser corkscrew/spiral

Just reading The Analytic Impulse, A. Duncan, 1988, I met the name "Heyser corkscrew" for the first time in my DSP life, for a 3D display of a cisoid or complex exponential $e^{i\omega }$ (often ...
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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 $A(s)$ ...
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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 $$E_{\textrm{s}} = \int^{+\... 1answer 3k views Is convolution distributive over multiplication? Is there any formula or expansion for$$a(t)*[b(t) \cdot c(t)]a(t) \cdot[b(t)*c(t)]$$where * denotes the convolution? By expansion I mean something like a(t)\cdot[b(t)+c(t)]=a(t)b(t)+a(t)... 1answer 6k views How to calculate the mean/center frequency of the spectrum? Assume that the Fourier Transform of x(t) is X(j\omega). And I want to calculate the \bar{\omega} which is the center freqency in the spectrum ( the highest). And a classmate tells me this ... 3answers 2k views Mathematically Inclined Signal and Systems / Signal Processing Book Recommendations I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ... 2answers 23k views What is the difference between continuous, discrete, analog and digital signal? It's my first time studying DSP and I've faced a problem finding a convenient definition. Are the following definitions correct? And if so why there are some resources defining it in other terms such ... 2answers 4k views What is the intuition behind convolution? [duplicate] I have been using convolution for finding outputs of various systems .I know how to use it.But I still don't know what does convolution exactly means? how one can define convolution ? 1answer 1k views Sampling signal after root raised cosine I am generating series of 1 and 0. then pulse shaped them with root raised cosine and after than deciding to do match filtering and recovering the bits however it turns out that I am not getting the ... 3answers 2k views Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD) I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ... 1answer 4k views When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start? Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ... 4answers 122 views Meaning of frequency and bandwidth of a signal, despite the fact that we do not know the signal First of all, I am completely new to the domain of signal processing. As far as I know, a signal can be represented with an infinite integral of infinitesimal complex exponentials, which is known as a ... 1answer 650 views How to analyse the sound of Motor I have a motor, that I want to analyse, using its sound, so I can its 'character' I was using the the simple fft, and figured out, that it wouldn't help, so I tried the order analysis, at least I ... 2answers 684 views Duality of the continuous-time Fourier transform - derivation and notation Suppose we have the Fourier transform pair x(t) and X(\omega) such that$$X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} \mathrm{d}t$$The duality property states that X(t) and 2\pi ... 6answers 76k views The difference between convolution and cross-correlation from a signal-analysis point of view I am trying to understand the difference between convolution to cross-correlation. I have read an understood This answer. I also understand the picture below. But, in terms of signal processing, (a ... 2answers 15k views Using continuous verses discrete wavelet transform in digital applications I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ... 4answers 17k views For an LTI system, why does the Fourier transform of the impulse response give the frequency response? I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a ... 4answers 1k views Is Fourier series a sampled version of Fourier transform? I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ... 4answers 22k views About Fourier transform of periodic signal In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao: The ... 1answer 15k views Proof of time-invariance of continuous-time system I have a system with the following input/output relation:$$ y(t)=x(-t) $$and I want to prove (not graphically/draw) that its not time invariant (TI). I tried to write down y(t-T) and compare it to ... 1answer 961 views Can a Fourier Transform exist even if the j\omega axis is not in the Region of Convergence in it's Laplace Transform A couple of confusions have been occurred. The Signal I'm considering is f(t) = sin(t)*u(t) Fourier Transform of it can be derived. -i \pi (\delta (\omega -1)-\delta (\omega +1)) According to my ... 1answer 2k views Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal? I have been studying signals and systems lately and I have came across the following claim: The uniform sampling of a periodic continuous-time signal may not be periodic! Can someone please ... 2answers 851 views why total energy of a finite duration continuous signal becomes infinite after sampling If I have a continuous-time energy signal and multiply it with an impulse train, the frequency domain representation has infinite replicas. The total energy if we sum them up becomes infinite. What ... 5answers 5k views Effects of linear interpolation of a time series on its frequency spectrum Situation In order to synchonisize different time series i have to apply linear interpolation on them. After the interpolation and synchronization the signal is transferred into its frequency domain ... 2answers 1k views Linear Constant Coefficient Differential Equations: Zero-Input and Zero-State responses The solution to a linear constant coefficient differential equation of the form$$\sum_{k = 0}^{N} a_k y^{(k)} (t) = \sum_{k = 0}^{M} b_k x^{(k)} (t)$$can be written as y(t) = y_{ZI} (t) + y_{ZS} (t)... 3answers 3k views Is the system represented by the equation y(t) = x(2t) time invariant? I came across this problem in the text book Signals and Systems - Oppenheim (Example-1.16). To solve this, I followed the following algorithm (described in the book earlier for a separate problem): ... 3answers 30k views Alias frequency Formula I'm taking a multimedia systems class in my MSc Computer Science, and I'm having some trouble understanding the formula for the alias frequency - this could stem from my misunderstanding of the alias ... 3answers 1k views Fourier Transform Identities We know the below,$$ \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(-...
In continuous time the standard exponential signal is usually defined as $$e^{st}, \quad\text{with}\quad s = \sigma+j \omega$$ In discrete time the standard exponential signal is usually defined as ...