# 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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### Continuous-time convolution of signals with negative amplitudes

While preparing for a mid-term exam, I encountered negative amplitudes for the first time while convolving two signals. I've already solved the problem, but my result and results from others conflict ...
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### How to plot a sawtooth chirp waveform using an array of frequency and time for an FMCW radar?

Before switching to use sawtooth I was using sine wave but in sine wave high frequency content was not clearly visible, But I don't have any experience with using sawtooth waveforms. I am going to ...
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### Unwindowed STFT of sine, closed form solution and insights (sliding FFT)

I seek to calculate, mathematically, the unwindowed Short-Time Fourier Transform of $$\cos(2\pi f t + \phi)$$ i.e. any arbitrary real-valued sine: any frequency, duration, phase shift, and number of ...
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### Inferring properties of a signal from its autocorrelation

In a previous thread, it was asked whether we can infer a signal from its autocorrelation, and the answer was a clear no, since the autocorrelation process is lossy. Still, is there anything we can ...
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### How can I find the following Fourier Transform without directly using FT pairs?

The question is to find the CTFT of $$x(t) = e^{-t}u(t)\cdot \sum_{n=-\infty}^{\infty} \delta\left(t-\frac{n}{2}\right)$$ Now I know that multiplication in time means convolution in the Fourier Domain ... 89 views

### Calculating DC from signal avg or rms value required?

If we want to calculate a dc value of any given signal, should the dc value be RMS or average value?
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I have a problem in signals and systems to solve which is basically math So suppose we have two functions x(t) = H(t) which is the Heaviside unit step function as input and an impulse response $$h(t)=... 0 votes 2 answers 69 views ### What is DC gain of sine wave multiple? I am testing about injection sine wave current to r,c impedance and measurement R + jX see fig.1 . When scope is Va . When sine wave multiple (Va*Vb). I put average to find DC of this signal.Is ... 2 votes 1 answer 77 views ### Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses? Let$$\dot{x} = Ax+Buy = Cx + Du$$be a linear ODE with x(0)=0. Here, I am assume A is invertible. As you can see, the relation$$H:u(.) \mapsto y(.),$$where (u(.),y(.)) is a solution to ... 0 votes 2 answers 69 views ### DFT modulus of a sine, closed form solution and insights A closed form solution to$$ X[k] = \texttt{DFT}\{\cos(2\pi f t + \phi)\} $$confirmed many known properties of a finite sine's spectrum, also revealed new ones. Can the same be done for |X|, or |X|... 0 votes 1 answer 63 views ### Effect of sampling rate and duration on discrete parameters of sine (spectrum)? The DFT of$$ \cos(2\pi f t + \phi) $$peaks at k=\pm f if t = \frac{1}{N}[0, 1, ..., N - 1] (for integer f, & within Nyquist). What about other t? What if we double the sampling rate or ... 0 votes 3 answers 165 views ### Power / energy of complex signals - physical interpretation I am wondering about physical interpretation of energy / power for complex signals. E.g. for signal energy definition: \begin{equation} E=\int\limits_{-\infty}^{\infty}|x(t)|^2 \, \mathrm{d}t \end{... 11 votes 3 answers 2k views ### What information does the Hilbert transform give? The Hilbert transform of a function is defined as :$$\mathscr{H}\big\{f(t)\big\} = \lim_{T\rightarrow \infty}\frac{1}{\pi}\int\limits_{-T/2}^{T/2}\frac{f(\tau)}{t-\tau}\, \mathrm{d}\tau$$Okay but ... 1 vote 3 answers 98 views ### How to separate Transient and Steady-State Expression from Periodic Summation Response? Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ... 2 votes 1 answer 69 views ### How can Haar basis be written as the impulse response of an LTI system? Haar wavelets are defined as:$$\phi_{0,0}(t) = \begin{cases} 1, & \text{ for } 0<t< 1/2\\ -1, & \text{ for } 1/2<t<1 \\ 0, & \text{ ... 1 vote
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### Laplace domain transfer function from system sampled at discrete times

I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is here (PDF page 6, slide marked 11); I'll explain further below. Suppose I have a ...
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### How EEG signal is windowed? Windowing vs Epoching are they same?

I am experimenting with EEG dataset from this (title: "The Perils and Pitfalls of Block Design for EEG Classification Experiments") paper. They have applied various ML models on different ...
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