# 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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### name the RF Impairments That Distort a Signal before it is converted to baseband form? [closed]

let's suppose we have a HF signal for instance what are the impairment or all the processing we need to do before we can get into matching filtering and equalizer: Phase/Frequency Offset , I/Q ...
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### Where did the k of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$?

Where did the $k$ of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$? We turn $\omega0$ to be $d\omega$, but $\omega=\omega_0k$, so shouldn’t there be a $k$ in the reverse ...
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### Is there an easy way to translate a Fourier transform table from angular frequency $\omega$ to Hertz $f$?

I have a table with transform operations, e.g. scaling: \begin{equation} \tag{0} \label{0} x(at) \iff \frac{1}{a} X(\frac{\omega}{a}) \end{equation} or frequency shifting: \begin{equation}\tag{1} ...
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### Difference between these two Continuous Wavelet Transforms?

I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
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### Design a LTI system which returns DC value of the input signal

Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
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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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### Initial rest condition for the linear constant-coefficient differential equations

Suppose that system has the input/output relation as follows $$\sum_{k=0}^{N}a_k \frac{d^ky(t)}{dt^k} = \sum_{k=0}^{M}b_k \frac{d^kx(t)}{dt^k}$$ Where $a_k, b_k \in \mathbb{R}$. Obviously we ...
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### Sampling rate and number of samples

I am doing an experiment where i have to excite a plate and scan a region on it using a laser signal. I am acquiring the signal from the laser continuously using an NI daq tool. i then have to divide ...
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### Unit impulse vs Kronecker delta vs Dirac delta?

Apparently these 3 terms are similar, but what is exactly difference between them and what is exact value of each of them at time zero,1 or infinity?
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### How can I generate a sine and cosine function using an exponential function?

I have been trying to generate sine and cosine sampled graphs by a given sampling frequency. ...
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### A check on the definition of the continuous periodogram, and does it assume ergodicity somewhere?

Can someone verify my understanding of what the continuous periodogram is/means, and please tell me if I say something wrong: As I've learned so far, the power spectral density of a wide-sense ...
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### Understanding Communication Theory Jargon for Statistical Linear Models

Coming from a statistical background, I understand the following formula: \begin{equation} y = X\beta + \epsilon \end{equation} as a linear regression model, with data input-output pair: $(X,y)$, ...
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### Difference in frequency spectrum of continuous time signal and discrete time signal?

I am studying chapter 4 of book signal processing first There i came across a concept which says that(what i have understood)the spectrum of continuous time signal has limited number of lines while ...
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### When deriving the power spectral density of stochastic processes, why does taking an expectation allow the $T\rightarrow\infty$ limit to be taken?

I am following the arguments presented in the paper AN-255 Power Spectra Estimation, from Texas Instruments, to learn how to derive the power spectral density for a stationary stochastic process, and ...
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### Time reversal of input signals in convolution

Let $f(t)$ and $g(t)$ be signals. I can't figure out what happens to the convolution of $f(t)$ and $g(t)$ if both $f(t)$ and $g(t)$ are reversed one of $f(t)$ and $g(t)$ is reversed I tried the ...
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### “plot” command for continous time signal in matlab?uses interpolation?

We know digital computer cannot deal with continuous time signals directly. But then how MATLAB "plot" command works? Does that uses interpolation technique to show an apparently continous time ...
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### Signals in real world?especially natural signals?

Do all the signals in real world ,that are of interest in engineering(for measurements or processing)are only continous/analog or there any other alternatives also? For example birds make voice,...
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### Discrete and Continuous Signals

I am new to the signals area and have been reading through a lot and have some questions. Suppose I have a saved audio file on my computer, .wav file. I can view the time domain of the signal by ...
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### Zero forcing vs matched filtering vs LMMSE

In what scenarios would you choose each of Zero forcing, LMMSE and matched filtering receivers: Possible points to consider are: Receiver SINR, High Interference levels, Low interference levels, ...
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### mathematical equation for Power Line communication channel [closed]

How can I derive the mathematical equation for the powerline communication channel to capture the input data signal, the power line channel, and noise?
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### 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 ...
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### Eye pattern construction and interpretation

I have read some text about the eye pattern (or eye diagram), but I do not understand how should I read it. The wikipedia definition of it is this one: In telecommunication, an eye pattern, also ...
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### Evaluating the continuous Fourier transform of a constant, and matching it up with the FFT result

I am following my optics textbook (Optics, by Eugene Hecht), throughout which are given various exact analytical results for the diffraction patterns that result from light passing through differently ...
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### How to update Kalman Filter with n-th order state translation?

In Kalman Filter, the hidden state translation is defined by $X_t=F_tX_{t-1}+W_t$, where $X_t$ can be a vector or a single value. This is actually derived from Bayes filter, in which 1-th order markov ...
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### Filter response to sinusoidal input signal

This question is related to Does 46 dB gain of a filter for a frequency imply 200 times more amplitude? In the accepted answer it is mentioned that "For a sine wave input the amplitude of the steady ...
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### What kind of periodic signals cannot be represented with the Fourier Series?

Oppenheim et al. state in Signals and Systems that there exist periodic signals which cannot be represented with Fourier series. What signals are these? Although Euler and Lagrange would have been ...
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### How to approximate a moving RMS without iterating over N samples for each required output?

I have a signal with a sampling rate of F Hertz. From it I want to produce an RMS signal, also with F samples per second with a window size of N samples. Using a standard moving RMS algorithm I must ...
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### How can I calculate time gap in different waves

I want, calculate the time gap between two signals .but that signal has frequently changed the frequency range. I want to combine with these two signal including phase shift I have a circuit for ...
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### std::cosf fluctuation: Results are off in low frequencies [closed]

I attempted to generate a continuous wave signal by using the C++ cos/sin functions. It's partly successful, meaning high frequencies seems ok, but very low frequencies give unexpected results. The ...
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### Functioning of a continuous data stream processing neural network?

I've been searching with unfortunately no relevant results about something I have trouble to figure out: neural networks which process continuous data stream (audio, video, anything with a state ...
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### machine learning on multiple signal at once

I am very new signal processing and I am asking this with the expectation that someone gives me a concrete guideline on how to approach my problem. The problem I need to solve is that I have 2 ...
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### Proving linearity and time-invariance

This question was asked in one of our quiz. Question is Determine if the system with the input-output relationship given by $$y(t) = \int_{t-10}^{t} \cos(\tau)x(\tau)d\tau$$ is linear ...
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### relation between DFT to CTFT

The signal $$x(t)\;\;\;\;0\leq t\leq 0.2s$$ We know that the CTFT of $x(t)=0$ when $|w|>2*\pi*10^4$ We sample $x(t)$ in sample space of $$T=25\mu s$$ or $$F_s=1/T=40000Hz$$and we get a series ...
I would really appreciate any help in understanding this. If $$y[n] = x[n]*r[n]\tag{1}$$ then what is $y[n-n_0]$ for any system? Is it $$y[n-n_0] = x[n-n_0]*r[n-n_0]\tag{2}$$ or y[n-n_0] = x[n-...