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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14 views

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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2answers
47 views

Autocorrelation function and correlation integral

I am confused by the definition of autocorrelation function. It is originally defined as the expected value $$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$ where $\langle\...
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3answers
34 views

Time scaling and shifting of delta function

Learning signals and systems. Solving time scaling and shifting problems. For the question $$x(t) = u(2t - 1)$$ First we shift by 1 to the right side and then we do time scaling , i.e divide by 2 ...
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2answers
38 views

Determining time-invariance of a system

I have a question about determining time-invariance of a linear system. We are given this system and we need to determine if it is time-invariant or not: $$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$ ...
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30 views

How to determine number of observations based on measurement frequency?

So I'm working on a problem where I'm measuring a signal with two different instruments -- one is a low frequency measurement system (1 Hz), and the other is a high frequency measurement system (200 ...
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4answers
75 views

Negative frequency in the Fourier Transform [duplicate]

Why use this instead of a positive frequency? I asked on the math forum but it just wasn't helpful. I understand the idea of a negative frequency is important in general since many real signals like ...
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2answers
95 views

Question about Hilbert transform

Hilbert transform of a function $g(t)$ which is defined in time domain, would result in another function in time domain. Is there any other transformation like Hilbert that the results be in time ...
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1answer
18 views

Baseline correction for continuous EEG signals

I'm new to the topic so forgive the trivial question. I am trying to understand data preprocessing for EEG signals. As I understand, after recording continuous EEG signals, they should be band-pass ...
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1answer
18 views

plotting exp signal in matlab

My program is as follows: ...
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1answer
30 views

Continuous frequency grid to discrete grid

I am designing a controller for a system using several methods, one of which is a discrete method. In the continuous time I am looking at a logarithmically spaced frequency grid in the range $$\omega \...
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5 views

Using delta MFCC for signal segmentation

Hello I am focused on implementing a method of speech segmentation into syllables based on delta mfcc. After the calculating of delta, I extracted their maximum local and the next step is to determine ...
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23 views

how to perform frequency convolution?

much has been said about convolution of continuous time signals. But what about frequency convolution? For instance, consider the function: $$f(t) = \text{sinc}(t)=\frac{\sin x}{x}$$ I take the ...
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2answers
86 views

Continuous vs discrete signal energy

I am looking to calculate the signal energy of real, sampled acoustic data. According to this source, the energy of a continuous signal is: $$\tag{1}\hspace{1cm} E_x = \int_{-\infty}^{+\infty}|x(t)|^...
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143 views

Cross correlation and cross power spectrum for signal + noise

Quick question about my understanding of cross correlations and cross spectral densities. Let $C_{ab}$ be the cross correlation between the signals $a$ and $b$, i.e., $C_{ab}(\tau) = \langle a(t)b(t+\...
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2answers
31 views

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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2answers
64 views

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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19 views

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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6answers
383 views

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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4answers
347 views

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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1answer
40 views

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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1answer
32 views

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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2answers
50 views

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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208 views

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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1answer
45 views

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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2answers
28 views

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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1answer
16 views

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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56 views

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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2answers
85 views

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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1answer
58 views

“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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2answers
55 views

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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1answer
61 views

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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1answer
76 views

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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1answer
25 views

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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96 views

Help with finishing this integral, to obtain the power spectral density of a pure cosine wave

I am trying to evaluate the power spectral density $S_{xx}(f)$ of a cosine signal $x(t) = A\cos(2\pi f_0t)$, by starting from its definition for deterministic power signals $$S_{xx}(f) = \lim_{T\...
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5answers
541 views

Inconsistency with the units of power spectral density and the definition the people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\infty}_{-\...
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3answers
227 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 ...
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2answers
61 views

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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1answer
322 views

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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16 views

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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51 views

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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1answer
59 views

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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1answer
85 views

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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19 views

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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1answer
35 views

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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12 views

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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1answer
61 views

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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1answer
59 views

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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1answer
74 views

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 ...
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3answers
69 views

Basic Understanding of Convolution Operation

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-...
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1answer
49 views

How to generate IQ samples of a signal?

I am using a HW with LMS7002 RF transceiver chip. This chip takes IQ values as an input. 1. Can anyone point me to a sample IQ value generator? That I can use to test. 2. What will be the IQ values ...

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