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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81 views

How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?

This result has been used in the second last line of the pic. I don't know why it's true. Both functions are zero for $t$ not equal to $-b/a$. But at $t=-b/a$, a scaling factor $1/|a|$ has been ...
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15 views

Using unlabeled EEG data for Machine Learning

I am working on a project that is basically a game for motor-paralyzed people. It should take an EEG signal from FP1 channel of brain and then after processing it should generate command for the game ...
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1answer
32 views

Is $y(t) = \cos(t) + x(t)$ a time-invariant system?

Is $y(t) = \cos(t) + x(t)$ a time-invariant system? $y(t-k) = \cos(t-k) + x(t-k)$ But it isn't equal to $\cos(t) + x(t-k)$ So, would it be time-invariant?
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14 views

In an automotive ECU application for STM32, what ADC modes should I use? [migrated]

I am writing an application for the STM32f407-Discovery board that will use the ADCs present on it. I want to have access to all 17 of the input channels, and I will be using the HAL library to write ...
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12 views

Signal similarity analysis after cross correlation

I have a time series signal and using this as reference, from the main data set extracted possible matching sections using cross correlation technique.(xcorr matlab).Based on with the threshold xcorr ...
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1answer
42 views

Fourier Series representation of a signal

Use the defining equation for the Fourier Series coefficients to evaluate the Fourier Series representation of the following signal: $$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
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31 views

Time Domain Behaviour of Thermal Noise

Let's consider the thermal noise (or Johnson–Nyquist noise): It is white noise, that means that its power spectral density does not depend on frequency. Now my question is: Which is a typical time ...
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2answers
99 views

What is the autocorrelation of a Dirac pulse?

What is the autocorrelation of $x(t) = \delta(t)$? Can you explain to me how to calculate it?
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2answers
49 views

Matlab - Bode plot of Lag Filter + Integrator

I am rather new to Matlab and I just cant make sense of what I see in the bode plot of the continuous and discrete version of the same function. The bode plot of the continuous function looks as ...
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1answer
19 views

Bessel filters: linear passband phase characteristic only for low pass filters?

I've found a test (internet) from the contest to signal processing teacher and it has a question (true) or (false). I cant find any book or paper to argue this statement. Is it really true?
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1answer
65 views

Initial Rest Condition for LCCDE causal LTI systems

I am self studying Alan Opennheim's course Signals and Systems. I am a math major and have no background in EE. I understand that for a LCCDE system to be linear its auxiliary conditions must be 0. ...
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42 views

Fourier series representation of a full wave rectifier output

I am trying to compute the Fourier series representation of a full wave rectifier output. The equation of the signal is: $ x_8(t) = | \cos (2 \pi f_o t) $ | I have tried to find the Fourier series ...
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1answer
27 views

Inverse Laplace Transform

A system given by $\frac{s-1}{(s+1)(s-2)}$ has to be inverse transformed so that it is anticausal and nonstable. The answer given is $h(t)=-\frac{1}{3}(2e^{-t}+e^{2t})u(-t)$ Why the minus sign at the ...
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1answer
23 views

Determining Stability of a continuous time system using Laplace Transform

I'm following Oppenheim's book. In exapmles, the laplace transforms of of the following signals $e^{-t}u(t)$ and $e^{-t-1}u(t+1)$ is given as $\frac{s}{(s+1)}$ and $\frac{e^{-s}}{(s+1)}$ both ...
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1answer
57 views

Step response of third-order continuous-time transfer function

I have a transfer function of the form: $$H(s) = \frac{b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}{s^3 + b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}$$ If it matters, $a=b=2$. Is anyone aware of ...
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1answer
57 views

How can the Poles of the Root Locus be negative?

My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...
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2answers
54 views

Cross-correlation of filtered random processes

I have a wide-sense-stationary (WSS) process $\{x(t)\}$ and two linear filters with impulse functions $h_1$ and $h_2$. Let $\delta(\omega)$ be the power spectrum of $\{x(t)\}$ and $$H_1:\omega\...
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37 views

Fourier Transform: interpretation of continuous spectrum at specific frequencies

B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform: When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
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2answers
162 views

Aliasing when interpolating with DFT?

I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me. I have created a noiseless signal as: ...
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1answer
39 views

What is Imaginary in Fourier transform?

How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
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2answers
44 views

Help regarding property of unit impulse function

We know that using properties of unit impulse function it can be shown that $$\int_{t_1}^{t_2} x(t) \delta^{(n)}(t-t_0) dt=(-1)^nx^{(n)}(t_0),\quad t_1<t_0<t_2$$ (source: Continuous and ...
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4answers
72 views

Determining LTI system response to a scale change

We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on. But my question is what will be the system response for the input $x(-2t)$...
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1answer
41 views

How to automatically identify a surge in a periodic signal

Say I have a periodic signal i.e. Sine wave, which sometimes can have spikes that are 100% larger than the peak value. These spikes can be periodic as well. I'm trying to find an algorithm that could ...
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4answers
695 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 ...
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3answers
198 views

How can I know if these two signal are orthogonal to each other

So the question is to determine if this statement is true or false. The question can be seen below. I know that two signals are orthogonal if their inner product is equal to 0. I know how this ...
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1answer
37 views

How to convolve $u(-t)$ with other signals?

How can I convolve the following $u(t+1)*u(-t)$ I know that convolution with $u(t)$ gives the integral of a function but what change occurs due to $u(-t)$?
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1answer
46 views

Continuity and its relationship with asymptotic spectral decay

The asymptotic decay of the magnitude of the Fourier transform of a function appears always to be determined by its continuity properties as follows, with examples given in Fig. 1: Continuous ...
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0answers
29 views

what is the co-variance of system output cooresponding to a non-iid random variable

Consider the following system.$\DeclareMathOperator{\sign}{sign}$ $$ \begin{aligned} &\dot{e_1}=c_1e_1+c_2e_2+\eta\\ &\dot{e_2}=c_3e_1+c_4e_2-c_5 \sign(e_1)+a \eta \end{aligned} $$ which $\eta$...
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1answer
59 views

analog-to-discrete-to-analog system sampling problem

This is not a homework problem, I am solving practice problems for my exam. Consider the analog-to-discrete-to-analog system shown in figure 1. The CT signal $x_a(t)$ is sampled at a frequency of $...
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3answers
48 views

Characterization of transfer functions with no local peaks

Assume that you are giving an arbitrary amplitude frequency response $A(\omega)=|H(j\omega)|$ Is there a characterization that ensures that $A$ is monotone? i.e, $A$ has a global maximum at $\omega=0$...
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1answer
77 views

Laplace transform of a finite duration signal

Consider the following signal: $$ x(t) = e^{-2t}[u(t) - u(t-5)] $$ This signal exists only from 0 to 5 time units. Elsewhere, it is zero. Now, let's find the laplace transform of this signal using ...
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23 views

Find LF component of AM signal

I'm trying to figure out how to find the low frequency component of an AM-signal when I have regained the carrier. So the signal is: $$U_{AM} = 2[3+0.4cos(2\pi\cdot2\cdot 10^3\cdot t)]\cdot sin(2\pi\...
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0answers
19 views

Signal Header:Physical Min is not less than Physical Max- after opening EDF file on the viewer

Whenever I open an EDF file on the Case Western Research University's EDF Viewer Application, I get a Scaling Warning-"Signal Header:Physical Min is not less than the Physical Max ". I am reading ...
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1answer
48 views

What is the effect on Hilbert transform of signal after multiplication by sinusoid?

Question : Find Hilbert transform of $[u(t-a)-u(t-b)]\cos2\pi f_{0}t\\\\$ such that $\\0<a<b$ my attempt: we know Hilbert transform of $[u(t-a)-u(t-b)]\xrightarrow{\mathcal H} \dfrac{1}{\pi}\...
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1answer
30 views

Continuous time double exponential filtering in state space form?

I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem. Typically, this model is expressed as a pair ...
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2answers
55 views

How is frequency defined for a periodic signal?

For sinsusoids, frequency is $2\pi/T$, but for general periodic signals, how is frequency defined? Is it $1/T$ or $2\pi/T$? ($T$ is the fundamental period of the signal)
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2answers
76 views

PSD of modulated signal

I know this question has been previously asked just saw it and tried to do myself but reaching an expression which is different from expression of PSD which I remember for modulated signal Actual ...
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0answers
30 views

Low pass representation of Bandpass Random process

Can A WSS random process with non-zero mean be also represented in such form.
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0answers
51 views

How to Derive Rayleigh distribution using transformation formula

Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
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3answers
167 views

Confusion in AC and DC signals

I have certain doubts in the fundamentals of AC and DC signals. Most of the time, we deal with DC signals in the form of batteries, whose waveform is a constant signal with peak as 1.5v However, i ...
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2answers
45 views

Independence of Functions of random Variable

Consider I am given two functions of one random variable each for example x=cos(at),y=rect(bt) where a and b are random variables.And I am given Probability density function for a and b then if I am ...
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29 views

Notch filtering minimizing artifacts in signal

I have to notch filter the following signal As you can see it is a signal with really high amplitude.And this causes me a lot of problems. I've designed a bandstop filter (46-55 Hz).The MATLAB code ...
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1answer
26 views

Diode demodulation for AM

What is the capacitor and resistance at output of LPF meant for in the document it was mentioned that it is DC blocker I don't get it can't message contain DC value.
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1answer
205 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)...
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34 views

Envelope detector for AM signals

How or what are the constraints for deciding factors of envelope detector for AM As far as I know that charging time of capacitor should be below 20T where T is periodic time of carrier and ...
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2answers
63 views

Digital Equations problem - The fundamental ones that everyone should know

I think I am looking at conflicting equations from a few sources, or maybe I just dont understand it. But please can someone help me with these fundamental equations that everyone should know $ \...
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53 views

How to find fundamental frequency of two signals?

I am facing difficulty with finding fundamental frequency of signals I mean by fundamental frequency=(1/Time period) Correct me if I am wrong consider two continuous time signals with Time period ...
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3answers
406 views

How to Prove a System Is Invertible?

what i know is that for a system to be invertibel it should be one-one , but I am confused that if i am given a transfer function of a LTI system how can I prove or verify if it is invertible. ...
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1answer
37 views

Peak Detection on ECG signal

I've been working on a ECG signal collected during exercise through my chest mount heart rate monitor. My goal is to accurately detect the location of the R-wave; R-wave is the narrow peak similar to ...
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1answer
110 views

Discrete Kalman filter for a continuous system

The question is related to the implementation of a discrete kalman filter given a description of the system model in continuous time. I will give an example. Suppose we have a mass, spring and damper ...