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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Find continuous signal given a condition on its samples

Let $x(t)$ be band-limited with $B = \omega_m$. Sampling gives us $$x(nT_s) = \begin{cases} 1, & n = 0 \\ 0, & n \not = 0 \end{cases}$$ And $\omega_s = 2\omega_m = \frac{2\pi}{T_s}$. Find ...
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Reconstruct $x(t)$ from $y(t)$ and $z(t)$

Let $x(t)$ be band-limited signal with $X(j\omega) = 0$ for $|\omega|\gt \omega_M$. We use $$s(t) = \sum_{k =-\infty}^{+\infty}(-1)^k\delta(t - \frac{kT}{2})$$ for sampling. So we have $z(t) = x(t)s(t)...
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What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
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2answers
42 views

How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?

How to compute transfer function $$G(s) = \exp \left( - \sqrt{s} \right)$$ in Matlab / Simulink? I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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1answer
50 views

Fourier transform of the sampled signal

I want to calculate Fourier transform of the sampled signal in two ways. Let $$s(t) = \sum_{k = -\infty}^{\infty}\delta(t - kT)$$And $z(t) = x(t)s(t)$. So we have $$z(t) = \sum_{k = -\infty}^{\infty}x(...
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For an LTI system, the zeos and poles are defined in the z plane. How to add additional poles and zeroes so LTI system is real valued?

The question already has a zero and a pole in the complex plane. It is asking to add additional zero and pole so LTI becomes zero valued. zeros=-1/2 + 1/2 i , poles = -1/3 -1/3 i . What I understand ...
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Output of LTI diagram with this question and is it stable

the input δ(t) and output of a LTI signal is shown below. 1- is this system casual? 2- is it stable? why? 3- draw the output of the system. Tnx in advance
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24 views

Extracting the DC component of a signal, that proportional to the displacement about the y-axis

I’m not sure that I clearly enough reflected the essence of a small problem in the title of the topic, but I’ll try to reveal its essence in the question itself. https://www.wolframalpha.com/input/......
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1answer
30 views

Compute output given input, transfer function and initial conditions

The problem statement is Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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1answer
37 views

Behaviour of integrator at steady state

I wanted to calculate response of integrator of sinusoidal input at steady state via these two methods as mention in image but these two methods give two different answers at steady state, so where ...
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72 views

Meaning of sampling frequency?

Say there is a communication system, which can manage sampling frequency up to 4 MHz (given by software). Can the system be able to process signals with maximum frequency more than 2 MHz? Because ...
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1answer
30 views

Accelerometer sensor's data analysis

Here is a sample data that I got from the accelerometer sensor: The first selected area shows the acceleration of the IMU device to right side and the second shows the movement to left side. I am ...
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2answers
76 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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1answer
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simulation of lin-log amplification

I struggle with two simple questions. First. What is the distribution of the signal on the output of the lin-log amplifier if Rayleigh noise is driven to the input of it. Using an approach with ...
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27 views

Apply Transfer Function in Continuous Domain in Matlab

I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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1answer
44 views

Fourier transform of an integrator filter

I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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How should I sample the signal $f(t) = \sin(24t)^3\chi_{[0,0.52]}$ on the interval $[0,1.25]$?

I am from an applied math/PDE background and I don't usually deal with proper sampling and signal processing. I just take roughly what seems to be a good number of samples. But I would like to be ...
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1answer
27 views

Determining if the system is linear and time invariant

The Fourier transforms of input $x[n]$ and output $y[n]$ of a discrete-time system are related by the following equation: $$Y(e^{j\omega}) + (e^{-j\omega})Y(e^{j\omega})= X(e^{j\omega}) - X^{'}(e^{j\...
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1answer
27 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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81 views

Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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1answer
70 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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1answer
301 views

How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?

Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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Pre-envelope of an FM signal $s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$ [duplicate]

I want to ask a question about pre-envelope of an FM wave: $$s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$$ Can someone explain briefly how we calculate the pre-envelope of this signal?
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23 views

Stability of a signal

I would like to know when I can determine that a system is stable. I've seen Stability of a system but this is very theoretically. My background is that I've set up a measurement system to detect the ...
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2answers
43 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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1answer
813 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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1answer
108 views

How to convert from Laplace Domain to Time Domain?

I want to convert the following equation from Laplace domain to continuous time domain: $F(s) = \frac{-2 m k v R}{2 m R s^{2} + m k s + 2 k R}$ m, k, v, R are all constants. If I can factor or put ...
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3answers
54 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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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
80 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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1answer
58 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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2answers
99 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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2answers
151 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
90 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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3answers
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When does the convolution of $2$ signals equal zero?

For example, how can I determine if the convolution of $x(t)$ with $y(t)$ is equal to $0$?
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1answer
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plotting exp signal in matlab

My program is as follows: ...
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1answer
32 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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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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0answers
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
89 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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2answers
34 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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4answers
362 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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2answers
187 views

Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
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2answers
65 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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0answers
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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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6answers
401 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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1answer
30 views

identify equilibrium region after large transient

I am looking at data from a mechanical system under an unsteady load. I'm trying to find the simplest way to identify the portion of the signal once the system reaches its new equilibrium. Here's a ...
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1answer
49 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 need ...
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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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5answers
565 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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