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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28 views

Why doesn't the magnitude of Fourier Transform change when signal is shifted (i.e when a time shift is introduced)?

I understand that a time shift in the time domain produces a corresponding phase change / phase shift in the frequency domain. But I don't understand why the magnitude is unchanged (I am referring to ...
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1answer
40 views

Ft and DTFT of negative frequency

I have a question that might sound silly but if I have a real and even signal x(t) can I define the FT and DTFT of the negative frequency if I can show: $$X(-\omega) = \int_{-\infty}^{\infty} x(-t)e^{...
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1answer
35 views

Fourier Series of a piecewise function

I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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1answer
24 views

Find fourier transform given the graph of a function

Cheers, I am given the following graph for $x(t)$: and I am asked to find the fourier tranform by using the integral property and knowing that $F(Π(t)) = sinc (\frac{\omega}{2\pi})$ The solution I ...
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1answer
24 views

Find the unit-energy for $\mathrm{rect}(t/T)$?

My book says: The width-1 NRZ pulse is $$ \mathrm{rect} (t) = \begin{cases} 1 , \qquad -1/2 \leq t \leq 1/2\\ 0, \qquad \mathrm{otherwise} \tag 1 \end{cases} $$ The unit-energy width-$T$ NRZ pulse ...
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What's the base and height of triangle obtained by FT{$\operatorname{sinc}^2(7\pi t)$}?

I'm a little confused about the $\operatorname{sinc}^2(7\pi t)$ function. How do you know the base and height of the triangle produced in the frequency domain only looking at the $\operatorname{sinc}^...
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1answer
44 views

What will the output of a system which has no Fourier transform?

Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?
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407 views

Confusions regarding differences between Fourier transform & Laplace transform?

Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard Number 1) Link of question https://electronics.stackexchange.com/questions/...
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Graph Plot On Time Shift of Cosine Signal Hanning Function

I am plotting time shift of the Hanning function. I find few plot result that I am not able to understand. Therefore I would like to ask my question here. The given Hanning function is: $$ x(t)={\tt ...
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1answer
60 views

Is the filter $1/(1-s)$ anti-causal?

The filter with the response function $$ H(s) = \frac{1}{1 - s} $$ Produces a positive phase shift and a negative group delay for all frequencies Is it anti-causal? Is there a way to deduce such ...
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1answer
96 views

How to design a digital Butterworth bandpass filter?

I am looking into designing a Bandpass Butterworth filter in python, but, I was not sure I am designing my filter correctly. What I have are the following: High cutoff frequency = 200Hz Low cutoff ...
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How to design function for Random Decrement technique in python and implement the function?

I was looking into a technique called Random decrement technique from the following links/articles: How can I use Random Decrement Method to convert a non-stationary signal into a decay function ...
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3answers
70 views

Doppler shift in signals

I have started doing some reading into the effects of the doppler shift on signals. In particular, radar signals from ships moving relative to a receiver. This might seem weird but I understand why ...
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1answer
76 views

Fourier transform of $\textrm{sinc}^2(100\pi t)$

I'm confused about a tutorial problem concerning the Fourier transform of the $\textrm{sinc}^2$ function. Specifically, the question involves the Fourier transform of $\textrm{sinc}^2(100\pi t)$, ...
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83 views

How are pole-zero plots, magnitude response plots, and phase response plots related?

Given that the Laplace transform of a continuous-time signal $h(t)$ is $H(s)$, what can a plot of the poles and zeros of $H(s)$ on the $s$-plane tell me about the magnitude response and phase response ...
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1answer
31 views

Time Invariance of Continuous Time System

I am trying to check whether the system given by the following input-output relation is LSI or not? $$y(t) = \cos(x(t)-x(0))$$ My work: The given relation: $$y(t) = \cos(x(t)-x(0))$$ If the input ...
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How to create an objective function for Mackey glass time series (using "bayesopt")?

I am optimizing 5 hyperparameters of Mackey-Glass time series and using built-in function "bayesopt" in MATLAB. My Mackey glass time series with fixed parameters shows correct results. ...
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21 views

How can we translate this statement into an input signal expression?

I want to make sure if I got this right, the following statement: if the operator enters a unity sloped linearly increasing input then the output must eventually track the input and be at most 0.1 cm ...
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22 views

Where is SNR and CNR calculated for LTE?

I read below that SNR and CNR are different and we have difference of post/pre modulation. In context of LTE which modulation do we refer to- Digital Data modulated using QAM/QPSK to IQ, or Baseband ...
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1answer
33 views

CTFT of $ X(j\omega) $ vs $ X(jf) $

The CTFT of a signal as a function of $ \omega $ and $ f $ is identical: $$ X(j\omega) = \int_{-\infty}^{\infty} x(t) \, e^{-j \omega t} \operatorname{dt} \;\;\;\;\bigg|\;\;\;\; X(j f) = \int_{-\infty}...
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1answer
91 views

How do we equate the signal energy before and after sampling?

I have a band-limited signal and sample it at sample rate of $f_\mathrm{s}$. By taking the continuous time fourier transform, I will see copies of the same signal at $n\cdot f_\mathrm{s}$ where $n \in ...
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16 views

Blind source separation for asynchronously observed mixture channels

Given your practical and theoretical expertise: Does ICA work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
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1answer
37 views

Convolution of a discrete continuous function for reconstruction

From chapter 9 page 198 of https://github.com/t4world/Computer-Graphics/blob/master/Fundamentals-of-Computer-Graphics-Fourth-Edition.pdf I am confused as to what this book's description is saying ...
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1answer
118 views

What would be an example for a continuous signal from "daily life"?

Please share an answer with a simple example from the "daily" (colloquial) lives of humans for a signal which is "continuous" and explain what is it that rigorously makes it "...
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1answer
61 views

Check whether a system has memory or not

My question is whether the systems below are memoryless or not: $1.) \ y(t)=K$ where $K$ is a constant $2.) \ y(t) = x(t_0) $ where $t_0$ is a constant So, from the definition I have been using so far ...
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2answers
37 views

Power spectral density after a modulator block

For random signals, the concept of Power Spectral Density is useful to analyze the signal. It can be shown that if the input $X(t)$ applied to an LTI system of impulse response $h(t)$ has the PSD $S_{...
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1answer
131 views

Fourier transform of an impulse-train sampled signal

I'm trying to calculate the Fourier transform of an impulse-train sampled signal in two differnt ways but I end up with different results. Impulse-train sampling of a continous signal $x(t)$ with ...
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0answers
51 views

How to remove noise from the signal? [closed]

I'm new to DSP and currently working on time-series data. The mentioned time series (of Toe) is extracted from a video tracking various body parts of an athlete. Ideally, there shouldn't be any ...
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1answer
57 views

Fourier transform of shifted periodic function

Assuming $x(t)$ is a periodic function of period $T$ and having the Fourier transform $X(\omega)$, it is required to calculate the Fourier transform of the signal $x(t)+x(t-T)$. Since x(t-T) is equal ...
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6answers
846 views

Do discrete-time series always have a continuous-time underlying?

Can one argue that discrete time-series coming from stocks or commodities (prices) are derived from a continuous-time process? One can probably argue that stocks or commodities at any time have a ...
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1answer
40 views

Integration of Sinusoidal functions

Since Differentiation of a sinusoidal function of a certain angular frequency gives a sinusoidal function of the same frequency, does the statement "Integration of a sinusoidal function of ...
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1answer
101 views

Comparing distribution of vectors with different length?

I have two vectors of different length, each vector contains similarity scores. I need to plot the probabilty density function of the scores in both vectors to compare their distribution using Matlab. ...
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1answer
68 views

Conditions for stability in $s$ domain?

What are the necessary conditions for stability in $s$ domain, especially in regards to ROC. I am able to understand that there are only two conditions First condition: all poles must be on left half ...
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6answers
291 views

What happens when we oversample?

I had an interview for a wireless communication position and one of the interviewers asked me this question in regard to signal processing. If I have signal and I sample at the Nyquist frequency and ...
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1answer
43 views

Is "Introduction to Statistical Signal Processing" by RM Gray good for starting?

I am working on noise processes in electronic devices for my studies, by now Ive been doing a fairly large amount of processing of time measurements, like calculate PSD, estimate thermal, flicker ...
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48 views

The definition of amplitude probability density

I'm trying to figure out the formal definition of "amplitude probability density"(APD). First of all I didn't find a textbook which defines APD but there are some sources that explain it ...
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1answer
82 views

When to zero-mean a signal?

I have two sets of signals. The first is a noisy sinewave, which I zero-mean before taking the FFT since I need to find the amplitude. The other is essentially noise with a gaussian distribution. I'm ...
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5answers
204 views

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period." If I take this to be literally true, then a sine wave with only 2-3 samples ...
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2answers
66 views

Are signals modeled either digitally or analogously or can signals modeled as both?

Are signals modeled either digitally or analogously or can signals modeled as both?
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1answer
87 views

Correlation and the Fourier transform

In the book Fundamentals of Music Processing: Audio, Analysis, Algorithms, Applications by Meinard Müller, the coefficients $d_\omega$ and $\phi_\omega$ are defined as where $\cos_{\omega,\phi}(t) = \...
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2answers
131 views

When joining two signals of different frequencies how do I find the phase shift that makes the join smooth?

I'm generating a sine wave and I want the second half of the signal to be in a different frequency. How do I find the phase shift I can apply to the second half so that the joining between the halves ...
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1answer
43 views

Different mathematical signal models for different applications

I am looking for some interesting and physically meaningful applications of different signal models. I am currently working with complex analytic signal model given below, but I couldn't come up with ...
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0answers
36 views

Estimate respiration rate from a respiration signal

I have a respiration signal sampled at frequency 125Hz, can I estimate respiration rate signal at a frequency 1HZ from the respiration signal? Is it possible to use FFT or FFT for this purpose in ...
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1answer
51 views

Is a continuous time aperiodic signal discrete in the time domain?

This is a statement I have read from a textbook: Whenever we have periodic signals continuous or discrete time the frequency domain is discrete and time domain is continuous. Whenever we have ...
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3answers
123 views

How is a constellation diagram constructed in practice?

I am simulating some optical signals in Matlab as they pass through a waveguide, get amplified, mixed with noises, etc. For the record, I am a theoretical physicist, not an engineer nor an ...
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54 views

convolving an LTI with filters

I just started learning signal processing and one of the very first topics I begun with is convolution. I want to learn signal processing practically, therefore I opted to work with circuits(also a ...
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1answer
36 views

Mixed - Discrete and Continuous system Laplace domain stability - Effect of Sampler and DAC

I have a system whose the plant transfer function is continuous and the compensation is discrete. I have an ADC which allows to measure the output of the system and a DAC which allows to control the ...
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2answers
66 views

Meaning of Rect and Train of Rect Spectra

The Fourier transform of $x(t)=\operatorname{rect}(t)$ is $X(f)=\operatorname{sinc}(f)$ The Fourier transform of a periodic train of rectangular pulses $x(t)=\sum\limits_{n=-\infty}^{\infty}\...
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2answers
377 views

A system having impulse response $ h(t)=u(t) $ stable or not?

I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess) I proceeded as$$ \int_{-\...

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