Signal Processing

Questions tagged [continuous-signals]

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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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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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63 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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Must Conditions for stability in s domain? [closed]

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 is that all poles must be on left ...
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6answers
232 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
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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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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
54 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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4answers
97 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
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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
80 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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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
28 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
32 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
107 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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44 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
31 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
57 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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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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1answer
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Fourier Transform of $u(t)$ [duplicate]

I am just unable to find the correct Fourier transform of these signals (unit step, sine and cosine functions) which are containing delta functions in their Fourier transform. For unit step function, ...
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Is it possible that the value of a continuous mother wavelet at origin is zero, i.e. $\psi(t=0)=0$?

According to Fourier transform, a continuous wavelet could be written as $$ \psi(t)=\frac{1}{2\pi}\int\hat\psi(k)\text{e}^{-ikt}\text{d}k $$ From the equation above, we know that $\psi(t=0)$ is $$ \...
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4answers
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Meaning of frequency and bandwidth of a signal, despite the fact that we do not know the signal

First of all, I am completely new to the domain of signal processing. As far as I know, a signal can be represented with an infinite integral of infinitesimal complex exponentials, which is known as a ...
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2answers
45 views

What's the point of defining the signal over the whole time domain?

This question is classic for anyone starting with some signal processing course, suppose $y(t)=x(t/2)$ then the system is noncausal because we have that the output at t=-6 depends on the input at t=-3 ...
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Finding the wiggles pattern in the original dataset. (Wiggles appear after performing division by another dataset)

I have multiple measurements regarding scientific observations. The problem is that there is a subtle noise pattern caused by the instrument - the wiggles. These wiggles are invisible when looking at ...
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Finding the integral of a signal

I'm trying to find the integral of the following signal: $x(t)=A, 0 \le t \le T$ $x(t)=0, otherwise$ The integral is defined as $y(t)=\int_0^t{x(\tau)d\tau}$ For $y(t)$, I'm getting $AT$ when $t \gt T$...
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1answer
60 views

Linear system stability criteria

Suppose we have a closed-loop system $H(s)=\frac{A(s)}{1+A(s)f(s)}=\frac{A(s)}{1+T(s)}$. I've seen the stability of the system stated a couple ways: If $H(s)$ has any poles in the RHP, then it is ...
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62 views

Periodicity of complex exponential in continuous and discrete time (Eq 1.51, Signals and Systems by Oppenheim & Wilsky)

Hi All: This is very basic but I've always wondered about it and now I see it in print in a textbook so I may as well ask. In Signals and Systems on page 26, it says $$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
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2answers
68 views

Best temperature compensation equation?

I'm looking for the correct temperature compensation equation to use on our project. We are measuring the output of a detector who's signal is very sensitive to temperature drift. Any external ...
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2answers
157 views

FFT of square wave - what does output represent?

I am really new to FFT and signal processing. I am doing an analysis of square waves with FFT and I am trying to understand why the FFT output on the frequency domain has a downward slope for square ...
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0answers
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Why we only can transmit a real signal? [duplicate]

i just wondering, why we always transmit a real signal but when we deal with a baseband signal we use a complex signal ? are this is related to up and down conversion of the signal (Because complex ...
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1answer
31 views

Can complex envelope be writen in the form of quadrature components when it has symmetric spectrum?

I am reading a chapter on VCO noise in "Design of CMOS phase-locked loops from circuit level to architecture level by Behzad Razavi";I am confused when the upconverted noise is writen as $...
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1answer
77 views

Does $\cos(bt)\cdot u(t)$ have a Fourier Transform?

If it does, $$\int_{-\infty}^{\infty} \cos(bt)\,u(t)e^{-j\omega t} dt = \int_{0}^{\infty} \cos(bt)\,e^{-j\omega t} dt = \int_{0}^{\infty} \frac{e^{jbt} + e^{-jbt}}{2}\,e^{-j\omega t} dt$$ Then how do ...
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1answer
47 views

Confused about the Fourier Transform of $e^{at}u(t)$

This is the problem at hand: I'm unaware of why we didn't have to say anything about $\omega$ like that it should be also greater than $0$, I know it's variable...but it's multiplied by $t$ ...
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1answer
32 views

MATLAB Plot of FT(Cos) Displays Weird Impulse

It is known that: $$ \mathcal{F}\{\cos(2\pi t)\}=\frac{\delta(f-1)+\delta(f+1)}{2} $$ However, on MATLAB, I used F=fftshift(fft(x))/N; to obtain the FT of $\cos(2\...
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2answers
87 views

Under what conditions is the convolution of an input signal with the system's impulse response periodic?

I'm currently solving the following convolution problem from Oppenheimer's book: In the solution, it was stated that "$x(t)$ periodic implies $y(t)$ is periodic" So I wondered if it's ...
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4answers
121 views

$\int_{-\infty}^{+\infty} |G(f)| \,e^{j2\pi ft}df=|g(t)|$?

Given the absolute value of the Fourier transform of a signal $g(t)$: $|G(f)|$ If I compute the inverse Fourier transform of $|G(f)|$, $$\int_{-\infty}^{+\infty} |G(f)|\, e^{j2\pi ft}df$$ do I obtain ...
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23 views

Application of the spherical Radon transform property in tomography

Let function $f$ be even and continuous on the unit sphere $S^n$. Let $R$-be a spherical Radon transform. There is a known property: $R(f^n)=f$ whenever $f$=constant. What would this property mean in ...
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1answer
54 views

The plot of instantaneous power of the Dirac function

I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer. I was wondering how would I go about plotting the instantaneous power in the ...
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3answers
163 views

How do I check for linearity for the following piecewise-defined system?

The problem at hand: Where I'm currently stuck: I'm not entirely sure about how to move on from this point, I'm trying to find the superposition of the responses of the two individual signals so I ...
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3answers
123 views

Is there processing gain for FMCW using heterodyne-style receiver as opposed to matched filter?

Beat signal of a single target will be a sinusoid in the idealized world, so theoretically the signal processing gain of an FMCW pulse correlated with Tx waveform in this way should be analogous to ...
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1answer
43 views

Chebyshev Filter Transfer Function

I'm trying to derive the transfer function for Chebyshev filter. $$|H(\Omega)|^2=\frac{1}{\sqrt{(1+\epsilon^2T_n^2(\frac{\Omega}{\Omega_c})}}$$ where $$T_n(x)=\cos(N\cos^{-1}(x)) \forall x \le 1$$ $$...
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Following a smoothing filter of a biological signal

)Following a smoothing filter of a biological signal. y[n] = Ay[n − 1] + Bx[n − 2] Please find the transfer function in the z-domain and find the impulse response function of this filter.
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1answer
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Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? [duplicate]

In my class we are taught that the range for the frequency is $-\pi<\omega<\pi$ for discrete time Fourier transform, however for continuous time the limit is $-\infty<\omega<\infty$ why is ...
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1answer
50 views

question with chirped signal

I have some difficulty understanding the following question. I have written a code to plot continuous and discrete version of the chirped signal. ...
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1answer
73 views

Update: Fourier Transform of a shifted and scaled $\operatorname{sinc}$ signal

Let $x_N$ be the function given by $$x_N(t)=A\frac{\sin(M\pi(t-N))}{\pi(t-N)}$$ The Fourier Transform of $x_N$ is $$\begin{align} X_N(j\omega)&=\mathscr{F}\{x_N\}(j\omega)\\\\ &=\int_{-\infty}^...
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1answer
83 views

3D (time, scale, amplitude) plot in Continuous Wavelet Transform

I will be extremely grateful if someone could please answer this basic question. How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients? ...
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1answer
33 views

Random function covariance

I was studying signal processing and I was frequently asked to verify if a certain covariance is possible for a given random function. I tried to check by verifying the property to prove it: ${γ}_{xx}(...
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1answer
42 views

How to simulate a continuous signal passing through a capacitor (simple coupling capacitor)

the differential equation for the current flowing through a serial capacitor (see for example https://www.allaboutcircuits.com/textbook/direct-current/chpt-13/capacitors-and-calculus/) indicates that ...
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2answers
262 views

Which step response matches the system transfer function

A system has the following open loop bode plot: - Which one of the plots below describe the closed loop step response for the entire system? My attempt My initial thought was to look at the static ...
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1answer
44 views

Finding Interval of Integration

If we let : $$ x(t)=\begin{cases} 1&\text{if $0<t<1$}\\ 0&\text{if otherwise} \end{cases} $$ and $$ h(t)=x(t/a)=\begin{cases} 1&\text{if $0<t<a$}\\ 0&\text{if otherwise}\...

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