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.
620
questions
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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 ...
2
votes
2answers
54 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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votes
2answers
67 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$$ \int_{-\...
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1answer
52 views
Fourier Transform of $u(t)$ [duplicate]
I am just unable to find the correct Fourier transform of these signals (unit step, sine and cosine functions) which are containing delta functions in their Fourier transform.
For unit step function,
...
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2answers
27 views
Is it possible that the value of a continuous mother wavelet at origin is zero, i.e. $\psi(t=0)=0$?
According to Fourier transform, a continuous wavelet could be written as
$$
\psi(t)=\frac{1}{2\pi}\int\hat\psi(k)\text{e}^{-ikt}\text{d}k
$$
From the equation above, we know that $\psi(t=0)$ is
$$
\...
2
votes
4answers
71 views
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 ...
0
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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 ...
0
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0answers
25 views
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 $t \gt T$...
2
votes
1answer
49 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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2answers
57 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
$$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
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2answers
59 views
Best temperature compensation equation?
I'm looking for the correct temperature compensation equation to use on our project.
We are measuring the output of a detector who's signal is very sensitive to temperature drift.
Any external ...
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2answers
84 views
FFT of square wave - what does output represent?
I am really new to FFT and signal processing. I am doing an analysis of square waves with FFT and I am trying to understand why the FFT output on the frequency domain has a downward slope for square ...
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0answers
41 views
Why we only can transmit a real signal? [duplicate]
i just wondering, why we always transmit a real signal but when we deal with a baseband signal we use a complex signal ? are this is related to up and down conversion of the signal (Because complex ...
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1answer
29 views
Can complex envelope be writen in the form of quadrature components when it has symmetric spectrum?
I am reading a chapter on VCO noise in "Design of CMOS phase-locked loops from circuit level to architecture level by Behzad Razavi";I am confused when the upconverted noise is writen as $...
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1answer
76 views
Does $\cos(bt)\cdot u(t)$ have a Fourier Transform?
If it does,
$$\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$$
Then how do ...
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1answer
43 views
Confused about the Fourier Transform of $e^{at}u(t)$
This is the problem at hand:
I'm unaware of why we didn't have to say anything about $\omega$ like that it should be also greater than $0$, I know it's variable...but it's multiplied by $t$ ...
0
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1answer
30 views
MATLAB Plot of FT(Cos) Displays Weird Impulse
It is known that:
$$
\mathcal{F}\{\cos(2\pi t)\}=\frac{\delta(f-1)+\delta(f+1)}{2}
$$
However, on MATLAB, I used F=fftshift(fft(x))/N; to obtain the FT of $\cos(2\...
1
vote
2answers
78 views
Under what conditions is the convolution of an input signal with the system's impulse response periodic?
I'm currently solving the following convolution problem from Oppenheimer's book:
In the solution, it was stated that "$x(t)$ periodic implies $y(t)$ is periodic"
So I wondered if it's ...
2
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4answers
120 views
$\int_{-\infty}^{+\infty} |G(f)| \,e^{j2\pi ft}df=|g(t)|$?
Given the absolute value of the Fourier transform of a signal $g(t)$:
$|G(f)|$
If I compute the inverse Fourier transform of $|G(f)|$,
$$\int_{-\infty}^{+\infty} |G(f)|\, e^{j2\pi ft}df$$
do I obtain ...
1
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0answers
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Application of the spherical Radon transform property in tomography
Let function $f$ be even and continuous on the unit sphere $S^n$. Let $R$-be a spherical Radon transform.
There is a known property:
$R(f^n)=f$ whenever $f$=constant.
What would this property mean in ...
0
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1answer
49 views
The plot of instantaneous power of the Dirac function
I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer.
I was wondering how would I go about plotting the instantaneous power in the ...
0
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3answers
148 views
How do I check for linearity for the following piecewise-defined system?
The problem at hand:
Where I'm currently stuck:
I'm not entirely sure about how to move on from this point, I'm trying to find the superposition of the responses of the two individual signals so I ...
0
votes
3answers
103 views
Is there processing gain for FMCW using heterodyne-style receiver as opposed to matched filter?
Beat signal of a single target will be a sinusoid in the idealized world, so theoretically the signal processing gain of an FMCW pulse correlated with Tx waveform in this way should be analogous to ...
0
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1answer
36 views
Chebyshev Filter Transfer Function
I'm trying to derive the transfer function for Chebyshev filter.
$$|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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0answers
14 views
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
50 views
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
69 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
$$\begin{align}
X_N(j\omega)&=\mathscr{F}\{x_N\}(j\omega)\\\\
&=\int_{-\infty}^...
1
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1answer
55 views
3D (time, scale, amplitude) plot in Continuous Wavelet Transform
I will be extremely grateful if someone could please answer this basic question.
How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients?
...
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votes
1answer
33 views
Random function covariance
I was studying signal processing and I was frequently asked to verify if a certain covariance is possible for a given random function. I tried to check by verifying the property to prove it:
${γ}_{xx}(...
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1answer
36 views
How to simulate a continuous signal passing through a capacitor (simple coupling capacitor)
the differential equation for the current flowing through a serial capacitor (see for example https://www.allaboutcircuits.com/textbook/direct-current/chpt-13/capacitors-and-calculus/) indicates that ...
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votes
2answers
213 views
Which step response matches the system transfer function
A system has the following open loop bode plot: -
Which one of the plots below describe the closed loop step response for the entire system?
My attempt
My initial thought was to look at the static ...
1
vote
1answer
43 views
Finding Interval of Integration
If we let :
$$
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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0answers
39 views
A. V. Oppenheim Problem $(1.14)$
Problem 1.14) Consider a periodic signal :
$$
x(t):=\left\{\begin{array}{ll}
1, & 0 \leq t \leq 1 \\
-2, & 1<t<2
\end{array}\right.
$$
with period $T=2$. The derivative of this signal is ...
0
votes
1answer
42 views
Removing white noise by taking the mean of many samples
I'm learning about signal processing, and I am attempting to remove white noise from an output of a blackbox system.
As you can see from the above image (left is the input sin(t), right is the output)...
0
votes
1answer
43 views
Time domain representation of a modulated signal when symbol rate >> carrier frequency?
I need to understand the relationship between carrier vs. bits with PSK modulation, and what the signal in the time domain would look like if my symbol rate is far greater than my carrier frequency. ...
3
votes
1answer
71 views
UPDATE : How to continue Computing the Convolution
$$
x(t):=\begin{cases}
1&\text{if $0<t<T$}\\ \\
0&\text{if otherwise}
\end{cases}
\qquad\text{and}\qquad
h(t):=\begin{cases}
t&\text{if $0<t<2T$}\\ \\
0&\text{if otherwise}
...
1
vote
1answer
58 views
Initial rest condition applied on $x(t)$ vs $h(t)$
Define the LTI system $\mathcal{H} : x\mapsto y$
Define the convolution for continuous-time system :
$$
(x*h)(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\;\text{d}\tau
$$
The initial rest condition ...
0
votes
1answer
21 views
I am looking for an analytic description of a continuous-time Butteworth High-pass filter in the time domain (=impulse response)
having derived the Butterworth Lowpass Time domain response, I am now struggling to find a similar function for a Butterworth Highpass filter. I understand you need to replace s by 1/s. But this leads ...
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votes
3answers
231 views
Linkwitz-Riley Crossover Sum as Allpass Filter
I was curious about crossover filter design, so I did some reading on Linkwitz-Riley filters. Seems to me that the general idea is that if you add HP and LP filters and they are properly designed, ...
1
vote
1answer
30 views
Do we assume modulating and carrier signal uncorrelated in AM modulation?
I am new to communication and studying amplitude modulation. Let us assume an amplitude modulated wave given by
$$\big(m(t)+ A\big) \cos(2\pi f_c t)$$
Now we have formula for efficiency as
$$ \eta=\...
0
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0answers
35 views
Separation of many signals all containing 1 common component
I have been struggling with a research question and would appreciate any pointers (or full solutions).
I have a data set of many (+/- 50k) observed - correlated - signals. These signals are known to ...
0
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0answers
37 views
Advice on generating stable FMCW waveform
I am trying to derive parameters for a triangular FMCW waveform such that the phase of the signal has consistency from one period to the next. Perhaps this is arbitrary and feel free to tell me so, ...
0
votes
2answers
159 views
From transfer function to differential equation
I have the below detailed solution (boxed in blue) that I don't understand completely:
I can reconstitute the differential equation from:
$$ (1+Ts) X(s) = K_v U(s) $$
$$ x(t) + T\dot x(t) = K_v u(t) $...
0
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1answer
133 views
Find the autocorrelation function of signal $x(t) = u(t) - u(t-1)$
I have used the energy-type signal autocorrelation function:
$$\mathcal{R}_{xx}(\tau)=\int_{-\infty}^{\infty}x(t)x^*(t+\tau)dt$$
I have rewritten the equation as:
$$\begin{align}
\int_{-\infty}^{\...
0
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1answer
35 views
How do I find the Energy Density Function of $g(t)$ if i am not given an input or impulse response?
$$g(t)=\frac{12a}{t^2+a^2}$$
I need to find the Energy Density Function of the signal, but everywhere I look has an input and an impulse response. Does anyone know how to solve this. Would I just take ...
1
vote
2answers
209 views
Difficulty with a Fourier Transform
What would be the best way to take the Fourier transform of
$$
f(t)\cdot \cos\big(\pi(t-1)\big)
$$
I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location ...
0
votes
1answer
54 views
How to find inverse Fourier transform of summ of delta functions?
I am practicing for my exam that I have this semester and I stumbled upon this one.
How can i find inverse Fourier transform given:
$$
X(j\omega) = \sum_{k=-\infty}^{\infty}\delta(\omega-2k+1)
$$
0
votes
1answer
29 views
Solution verification for this Fourier series problem
We have a signal with period $T = 2$
We want to find the continuous time fourier series for this signal.
Since $T = 2$, $\omega = \pi$. All we have to do know is find the frequency domain.
$$x(t) = \...
