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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Continuous-time convolution of signals with negative amplitudes
While preparing for a mid-term exam, I encountered negative amplitudes for the first time while convolving two signals.
I've already solved the problem, but my result and results from others conflict ...
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Calculation of response of continuous-time LTI system [closed]
Consider an LTI system defined by the following impulse response $S_{1}$
$$ h \left( t \right) = u \left(t - 6 \right) - u \left( t \right) \tag{1} \label{1} $$
Assuming $x \left( t \right) = 5 \left[ ...
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Energy and power of time-continous signal $x(t)=t$?
Preparing for my exams, I stumbled upon this particular problem.
I tried to calculate it using following formulae:
$$ E = \int_{-\infty}^{\infty}|t|^2dt $$
Dividing it into two cases because of the ...
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For unit step $g(t) = u(t)$, why does $G(z) = \frac{z}{1-z}$, whereas $G(s) = \frac{1}{s}$?
Edit:
The source of my confusion is over the existence of multiple s-z mappings.
After researching these mappings and where they came from, I couldn't find why $z=e^{sT}$ can be ignored and replaced ...
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Alternative way to find fourier transform
Let $$x(t) = A \text{rect}_T({t-\tau})$$I calculated its fourier transform through the direct way: $$X(\omega) = Ae^{-i\omega \tau} \int_{-T/2}^{T/2} e^{-i \omega t} dt = Ae^{-i\omega \tau} \frac{\sin(...
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Magnitude and phase spectrum of a periodic signal
Let the following T-periodic signal :
I found that
$$ x(t) = \frac{A \cdot t}{T} \qquad 0 \le t < T $$
and its Fourier series is :
$$ x(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{n=1}^\infty \frac{\...
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Are complex exponentials the only eigenfunction for arbitrary LTI systems?
After reading a few posts, like this. I know that arbitrary LTI systems always have complex exponential eigenfunctions. And that for specific LTI systems you can also have other types of ...
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Can the total energy of a signal diverge while its average power converges to zero?
If the integral used to calculate the total energy for a continuous time real signal converges, its average power is equal to zero. But could the average power still equal zero if the total energy ...
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Checking Invertibility of continuous-time system
While solving a problem, there is a problem that I don't understand.
$$
Y(t) = \{X(t)\}^3
$$
A system has a response that is the cube of its excitation.It is a problem of determining the Invertibility ...
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Why a windowed signal is considered to evaluate the Power Spectral Density?
Let's consider a real function of time $x(t)$ being a Fourier-transformable signal. The synthesis equation states that:
$$x(t)=∫_{-∞}^{+∞}X(f)⋅e^{2πjft} df $$
Meaning: $x(t)$ can be seen as the sum of ...
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what am i not doing right while using squarewaves?
I have been applying square waves at 40hz and 10 volts via a function generator amplified by a power amplifier by 2 times(2A) on a 6mm steel specimen.
My signals captured from the AE sensor are not ...
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What am i doing wrong?
How do I remove the noise (long vertical lines) from signal? I am applying AC voltage via function generator which is amplified by the power amplifier to a 6mm thick steel specimen. The signals are ...
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Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate
I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
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Sinus Pattern analysis
i have 1000 data which range between 50 and 180 ( heart BPM data in a day) how can i measure its similarity to a Sinus pattern?
for example, for 20th recorded data (for example it is 60BPM), evaluate ...
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Does bandwidth include negative frequencies?
I've seen countless definitions of bandwidth that disregard negative frequencies.
Is that done due to the symmetrical nature of a certain signal eg. a cosine or due to the inherent lack of meaning ...
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Why do complex signals and their real world equivalents have different measurements of power?
My understanding is that the relationship between complex signals and real signals is such that for some complex signal $f(t) = s(t) \cdot e^{j2\pi f_c}$, the actual broadcast signal sent through the ...
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Incorrect epoch labelling
I am processing an EEG signal acquired by showing 10 image of each of 40 classes. I want to label the signals converted to epochs to their corresponding class labels.
The ...
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How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator
How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator.
The bottom equation is supposed to be the answer.
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What Is Continuous White Noise in The Context of Signal Processing and Broadly
How can one define Continuous White Noise in a coherent way?
Is there a way to derive it Mathematically?
Specifically, is there a way to define it which will works as the model in Signal Processing ...
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Frequency domain derivation of Hilbert transform of $\cos(\omega t)$
I'm reading "Understanding Digital Signal Processing, 3rd Edition" by Richard Lyons. Chapter 9 derives Hilbert transform impulse response by defining it in frequency domain first and then ...
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How to discretize a continous signal
I want to transform the continuous signal $$u(t)=u_0+\hat{u}\cdot \cos(2\pi \frac{t}{T_0})$$ to a discrete signal. The discrete signal should contain $N$ values and exactly $m$ periods (starting with $...
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How to plot a sawtooth chirp waveform using an array of frequency and time for an FMCW radar?
Before switching to use sawtooth I was using sine wave but in sine wave high frequency content was not clearly visible, But I don't have any experience with using sawtooth waveforms. I am going to ...
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Unwindowed STFT of sine, closed form solution and insights (sliding FFT)
I seek to calculate, mathematically, the unwindowed Short-Time Fourier Transform of
$$
\cos(2\pi f t + \phi)
$$
i.e. any arbitrary real-valued sine: any frequency, duration, phase shift, and number of ...
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Inferring properties of a signal from its autocorrelation
In a previous thread, it was asked whether we can infer a signal from its autocorrelation, and the answer was a clear no, since the autocorrelation process is lossy.
Still, is there anything we can ...
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How can I find the following Fourier Transform without directly using FT pairs?
The question is to find the CTFT of $$x(t) = e^{-t}u(t)\cdot \sum_{n=-\infty}^{\infty} \delta\left(t-\frac{n}{2}\right)$$
Now I know that multiplication in time means convolution in the Fourier Domain ...
user67157
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Calculating DC from signal avg or rms value required?
If we want to calculate a dc value of any given signal, should the dc value be RMS or average value?
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Convolution of step function with exponentials
I have a problem in signals and systems to solve which is basically math
So suppose we have two functions x(t) = H(t) which is the Heaviside unit step function as input and an impulse response
$$h(t)=...
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What is DC gain of sine wave multiple?
I am testing about injection sine wave current to r,c impedance and measurement R + jX see fig.1 .
When scope is Va .
When sine wave multiple (Va*Vb).
I put average to find DC of this signal.Is ...
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Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses?
Let $$\dot{x} = Ax+Bu$$ $$y = Cx + Du$$ be a linear ODE with $x(0)=0$. Here, I am assume $A$ is invertible.
As you can see, the relation $$H:u(.) \mapsto y(.),$$ where $(u(.),y(.))$ is a solution to ...
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DFT modulus of a sine, closed form solution and insights
A closed form solution to
$$
X[k] = \texttt{DFT}\{\cos(2\pi f t + \phi)\}
$$
confirmed many known properties of a finite sine's spectrum, also revealed new ones. Can the same be done for $|X|$, or $|X|...
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Effect of sampling rate and duration on discrete parameters of sine (spectrum)?
The DFT of
$$
\cos(2\pi f t + \phi)
$$
peaks at $k=\pm f$ if $t = \frac{1}{N}[0, 1, ..., N - 1]$ (for integer $f$, & within Nyquist). What about other $t$? What if we double the sampling rate or ...
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Power / energy of complex signals - physical interpretation
I am wondering about physical interpretation of energy / power for complex signals. E.g. for signal energy definition:
\begin{equation}
E=\int\limits_{-\infty}^{\infty}|x(t)|^2 \, \mathrm{d}t
\end{...
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What information does the Hilbert transform give?
The Hilbert transform of a function is defined as :
$$\mathscr{H}\big\{f(t)\big\} = \lim_{T\rightarrow \infty}\frac{1}{\pi}\int\limits_{-T/2}^{T/2}\frac{f(\tau)}{t-\tau}\, \mathrm{d}\tau$$
Okay but ...
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How to separate Transient and Steady-State Expression from Periodic Summation Response?
Background
My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input.
How to determine the transient response of a circuit to causal periodic inputs?
...
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How can Haar basis be written as the impulse response of an LTI system?
Haar wavelets are defined as:
$$\phi_{0,0}(t) = \begin{cases}
1, & \text{ for } 0<t< 1/2\\
-1, & \text{ for } 1/2<t<1 \\
0, & \text{ ...
user64710
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Laplace domain transfer function from system sampled at discrete times
I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is here (PDF page 6, slide marked 11); I'll explain further below. Suppose I have a ...
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How EEG signal is windowed? Windowing vs Epoching are they same?
I am experimenting with EEG dataset from this (title: "The Perils and Pitfalls of Block Design for EEG Classification Experiments") paper. They have applied various ML models on different ...
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Why can't I use the differentiation property of the Fourier transform?
I have some question about the function in frequency domain and I'd like to know its inverse fourier transform (IFT)
$$G(jw) = \dfrac{jw\cdot (jw+1)}{(2+jw)(3+jw)}$$
I know that:
$$\dfrac{d}{dt}x(t)\...
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FMCW Radar timing of transmission and reception
I have a question regarding the implementation of FMCW radars that seems rather basic to me, but for some reason I am a bit unclear about this.
So I understand that in FMCW radar, transmitter and ...
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Effect of BIBO-Instability on the frequency response of a ideal LPF
I recently came across this post stating that the continuous ideal LPF is BIBO-unstable since the impulse response is not absolutely integrable, and this post stating some examples.
I have been trying ...
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Complex exponential Fourier series coefficient of periodic convolution
Let the complex exponential Fourier series coefficients of two periodic signals $x_1(t)$ and $x_2(t)$ be $C_{1n}$ and $C_{2n}$, respectively, with $T_0$ being the fundamental time period of both the ...
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Calculating transfer function of a linear time varying system?
If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
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DFT of a sine, closed form solution and insights
I seek to calculate, mathematically, the Discrete Fourier Transform,
$$
\texttt{DFT}\{x\}[k] = \sum_{n=0}^{N - 1} x[n] e^{-j2\pi k n / N}
$$
of any arbitrary real-valued sine: any frequency, duration, ...
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Why can FM be used to encode a message, intuitively?
I am reading about FM.Suppose the message signal $m(t) = \frac{1}{2}cos(t)$ and the frequency of the carrier signal is twice the frequency of the message signal and its amplitude is 1.The resulting ...
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Unit impulse added to non-zero interval of a function - graphical representation?
Followup to this question, let the ramp be $r_0(t)$. We seek to plot $x(t) = r_0(t) + \delta(t + 1)$. Should it be as in left, right, or neither? Is there a convention?
Note, in either case we could ...
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Trouble with subtracting a signal by a unit impulse
For my homework I was given the signal by the illustration:
I was asked to draw the illustration for $$x_1(t) = 3x(-1+0.5t) - \delta(-t+3)$$
I have figured out how to draw the $3x(-1+0.5t)$ part, but ...
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How to calculate the bandwidth of a continuous signal in an interval?
I am struggling with a task I thought would be a good exercise. I am tasked with calculating the bandwidth of the equation below and I'm struggling. I managed to find and understand why $\text{sinc}(t)...
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Impulse response of linear time-varying system
I am confused about linear time-varying system. For a time varying system, the output is given by
\begin{align}
y(t)=\int x(\tau) h_{\tau}(t) d\tau,
\end{align}
where $ h_{\tau}(t)$ is the output of ...
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The correct way to perform signal processing on S-parameter data
I have a question to ask you which has been bugging me as of late.
I have s-parameter data with 5001 samples acquired from a vector network analyzer. I am trying to 'gate' this s parameter data, i.e. ...
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How to epoch EEG data with continuous stimuli for TRF analysis
I'm running a study with continuous stimuli, I send triggers at the beginning and end of a period of recording (the time duration for each period is not fixed). I'm planning to analyse the data with ...
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