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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Fourier transform processing of iq data
I want to perform fourier transform on the iq data that is taken from spectrum analyzer. The purpose is to estimate phase noise from iq data.
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Smoothing sensor signal with discontinuities on DSP for obtaining signal derivative
I am trying to implement PID control on a sensor signal that has many discontinuities in it. Due to these discontinuities, the differentiated signal does not provide a meaningful or useful signal I ...
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How to recover carrier frequency from pm signal
I have a signal $$x(t)=\sin(\omega t + g(t))$$ where $\omega$ is carrier frequency and $g(t)$ is message signal.
Given that message bandwidth is much less than carrier frequency, how do I extract ...
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Doubt on LTI systems (Zero input-Zero Output)
So, I have a problem where the input and output of a system are given :
\begin{align}
x(t) &= \sin(10t) \\
y(t) &=5\cos(10t+\frac{\pi}{6})
\end{align}
So, I need to determine whether this ...
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How to design a system that stretches input by factor of 2?
In general, How do we design a system that takes input x(t) and outputs x(t/2)? I know that if system outputs x(t/2) then the frequency domain of output signal has the form X(2f). But what should be ...
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Implementing signal processing techniques for consistent RSSI signal reception
I've tried to optimize the LoRa setup using Arduino IDE libraries to ensure accurate or acceptable RSSI measurements and for distance estimation between multiple nodes and a master in an outdoor ...
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Signal plotting on a paper
I needed help in plotting this in a paper, I have 2 signals:
x(t) = 4 Tri ((t + T) / 2T)
x(t) = sin((2 pi t)/ T).rect((t - 3T) / 2T)
I have added my solutions to these signals in the attached image, ...
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How do i know which operations transformed a signal?
I am doing an undergrad assignment and one of the exercises is as follows:
Given the following signal $x(t)$:
and another signal $y(t)$ which was transformed from $x(t)$:
Describe $y(t)$ in function ...
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Multiplication of function with Dirac impulses: sketch signal
I should sketch the signal below:
I think I should use delta dirac function sampling theorem but I don't know how in this special case
I know that $x(t)δ(t-t_{0})=x(t_{0})δ(t-t_{0})$ but I don't have ...
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OFDM: From DFT to time-continuous signal
I try to write down the equations that show how constellation symbols (PSK, QAM etc.) are modulated into a time-continuous signal. I read the articles referenced at the end. However, I am still stuck ...
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Orthogonal signals basics [closed]
Suppose we have 2 orthogonal signals $x_{1}(t)$ and $x_{2}(t)$ and we add them up.
Can we always say that the resulting signal will be of this form:
$$x_{3}(t)=x_{1}(t)+jx_{2}(t)$$ ?
If that is true ...
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Shot noise at an imaging system - is it white?
Shot noise is generally a white noise. For an imaging system based on detectors the shot noise variance that scalers linearly with flux and time (details here and here):
$$\sigma^2=I\cdot QE\cdot\...
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When discretizing a stochastic signal , are there random variables independent of those that follow in time and dependent on previous ones in time?
$X(t)$ is a stochastic process defined on the time interval $(0, T)$. Discretizing the time interval one specify the time instants $t_0=0 < t_1 < t_2,\cdots,< t_{n-1} < t_n = T$.
A random ...
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I want to transmit a CW signal using SDR could be pluto or hackrf but I haven't used any one of them can anyone help me
I am using HackRF or Pluto SDR for transmission of a CW signal, after reading the documentation of the HackRF one SDR I found out that it transmits data in only 8-bit signed quadrature samples. Now I ...
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Calculation of a position from the angles of arrival
For locating a target by TDOA (Time Difference Of Arrival) with $3$ stations we have the Chan method which gives an exact solution of the position.
I keep the $3$ stations but instead of measuring the ...
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error on angle of arrival
I have $2$ sensors allowing me to measure angles of arrival. These sensors are a distance $d$ ($d \simeq 10$ m) apart and the target to be located is at a distance $R$ with $d<<R$. In the ...
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I am trying to plot range of a target in a FMCW radar
I am working on the simulation of FMCW radar, and I am trying to figure out how to plot the target range using the impulse response of the beat signal. I have successfully generated the chirps and the ...
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Discontinuities in the frequency domain
I'm trying to implement a waveform such the frequency will look like this -
$f(t)=f_0+\left(f_1-f_0\right) e^{\frac{\left(t \pm \delta_t / 2\right)^2}{2 \sigma^2}}$
To do so, I calculate it like this -...
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Calculate power of a signal
The task is to calculate power of signal below:
$$ x(t)=\sum^{\infty }_{k=-\infty }(t-k)[u(t-k)-u(t-k-1)]$$
The answer is 0.33 but I don't know how to calculate this even though I applied the formula, ...
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A necessary condition for the signal energy be finite by Lathi
In the book Modern Digital and Analog Communication Systems by B.P. Lathi and Z. Ding, on page 21, the authors wrote: "A necessary condition for the energy to be finite is that the signal ...
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In wireless communication, is pulse shaping applied to each BPSK signal before OFDM is used, or not?
I have read a number of posts that seem to ask this question but have not been able to find a definitive answer. Here goes...
I understand that BPSK with NO pulse shaping would produce a signal in ...
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How to simulate multiple targets in FMCW radar simulation in python?
I have simulated a FMCW radar for a single stationary target, now the next step in my project is to simulate multiple moving targets. For this I had thought of using doppler shift to show a difference ...
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Applying Blahut-Arimoto Algorithm for AWGN Channels Capacity Calculation with Cost
I am exploring the Blahut-Arimoto algorithm (or any numerical method) for channel capacity calculations, particularly for continuous channels. I understand its application in discrete scenarios, but I ...
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Power Spectral Density and Total Power Calculation for Signal
I am currently working on analyzing a signal with the autocorrelation function given by:
$$R(\tau) = 100 \cos( 10000\pi\tau) (Λ(2000\tau))^2$$
I need assistance in plotting the power spectral density ...
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Continuous-time convolution of signals with negative amplitudes
While preparing for a mid-term exam, I encountered negative amplitudes for the first time while convolving two signals.
I've already solved the problem, but my result and results from others conflict ...
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Energy and power of time-continous signal $x(t)=t$?
Preparing for my exams, I stumbled upon this particular problem.
I tried to calculate it using following formulae:
$$ 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)$$
Now I know that multiplication in time means convolution in the Fourier Domain ...
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Calculating DC from signal avg or rms value required?
If we want to calculate a dc value of any given signal, should the dc value be RMS or average value?
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345
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Convolution of step function with exponentials
I have a problem in signals and systems to solve which is basically math
So suppose we have two functions x(t) = H(t) which is the Heaviside unit step function as input and an impulse response
$$h(t)=...
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