# Questions tagged [signal-processing]

The subfield of electrical engineering that focusses on analysing, modifying, and synthesizing signals such as sound, images, and scientific measurements.

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### Phase Slope Distance Calcuation

After trying to implement IFFT algorithms for phase-based ranging, as outlined in this very interesting and descriptive blog post; I've been getting horrendous results (orders of magnitude inaccurate),...
77 views

### Why the $T_1$ recovery & $T_2$ decay are independent?

In MRI, I was thinking that the decrease in transverse magnetization results in the recovery of longitudinal magnetization. However, recently, I found it was wrong. I saw a diagram (McRobbie 2014. ...
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### How exactly does a seashell make the humming sound?

My little brother asked me where the ocean-like sounds came from inside of a sea shell. I told him that the air trapped inside the shell vibrates, making a sound. But then he asked me why the air had ...
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### Weird looking sine wave behavior in an electric circuit

while studying an RLC circuit I noticed some weird like sine waves at low frequencies (1-9 kHertz) on the inductor, The amplitude behavior did not follow the theoretical model. Instead, suggested the ...
• 31
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### What does "DC" mean in gravitational physics?

I have came across a few works in gravitational physics using the term "DC" without further explanation of its meaning. For example, consider Strominger's 1703.05448, which states in p. 2 ...
• 22.1k
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### How to solve the transient response of a general $RLC$ network?

There is a $RLC$ network $\{V_i\}$ with a complex impedance $Z_{ij}$ on each edge. all vertices have initial voltage $V_i$ and all edges have initial current $I_{ij}$. Now, is there a general way to ...
• 151
53 views

### How can I determine an error on total noise?

I am analyzing the data for an experiment, where we measured the total noise in a system. The total noise is defined as the variance of the signal (and is equal tot the integral over the noise ...
46 views

### Fourier Transform of periodic Signals

If $f(x)$ is a periodic signal with a period $A$ then the Fourier transform of the signal $F(k)$ is zero, unless $k A$= $2 \pi n$ where $n$ is an integer. How can there Be a Fourier transform of a ...
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### Is there a name for the number of '9's in numbers such as 0.999 (where it would be 3)?

I am doing an optics simulation involving transmission and reflection coefficients very close to 1, such as 0.999. While I was an undergraduate student, a professor mentioned that, in certain fields, ...
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### Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?

In The Feynman Lectures on Physics, Dr. Richard Feynman claimed that the ear (I assume he meant the human ear) is not sensitive to the relative phases of harmonics. However, I was asked to test ...
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### Phase-Based Ranging

I've been reading a lot about Phase-Based Ranging (PBR), and it's all starting to become very intuitive. BUT; There is one technical, but extremely important, detail that seems to escape me. When the ...
44 views

### How to extract the "matter fluctuation amplitude" from the CMB power spectrum?

How do you convert the value listed in Planck 2018 results. VI. Cosmological parameters, $A_s = 2.101\times10^{-9}$ to the value of the matter fluctuation amplitude $\sigma_8=0.8111$? I tried ...
1 vote
25 views

### Signal recovery limits, magnetic

This question is about signal recovery. I am interested in what is the best that has been done so far, in the case of a signal of known form and which is not simply a sine wave, and what might in ...
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### What relationship between the time recording length and the frequency bandwidth?

In model testing for ocean waves, the data recording duration is usually longer the better especially for irregular waves. The recording length shall be long enough to achieve sufficiently small ...
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### I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase

I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase
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### Does sunlight have a modulation frequency?

By frequency, I don't mean electromagnetic frequency, I mean modulation frequency. For example, I can put a PWM square wave on an LED at some frequency, which I can detect with a photodiode and a ...
28 views

### Using Long-pass Filters with Gaussian Edges to Measure an Optical Spectra

Imagine you have some optical spectra (intensity vs wavelength) you want to measure. You do so by measuring the intensity of the spectra hitting a detector after placing multiple long pass optical ...
14 views

### Continuity of a quantity in a conical system to determine the velocity field

My research is on radar images and the images are collected in several conical surfaces. These conical surfaces have the same origin, the same maximum length (max flare or max range), but different ...
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1 vote
54 views

### How to justify sound propagation is a linear time-invariant (LTI) system?

Background A linear time-invariant (LTI) system (black box) is one described by the system: \begin{align} \dot{\xi}(t) & = A\xi(t) + B\omega(t), \; \xi(0) = 0 \label{eq-abc-1}\\ \lambda(t)...
• 151
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### Pulse to sine with the same frequency

I have a pulse signal with frequency f(t) And i want to generate from it a sine signal with frequency f(t) (f(t) doesn't vary a lot in time) Is there a method to do it directly with a function ...
1 vote
89 views

### Kramers-Kronig relations for a Gaussian function

Consider a function of a complex variable $\omega$ which is given by $f(\omega) = e^{-\omega^2/2}$. This function is symmetric, holomorphic everywhere, and vanishes as $|\omega| \rightarrow \infty$. ...
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### Second-order variation of an integral

I was reading the paper SISAR Imaging for Space Debris based on Nanosatellites, in which the Fresnel-Kirchoff diffraction formula is applied for a scenario in which the receiver, transmitter and ...
49 views

### How a switching mixer works in this example circuit?

I am reading about lock-in amplifiers and came across this example circuit of a mixer: You have one sinusoidal input signal $e_1$ with a phase $\phi_1$ and the local oscillator has a square-wave ...
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### Comparison between wave equation theory and transfer function theory

I deal with analysis of acoustic signals in solids. And after some literature research in physics and mathematic, I have a question about the followings two theories: Wave equation theory: Imagine I ...
1 vote
47 views

### Is it possible to, like white noise, excite all audio frequencies equally, but with a more immediate & less random burst? Like a signal discontinuity?

I am trying to generate an audio signal that, like white noise, has "equal intensity at different frequencies, giving it a constant power spectral density", but unlike white noise, can be ...
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### Does it make sense to whiten the data in order to apply a matched filtering algorithm if my dataset consist of a sinusoid + random Gaussian noise?

With a Python program I generated a sinusoid signal and I added to it Gaussian noise. Now I want to compute the optimal SNR by applying a matched filtering algorithm. Since the noise is white (at ...
35 views

### Feedback control system in gravitational wave detectors

I am preparing for a seminar on ground-based gravitational wave detectors. One topic I have very little idea about is feedback control systems. I have a basic knowledge of it, but I need to read some ...
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1 vote
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### Spectral representation of a white stationary process

I am trying to better understand the spectral representation of stochastic processes. From the book "Spectral Analysis for physical applications" by Walden and Persival: The spectral ...
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### Why does audio signal amplitude always fall off at higher frequencies?

In the frequency spectrum of every real audio sample that I've ever seen, the amplitude of the frequency components is always higher at low frequencies, then rapidly falls off at higher frequencies. ...
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