Questions tagged [theory]
The theory tag has no usage guidance.
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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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What is the effect of multiplication on the value of discontinuities?
I see that the values of a distribution at discontinuities are essentialy equal to the mean of the right-hand and left-hand limit values when dealing with distributions in relation to the Fourier ...
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In Bluetooth Low Energy, why are Enhanced Data Rate packets only 3 Mb/s?
In the "Introduction tu Bluetooth Device Testing" document ( https://download.ni.com/evaluation/rf/intro_to_bluetooth_test.pdf ), the modulations for Bluetooth Classic are said to be a ...
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Why is the reference pressure for dB SPL 20uPa?
The article here says that
This 20-micropascal reference was selected because it was the quietest
sound pressure level that a group of normal hearing test subjects
could detect.
which makes me think ...
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FMCW Transmit Signal and Fly-back Effect
I am studying a thesis about nonlinearities in the transmit signal and it mentions the following:
The first 2,500 samples, which correspond to the Tmax of each of each
sweep period and are affected ...
user63658
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how to tune and demo
How does one go about tunning your fm demod algorithm to a given carrier frequency.
Consider the following algorithms that are present in this website:
DSP Tricks: Frequency demodulation algorithms
...
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143
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Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes
I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
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Shortened linear codes
I've been working on my linear code assignment in my coding theory course and I have encountered a problem I would like to get help with. the question is described below. I will try to expalin what I ...
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Qualitative Explanation of Fourier Transform
I am reading the book Fundamentals of Music Processing by M.Muller and I am close to understanding the idea behind the decomposition of a signal into basic frequencies, and would appreciate some help ...
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3
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Are all exponential functions eigensignals of LTI systems?
I know that complex exponential functions are eigensignals to LTI systems. Do these include real exponential functions? E.g. $2^t, e^t, ...$
Thanks for the help!
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How is time used in this autocorrelation expression?
There are two papers I'm working through that explain applications of autocorrelation.
The first - by Monti - is quite clear to me:
It runs a sum over the time axis.
The second one by Brown makes no ...
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Multiplying signals in discrete-time vs continuous-time
Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is
\begin{align}
c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
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Validity of applying Heaviside function for signal processing applications
I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one.
I am currently ...
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How does Overlap-Add work for IIR filter?
So let's say I'm trying to implement something like an LPC vocoder. I analyse a speech signal by breaking it up in small chunks and determining their LPC coefficients, which are by design, the ...
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3
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Is there any new scientific capability to build non-causal filters in real world?
According to this post:
In discrete-time systems, causality is a requirement only when
processing (filtering) signals in real time; i.e. when the
index nn corresponds to a physical time n×Tsn×...
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Derivation of Nyquist Frequency and Sampling Theorem [closed]
I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
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Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?
In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
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LTI system and initial conditions
I suspect this is rather obvious once explained; I must be misunderstanding something.
From reading various answers here (such as this one), I understand that an LTI system must have zero output for ...
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Maximizing entropy on a channel
In Shannon's paper "A Mathematical Theory of Communication", in Theorem 8 he states:
Theorem 8: Let the system of constraints considered as channel have a capacity $C = \log W$. If we assign
$$p^{(s)}...
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The mean value of phase noise as a stochastic process
What is the mean value of phase noise as a stochastic process?
Where can I get a theoretical analysis of this topic?
PS: PLL produces cos(2*πfct+φ(t)). The phase noise refers to φ(t). The mean value ...
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explanation of Hybrid systems?
I want to study Detailed explanation of hybrid systems?Which incorporate both continuous and discrete time signals & systems?
for example
In which a continuous-time input signal is transformed ...
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Is the definition of recursion and iteration in signal processing different from computer science?
I was talking to my advisor today about this. He is a very experienced professor in this field, so I assume he is very knowledgable about it.
He pointed out that in signal processing, the word ...
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Does dividing the magnitude spectrum of white noise by sqrt(2) give an RMS magnitude spectrum?
I understand that the RMS Amplitude of a sinusoidal signal is around 0.707 ($\frac1{\sqrt2}$) times the Peak Value, but this is not true for noise.
However, an FFT of a noise signal indicates ...
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Relationship between the IDFT of a sampled DTFT and its discrete-time domain signal
Suppose we are given an input signal s[m,n] with DTFT $S(\omega_1, \omega_2)$.
We sample it at $\omega_1 = \frac{2 \pi k}{256}$ and $\omega_2 = \frac{2 \pi l}{256}$ to get a 256 point DFT S[k,l]. ...
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transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?
From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
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should block diagrams in Direct Form 1/2 contain empty branches to fit structure?
When creating a block diagram in a well-recognized structure (Direct Forms 1&2 in particular), does one remove branches where the coefficient is 0?
This picture includes a coefficient of $b_1=0....
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What is the Fourier Transform of a constant signal?
I am trying to figure out what the fourier transform of a constant signal is and for some reason i am coming to the conclusion that the answer is 1. Or better yet a step function.
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Is sampling at double the desired reproduction frequency accurate?
This is probably a general principles question, though I'm thinking specifically in relation to sound, which is commonly sampled at a rate of 44.1 kHz in part because the maximum frequency the average ...
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What really means stochastic in field of signal processing
I met two definitions of word stochastic, the first one (cited from wikipedia Stochastic)
The word stochastic is an adjective in English that describes
something that was randomly determined
The ...
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Overlapping power-of-cosine windows with constant weight
I would like to refer you to a relevant question I posed on the Math StackExchange: A generalisation of the Pythagorean trigonometric identity.
As can be seen from the question and the answer, what ...
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Is there a strategy for discrete control of a system with dynamics near sample rate?
I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to ...
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Are these Linear and Time Invariant Systems?
We were given the above systems and we were asked to tell whether they are linear (or not) and time invariant(or not).
$y(m,n)=x(m,n)+c,\quad c>0$
$ y(m,n)=x(m,n)+x(m,-n)$
$y(m,n)=x(m,n+m)$
$y(m,n)...
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Spectrum of a time-domain impulse train
I am trying to learn DSP. I'm reading the 2nd edition of Oppenheim & Schafer's "Discrete-Time Sig. Proc." book. On the topic of converting a continuous signal to a discrete-time signal the idea of ...
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Frequency range for set of all discrete-time sinusoids
Consider discrete time sinusoids of the form $$x[n] = \cos(\omega n) \ ,$$ where $n$ is an integer. What frequency range of $\omega$ would constitute all the possible sinusoids? I'm thinking that $0\...
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Finding a signals complimentary sound / frequency
I know about complimentary colors and how to get them, since colors are basically frequency / wavelengths. Is it possible to find a signals complimentary, additive or subtractive frequencies in an ...
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Baseband vs. Passband
I am a bit confused if the following signal is baseband or passband:
$f(t) = x(t) \cos(2 \pi f_c t) - j \: y(t) \sin(2 \pi f_c t),$
where $j = \sqrt{-1}$.
Since it is clearly not real, I cannot say ...
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Baseband vs Passband modulation
I am taking a graduate level course in Networking theory and applications and I am still a bit shaky on the difference between baseband and pass band scheming. The book I am using is Computer Networks ...
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Integral of unit step function [closed]
Can someone help me understand how did we get from the second line to the third one?
$$\begin{align}
u(t-1)*u(t) &= \int_{-\infty}^{\infty}u(\tau-1)u(t-\tau)d\tau \\
&=\int_{1}^{t}u(t-\tau)d\...
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Discrepancy when calculating LTI system output using inverse z-Transform
I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$.
...
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BIBO stability and input at system's pole
My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...
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Output of a discrete-time LTI system different form than input?
This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
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Output of discrete-time LTI system guaranteed to be same form as input?
I know that in the continuous-time context, if I supply a complex exponential input to a Linear Time Invariant system, the output will be of the same form as the input - for example, if the input is $...
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What is the difference between wide sense and strict sense stationary processes?
What is the difference between wide sense and strict sense stationary processes (SP) ?
According to the definition (by Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel in "Synchronization, Channel ...
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Does the system matrix being singular tell us anything about the system?
If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system?
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DFT independent variable as fraction of sampling rate
When the frequency domain's independent variable is labeled as a fraction of the sampling rate, the values along the horizontal axis always run between $0$ and $0.5$, since discrete data can only ...
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How to compute the Fourier Transform of this ramp-like signal?
I have the following signal:
and this as the solution to the problem:
$$\begin{align}
X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\
&= \int_0^\tau \frac{E}{\tau}t\; e^{-j\...
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Is it theoretically possible to perfectly quantize a continuous signal?
So, I'm completely new to digital signal processing, but while reading a piece this morning about quantization it got me daydreaming: could a machine ever be fast enough to sample the position and ...
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Block diagram reduction
I have the following block diagram
I know that it's solution is:
$$\dfrac{10 K_p}{Js^2+(B+2K_pK_v)s+10K_p} $$
But when I try to derive the solution with reduction rules I get different result.
...
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Looking to educate myself in dsp theory [closed]
I'm currently studying sound design, however over the past couple of years i started creating audio effects/instruments. I have also been programming in C++ for quite some years.
I noticed my ...
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