Questions tagged [theory]
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60
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4
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Why is sampling not “idempotent”?
This answer describes succinctly what sampling a continuous signal means in the frequency domain:
$$
\begin{align*}
x(t)\sum_{n=-\infty}^{\infty}\delta(t-nT)
&\leftrightarrow \frac{1}{T}\sum_{k=-\...
- 31
0
votes
0
answers
12
views
Matching closed form BER with integrals for QPSK modulation
I am trying numerically compute the $\bar{P}_b$ for QPSK in a Rayleigh fading channel according to the formula,
$$
\bar{P}_b = \int_0^\infty P_b(\gamma)p_{\gamma_s}(\gamma)\ d\gamma
$$
for QPSK $P_b(\...
- 154
1
vote
0
answers
43
views
Plotting Theoretical Maximum ratio combining
I am try to plot the maximum ratio combining of BPSK on a Rayleigh fading channel by integration i.e,
$$
\bar{P_e} = \int_0^\infty Q(\sqrt{2\gamma})p_\Sigma(\gamma) \ d\gamma
$$
but I can't seem to ...
- 154
2
votes
1
answer
119
views
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 ...
- 125
1
vote
1
answer
54
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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 ...
- 95
0
votes
1
answer
24
views
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 ...
- 35
3
votes
2
answers
663
views
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 ...
- 533
2
votes
1
answer
73
views
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
0
votes
1
answer
67
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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
...
- 103
1
vote
0
answers
210
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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 ...
- 21
-1
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1
answer
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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 ...
- 106
7
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7
answers
3k
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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 ...
- 171
2
votes
3
answers
989
views
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!
- 425
1
vote
1
answer
621
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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 ...
- 113
3
votes
1
answer
302
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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] ...
- 473