Shannon ad fc/2 tricks

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#81
I too am finding this thread rather boring. If the OP had come here expressing puzzlement and seeking explanations then by now he should have gone away enlightened. Instead he appears to be digging in and telling the world that the theory of sampled data systems contains a fundamental flaw.

Unless he starts asking instead of telling then I am out too.
 
#82
DF96 said:
I too am finding this thread rather boring. If the OP had come here expressing puzzlement and seeking explanations then by now he should have gone away enlightened...
Click to expand...

Not just boring but misinforming. And doing it at a 'medium level' that can easily confuse/misdirect those with less understanding. (Exactly what snake oil marketers do)

That's why it's more serious that just a guy-wrong-on-the-internet and thank you guys-in-the-know for setting things straight (or at least according to the basic theory/reality). Those who've been around diyaudio awhile have witnessed the exhausting and frustrating work of a handful of people correcting basic and not-so-basic misunderstanding. I hope you know who you are and that a quiet many appreciate it. 🙂



What I don't get is the arrogance that after dabbling in a field, you've discovered a 'flaw' and further, 'fixed it'?!? (Like that guy making up theories about Primate Evolution ?!??11?! 🙄 )

..."expressing puzzlement and seeking explanations"... is a perfect approach, or if you really wanna live the high-school, ego-stroking fantasy of the 'eccentric new scientist that over-turns a discipline' then do it as a joke


ItsaJokeSon.jpg~c200.jpg



Jeff

PS All that's missing now is a low-level reference to issues discussed (not just wikishannon) and a mid-level, specific reference. (Takers?)
 
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#84
Your llusion to knew all

pergo said:
Gumo, it's a simple optical trick.
Nothing more simple.
You can test it in practice 😉
Click to expand...

If you see the circles envelope and separate them by simple selection of samples you can see that is no an optical illusion is similar an ssb modulation where fd+ and fd-
are not in phase or fc-fd an fd+fc idem are not in phase
on Fourier
This was happen on Fourier domain for all the kids that unknown signals theory . See below
 

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#85
My first video explains a lot. I suggest you to see it (20 minutes).
Maybe it will help. It's more practice. 🙂

Sorry but you've several lacks on Signal Theory or, simply, Math*.
I can't explain something known, neither in English.
See ya on CHF Forum if you want discuss in Italian.


*you can't draw a negative module!!
If you wanna talk about phase, show phase plots..not amplitude.
 
#92
In PM you wrote me about modulation.
I quote you: "you've study modulation and you don't recognize one"

Modulation has strong mathematical definition.
Sampling too, and different.

If you "see" modulation, nothing simpler than prove it with its definition. No?
And which kind of modulation do you see?!

When you have these answers, apply the inverse concept: demodulation.

There are few modulation that uses LP filter for reconstruction.
Those ones have a mathematical definition too.
So you've to check your idea with reality....maybe books.

For example:
Do you think it's AM?
Good. AM has strong definition. Use it. It works? Mmh...
How demodulate AM? With LP filter? Mmh...not really. You can try with a circuit 😉


This should be a way to prove something....as Galileo did... 🙂
You've to match different definition, real and solid ones, and go ahead.
If you have "new" theories you've to use proper methods.

See a graph and claim a novelty is far enough from science.

Chop chop! 🙂
 
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#93
Convolution

peufeu said:
Here ya go.

First I create an "analog" signal (it's just oversampled but that's well enough so it looks pleasing to the eye).

Since it is a pure 15k sine, it is perfectly bandlimited and by sampling it at 44.1k, no information is lost. The samples are the black dots.

It looks like there is a beat frequency, visually.

Note I do not display lines between samples because it makes no sense. Lines should only be displayed when the oversampling is high enough (or the signal slow enough) that linear interpolation doesn't give too much bogus results. Which is obviously not the case here.

The sinc reconstruction brings back the original "analog" signal, as you see. No problem.

Code: 
from numpy import *
import matplotlib.pyplot as plt

# create "analog" signal

def make_signal( Fs, NSamples, freq, oversampling ):
	Fs *= oversampling
	NSamples *= oversampling
	t  = arange(NSamples) * (1.0/Fs)
	return t, cos( 2*pi*freq*t )

Fs       = 44100.
NSamples = 100
freq	 = 15000.

plt.figure(1)

plt.subplot(3,1,1)
analog_t, analog_signal = make_signal( Fs,  NSamples, freq, 16 )
plt.plot( analog_t, analog_signal, "b-", label='"analog" signal' )

digital_t, digital_signal = make_signal( Fs,  NSamples, freq, 1 )
plt.plot( digital_t, digital_signal, "ko", label='"digital" signal' )

plt.xlabel("time (s)")
plt.title("signal and samples")
plt.legend() 
plt.tight_layout()

plt.subplot(3,1,2)
reconstruct_oversample_ratio = 8
reconstruct_length = 32 * reconstruct_oversample_ratio

impulse = sinc( (1.0/reconstruct_oversample_ratio) * arange( -reconstruct_length, reconstruct_length ) )

plt.plot( impulse )
plt.xlabel("sample #")
plt.title("reconstruction filter")
plt.tight_layout()

plt.subplot(3,1,3)

# recondtruct sampled signal
# first insert zeros
digital_signal_padded = zeros( NSamples * reconstruct_oversample_ratio )
digital_signal_padded[::reconstruct_oversample_ratio] = digital_signal

# then convolve (very dumb method)

reconstructed = convolve( digital_signal_padded, impulse )

plt.plot( reconstructed )
plt.title( "reconstructed" )
plt.show()
Click to expand...


Why on your demonstration you use on time domain Convolution between samples and
sinc

reconstructed = convolve( digital_signal_padded, impulse )

If you are on freq. domain you convolution by a rect but on time domain you have a simple multiplication

See the recostruction equation
Nyquist?Shannon sampling theorem - Wikipedia, the free encyclopedia

Under discrete domain (digital) you cant see additional noise because on this domain is
invisible and have a null median.
 
#98
Calculus

pergo said:
Thread speaks 😉
Click to expand...

why you write about nothing.
You don't have resolving the calculus by any other different manner .
You toking about optical illusions (but they are de seme psychical phenomenon )
Now you attempt to demonstrate your learning preparation with nothing of concrete calculus
Next post you toking about black magic phenomenon ?
 
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#99
Dude,
a practice video and some graphs should be enough.
If you can't understand those, it's useless to go on. 🙂

I'm not the only one who told you're wrong.
Ok..everyone is stupid, you not: great, so..PROVE IT!

More math, less pew pew. 🙂
 
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