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Warp wrote:
> Invisible <voi### [at] dev null> wrote:
>> [We casually overlook the fact that JPEG doesn't work in the RGB colour
>> space, it works in some weird custom space to better accomodate the
>> peculiarities of the human eye.
>
> It's not a "custom space". It's the YCbCr color space, which has been
> used in television and video for like 50 years.
OK, I rephrase: It looks pretty exotic to me. ;-)
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>> A function that is 0 everywhere except for f(0)=1 is not a delta
>> funciton. A delta function has f(0)=infinity and when integrated it gives
>> a non-zero value (ie it has area, unlike the function Kevin described).
>
> http://en.wikipedia.org/wiki/Kronecker_delta
> http://en.wikipedia.org/wiki/Dirac_delta_function
>
> So you see, we are in fact both right, for a suitable definition of "delta
> function". (I'm going by a DSP textbook.)
>
> The Dirac delta doesn't interest me - my signals won't ever contain
> infinity.
Ok, well if you are dealing with discrete digital functions then the concept
of a function having "zero area" doesn't really make any sense, so yes, any
function can be made from a series of sine and cosines.
>> Have you read:
>>
>> http://en.wikipedia.org/wiki/Wavelet
>
> I have. Multiple times. I still don't understand.
Did you check out some of the links at the bottom? I just read this one and
it was ok to understand:
http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html
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scott wrote:
>> The Dirac delta doesn't interest me - my signals won't ever contain
>> infinity.
>
> Ok, well if you are dealing with discrete digital functions then the
> concept of a function having "zero area" doesn't really make any sense,
> so yes, any function can be made from a series of sine and cosines.
...and hopefully some other functions too? :-)
>>> Have you read:
>>>
>>> http://en.wikipedia.org/wiki/Wavelet
>>
>> I have. Multiple times. I still don't understand.
>
> Did you check out some of the links at the bottom? I just read this one
> and it was ok to understand:
>
> http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html
I read that back in 1997. (Yes, that's how old it is.) I had trouble
understanding it back then, and having reread it a few times since then,
I still have trouble comprehending it.
I think essentially wavelets are just too complicated to understand. So
I'll stick with my original approach...
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>>> [We casually overlook the fact that JPEG doesn't work in the RGB colour
>>> space, it works in some weird custom space to better accomodate the
>>> peculiarities of the human eye.
>>
>> It's not a "custom space". It's the YCbCr color space, which has been
>> used in television and video for like 50 years.
>
> OK, I rephrase: It looks pretty exotic to me. ;-)
It's much better than RGB for two reasons.
1) The Y matches the high resolution bit of your eye, and the CbCr bits
match the lower resolution color detector bits of your eye. Thus they can
be compressed different amounts.
2) Equal distances in the CbCr space give a roughly equal difference in
colour perception.
If you tried to compress RGB channels separately the same amount as a YCbCr
signal it would look much worse.
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scott wrote:
>> OK, I rephrase: It looks pretty exotic to me. ;-)
>
> It's much better than RGB for two reasons.
>
> 1) The Y matches the high resolution bit of your eye, and the CbCr bits
> match the lower resolution color detector bits of your eye. Thus they
> can be compressed different amounts.
>
> 2) Equal distances in the CbCr space give a roughly equal difference in
> colour perception.
>
> If you tried to compress RGB channels separately the same amount as a
> YCbCr signal it would look much worse.
Yes, I'm sure this is exactly why they use it. Still, it's not very easy
to comprehend...
(Similarly, almost all known audio codecs don't compress the left and
right stereo channels seperately; they compress "center and side"
instead, since usually the side channel will contain very much less
signal energy - and getting it wrong is far less serious sonically.)
PS. Is this why all MPEG-based algorithms utterly mutilate blue images?
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> I read that back in 1997. (Yes, that's how old it is.) I had trouble
> understanding it back then, and having reread it a few times since then, I
> still have trouble comprehending it.
>
> I think essentially wavelets are just too complicated to understand. So
> I'll stick with my original approach...
I don't claim to be anything like an expert on wavelets, but for someone who
apparently knows about fourier transforms it goes like this (roughly):
If you do a normal FT on a signal, you get a nice graph of amplitude against
frequency.
If you have a longer signal (eg a song) then you can split it up into chunks
and do FT on each chunk. You then get a nice 3D graph of how amplitude
against frequency changes over time.
The problem is that the shorter you make the chunks, the less accurate the
frequency information is. The longer you make the chunks, the less accurate
the time information is and the (more accurate) frequencies get blurred
together over time.
What wavelets do is allow you to use a different chunk size for different
frequencies. In a song you probably want a small chunk size for high
frequencies (the absolute frequency is not so important, just the timing),
and a large chunk size for low frequencies.
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scott wrote:
> If you do a normal FT on a signal, you get a nice graph of amplitude
> against frequency.
But, sadly, only for a sationary siganl.
The problem, essentially, is that standard Fourier theory lets you look
at a signal purely in the time domain, or purely in the frequency domain
- but humans perceive sounds in *both* domains simultaneously.
> If you have a longer signal (eg a song) then you can split it up into
> chunks and do FT on each chunk. You then get a nice 3D graph of how
> amplitude against frequency changes over time.
>
> The problem is that the shorter you make the chunks, the less accurate
> the frequency information is. The longer you make the chunks, the less
> accurate the time information is and the (more accurate) frequencies get
> blurred together over time.
Or rather, the problem is that if the chunk bounderiess don't line up
nicely with wave cycles, you get spurious high-frequency components
being reported that don't actually exist in the original signal.
> What wavelets do is allow you to use a different chunk size for
> different frequencies. In a song you probably want a small chunk size
> for high frequencies (the absolute frequency is not so important, just
> the timing), and a large chunk size for low frequencies.
Yeah. I get all that. I just don't understand how the maths works.
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> Or rather, the problem is that if the chunk bounderiess don't line up
> nicely with wave cycles, you get spurious high-frequency components being
> reported that don't actually exist in the original signal.
Use a non-rectangular window function?
>> What wavelets do is allow you to use a different chunk size for different
>> frequencies. In a song you probably want a small chunk size for high
>> frequencies (the absolute frequency is not so important, just the
>> timing), and a large chunk size for low frequencies.
>
> Yeah. I get all that. I just don't understand how the maths works.
Maybe you should get a real book? I have no idea if it is valid or not, but
you could start off by doing repeated FTs with different chunk sizes for
different frequencies...
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scott wrote:
>> Or rather, the problem is that if the chunk bounderiess don't line up
>> nicely with wave cycles, you get spurious high-frequency components
>> being reported that don't actually exist in the original signal.
>
> Use a non-rectangular window function?
Mmm, that's equivilent to a convolution in the frequency domain. ;-)
>>> What wavelets do is allow you to use a different chunk size for
>>> different frequencies. In a song you probably want a small chunk
>>> size for high frequencies (the absolute frequency is not so
>>> important, just the timing), and a large chunk size for low frequencies.
>>
>> Yeah. I get all that. I just don't understand how the maths works.
>
> Maybe you should get a real book?
Possibly, yes...
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Invisible wrote:
>> This isn't quite true over the reals, even assuming you're only
>> looking for functions with a given period. For example the function
>> which is zero everywhere except being 1 at a single point will
>> generate the same Fourier representation as the constant zero function
>> since it will have the same integrals.
>
> O RLY?
>
> My DSP textbook says the Fourier transform of the delta function yields
> an amplitude of 1 for all frequencies. (Whereas the Fourier transform of
> a zero signal would be a zero signal.)
Both your book and Kevin are correct. He was not talking about the
delta function (which never has a value of 1).
--
ASCII stupid question... get a stupid ANSI!
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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