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Fourier Transforms
 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-13 20:04 [#02494260]
Points: 30707 Status: Regular



I was watching a having a discussion tonight with my
brother tonight about fourier transforms and how they are
used for digital encoding, etc, and i was discussing in the
context of sound and how every conceivable soundwave can be
constructed by compiling an infinite number of sinewaves
with different frequencies and no amplitude.

Well i was thinking of if you had a finite series of
sinewaves and you could vary their frequency coefficients on
the fly how you could create really wild and interesting
sounds. Is this in essence what digital synthesizers do in a
finite sense, as i imagines its very computationally
expensive to do things in real time, i suppose thats what
wavetable synths do.

does anyone know what im on about, has anyone go a concept
of what im getting at?


 

offline fleetmouse from Horny for Truth on 2016-04-13 21:27 [#02494263]
Points: 18042 Status: Lurker



sure that's additive synthesis bruv



 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-13 21:51 [#02494264]
Points: 30707 Status: Regular



^ syeah your right

what i meant with the wavetable is a list of variables
stored for manipulation, like a look up table, like a very
simple fourier transform, im not sure im right about that,
actually just checked the wiki article they are different
methods of achieving the same thing.




 

offline fleetmouse from Horny for Truth on 2016-04-13 22:21 [#02494266]
Points: 18042 Status: Lurker



Kind of yes, in both cases you're morphing between spectra,
the difference is how you model them, whether as waveshapes
or a graph of partials and their amplitudes. IMO U-he Zebra
is the best for this kind of thing even if the default GUI
looks a little ropey in 2016 terms.


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-13 22:28 [#02494267]
Points: 30707 Status: Regular



cheers, yeah sorry i only partially understand what im going
on about, that zebra thing looks like what i was initially
trying to describe


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-13 22:29 [#02494268]
Points: 30707 Status: Regular



discrete or continuous methods of generating a waveform


 

offline steve mcqueen from caerdydd (United Kingdom) on 2016-04-14 02:13 [#02494269]
Points: 6148 Status: Addict



it is 'quite interesting' - eg for analysis - the longer the
time you look at the more frequencies you can see but less
information about WHEN they occurred - shorter time the
opposite... makes you think about how much the two things
are literally just different ways of looking at the 'same
"thing"'


 

offline steve mcqueen from caerdydd (United Kingdom) on 2016-04-14 02:19 [#02494270]
Points: 6148 Status: Addict



like, if you play a sine wave who's cycle lasts a year, and
you analyse the first weeks worth and try to build that up
from sine waves lasting a week...


 

offline steve mcqueen from caerdydd (United Kingdom) on 2016-04-14 02:20 [#02494271]
Points: 6148 Status: Addict



How do you know how long the wave will last if we've seen a
just little bit


 

offline steve mcqueen from caerdydd (United Kingdom) on 2016-04-14 02:30 [#02494272]
Points: 6148 Status: Addict



best u ignore most of that, cant explain for toffee



 

offline steve mcqueen from caerdydd (United Kingdom) on 2016-04-14 03:03 [#02494273]
Points: 6148 Status: Addict



been loads of good spectral synthesis things like MetaSynth
and ZynAddSubFx etc. but they don't get much of a mention in
books I've seen...seems like we've invented all the
synthesis techniques possible! bonkers.


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-14 14:24 [#02494277]
Points: 30707 Status: Regular



yeah all the fundamentals have been covered i agree, its
amazing to think the concept of fourier transforms existed
in pure maths hundreds of years before it had practical
applications in the modern world, blows me noggin,

imaging a program that could generate radically different
waveforms quickly and programatically without you having to
change any parameters, you could observed the creations and
save preferred settings, there is so many variables im sure
there are still many many sounds unexpected out there.

deep note


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-14 14:27 [#02494278]
Points: 30707 Status: Regular



imagine a hardware synth where you can have almost vast
banks of waveforms interacting, but generating something
that approximates usable sounds that complement each other
rather than generating something that sounds like white
noise


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-14 14:31 [#02494279]
Points: 30707 Status: Regular



suppose granular synthesis is the closest to what im talking
about but thats individual grains, im talking about
something that has so many oscillators you couldnt manually
change any of the varibles cos there is so many of them, but
if you had a system behind it that handles maths, you could
have preset algorithms to handle everything for you, so you
could change any of the variables in the algorithm and it
would change everything, you could have it as attuend or
chaotic as you wanted


 

offline EpicMegatrax from Greatest Hits on 2016-04-15 02:40 [#02494310]
Points: 23981 Status: Addict



what if i should want five?


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 14:45 [#02494436]
Points: 30707 Status: Regular




yes we could do five

your the technical guy arent you Epic

we would need a super computer for that, or an array of
raspberry pi's to spread the load


 

offline freqy on 2016-04-16 16:12 [#02494454]
Points: 18724 Status: Regular | Show recordbag



sample and phase accurate sync between computers would be
required else you would have phase distortion, cancellation
or reinforcement of freqys.

you should check out max msp

you can achieve what you like with that.



 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:18 [#02494455]
Points: 30707 Status: Regular



yes phase cancellations would deffo be something i would
envisage if i was rendering in real time performance,

I think if the system was programmed correctly that wouldnt
be an issue as id get it to render sound only when
calculations were complete,

yes max msp looks very good, i might see what i can
accomplish with something like supercollider for a laugh,
get my classes running on separate threads


 

offline freqy on 2016-04-16 16:19 [#02494456]
Points: 18724 Status: Regular | Show recordbag



max 6 opens doors to new worlds of creativity.

max 6 demo


 

offline freqy on 2016-04-16 16:21 [#02494457]
Points: 18724 Status: Regular | Show recordbag



ah you know already, I posted as you posted.


 

offline freqy on 2016-04-16 16:22 [#02494458]
Points: 18724 Status: Regular | Show recordbag



max is great because there are allot of tutorials.



 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:22 [#02494459]
Points: 30707 Status: Regular



thanks for link, i havent checked it out for ages


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:24 [#02494460]
Points: 30707 Status: Regular



the flow chart reminds me of stuff like reaktor, but i
suppose behind that are you own classes rather than pre
configured objects


 

offline freqy on 2016-04-16 16:33 [#02494464]
Points: 18724 Status: Regular | Show recordbag



you can make your own objects but there are hundreds
already made and very efficient. you can change how they
behave too

just join them up with wires/cords. lol its fun.

random frequencies

LAZY_TITLE


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:39 [#02494466]
Points: 30707 Status: Regular



so much fun creating funny noises, first thing i did on
supercollider was create a waterfall sound, low pass filter
on white noise, can remember what else i did


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:44 [#02494468]
Points: 30707 Status: Regular



i wouldnt necessarily use supercollider to make music but to
make really cool samples its ace


 

offline freqy on 2016-04-16 16:49 [#02494469]
Points: 18724 Status: Regular | Show recordbag




You can make so much stuff these days with these types of
programs.

i love using objects and cords.



 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-16 16:51 [#02494470]
Points: 30707 Status: Regular



yes, its a more than legitimate alternative, i would do that
if i had the cash, you can get the sounds you want quicker


 

offline umbroman3 from United Kingdom on 2016-04-22 09:56 [#02494801]
Points: 6096 Status: Regular



https://www.youtube.com/watch?v=GtAMYafil2Q


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-22 18:10 [#02494816]
Points: 30707 Status: Regular



imagine if we could genetically modify ourselves to be human
synths, we could think waveforms, and have midi ports under
our armpits


 

offline dave_g from United Kingdom on 2016-04-22 22:19 [#02494850]
Points: 3372 Status: Lurker | Followup to steve mcqueen: #02494270



That's an interesting idea, the year long sine wave. Got me
thinking...
You could measure the rate of change of phase over the two
week sampling period, and compute the frequency with good
temporaral resolution because the rate of change of phase is
constant for a sinusoid.
That's great but it's really a special case - other
waveforms wouldn't work.
e.g. how would you do a square wave when it is off for 26
weeks and you only measure two weeks of 'off'.

There are lots of interesting fourier techniques and things
to wrap your head around, it really is amazing that it was
developed mathematically so long before we could create DSP
chips and properly utilise it.



 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-22 22:47 [#02494852]
Points: 30707 Status: Regular



^ does phase shift occur with any sine source, is there
nothing that doesn't eventually drift? is that just the
limitation of electronic?


 

offline dave_g from United Kingdom on 2016-04-22 23:08 [#02494855]
Points: 3372 Status: Lurker | Followup to Hyperflake: #02494852



Frequency is rate of change of phase. A sinusoid is a single
frequency so a constant rate of phase change. Any distortion
on the sinusoid affects the phase.

In my imagination I can create a perfect environment where
can ignore friction, etc.
Imagine a wheel rolling past a long white wall. The wheel
has a pen at one position on its perimeter.

As the wheel rolls past the wall the pen plots a sinusoid on
the wall.
The wheel rolls at a constant speed because there is no
friction.
Constant speed also means constant frequency, so if it takes
1s to do a full turn then it is 1Hz.
Rate of change of phase is 360 deg per second.

By inspecting the line drawn on the wall after 0.1s it is
easy to extrapolate to the end point because the curve of
the line is constant, i.e. it forms a circle...
it's just in this case the wheel rolls forward so the circle
never closes.

N.B.
If we take the same wheel and put it on an axle it is clear
that the pen plots a circle rather than a sinusoid.

Obviously in the real world there is friction so it doesn't
work out so well.

Now if there was a year long sinusoid it could be very
accurate.
We could use an atomic clock to create 'ticks' that counted
up. Each count indexed a memory location that stored a
sample of our sinusoid.
The sample read out of memory could be passed to a dithered
ADC, where we can easily filter the dither with a low pass
response without affecting the 1yr sine but smoothing out
the changes.
Everything would be held at a constant temperature. All
voltages would be heavily regulated and filtered. All
vibrations heavily damped.

Or maybe the sinusoid is generated from some piece of junk
that drifts all over the shop like an early Moog. Oh and
perhaps it is distorted so the sinusoid is a bit wonky.

The universe drifts so I suppose everything depends on where
you are observing it from. I used to work with v. precise
equipment and in the end it came down to loads of statistics
and some philosophy about such things.

Quite interesting.


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-22 23:30 [#02494856]
Points: 30707 Status: Regular



^ thanks for the explanation, i was thinking about atomic
clocks before
yes everything drifts from a relativistic sense,


 

offline freqy on 2016-04-23 00:07 [#02494858]
Points: 18724 Status: Regular | Show recordbag




you don’t have to worry about this as long as all your
experiment shares the same clock source.



 

offline EpicMegatrax from Greatest Hits on 2016-04-30 07:11 [#02495124]
Points: 23981 Status: Addict



context addressable wonk sauce. is the universe quantized?
is time discrete or continuous? i suspect the answer is yes


 

offline Hyperflake from Wirral (United Kingdom) on 2016-04-30 12:01 [#02495135]
Points: 30707 Status: Regular



isnt the planck length something to do with it or the fine
structure constant or am i talking gibberish


 


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