[music-dsp] Window presum synthesis

[Dave Hoskins]

On 23/04/2012 11:49, Domagoj Šarić wrote:
> On 23 April 2012 12:20, Domagoj Šarić<dsaritz at gmail.com>  wrote:
>> More importantly, yes, the code does have resynthesis and the way it
>> avoids the flanging (or echo for larger frame sizes) artefacts (that
>> you get from adding the frame-size-delayed copy of the signal to
>> itself) is by applying a sinc to the analysis and synthesis windows...
> OTOH this linking of the analysis and synthesis windows creates
> another problem that links it to the "WOLA and the phase vocoder"
> thread (how to have both analysis and synthesis windows and perfect
> reconstruction but without modifying, sqrt-ing, the analysis
> window)...
Search Google for "MDCT", and "MDCT Ogg". I've played around with OGG's 
version, and it works very well for reconstruction at 50% overlap (if 
you go to 1024 in size, at least), but the information you get out of it 
might not be useful, it depends on what you're trying to achieve in the 
long run.
But it's interesting...  : )

http://en.wikipedia.org/wiki/Modified_discrete_cosine_transform

"The*modified discrete cosine transform (MDCT)*is aFourier-related 
transform 
<http://en.wikipedia.org/wiki/List_of_Fourier-related_transforms>based 
on the type-IVdiscrete cosine transform 
<http://en.wikipedia.org/wiki/Discrete_cosine_transform>(DCT-IV), with 
the additional property of being/lapped/: it is designed to be performed 
on consecutive blocks of a largerdataset 
<http://en.wikipedia.org/wiki/Dataset>, where subsequent blocks are 
overlapped so that the last half of one block coincides with the first 
half of the next block. This overlapping, in addition to the 
energy-compaction qualities of the DCT, makes the MDCT especially 
attractive for signal compression applications, since it helps to 
avoidartifacts 
<http://en.wikipedia.org/wiki/Compression_artifact>stemming from the 
block boundaries. As a result of these advantages, the MDCT is employed 
in most modern lossy audio formats, includingMP3 
<http://en.wikipedia.org/wiki/MP3>,AC-3 
<http://en.wikipedia.org/wiki/Dolby_AC-3>,Vorbis 
<http://en.wikipedia.org/wiki/Vorbis>,Windows Media Audio 
<http://en.wikipedia.org/wiki/Windows_Media_Audio>,ATRAC 
<http://en.wikipedia.org/wiki/ATRAC>,Cook 
<http://en.wikipedia.org/wiki/Cook_codec>, andAAC 
<http://en.wikipedia.org/wiki/Advanced_audio_coding>..."

Dave.