### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

ight be helpful. L8r, r b-j Original Message ---------------- Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "gm" Date: Fri, November 9, 2018

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

vocoder implemented to do time scaling.� lemme know if that might be helpful. L8r, r b-j � Original Message Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "gm" Date: Fri, November 9,

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "gm" Date: Fri, November 9, 2018 4:19 pm To: music-dsp@music.columbia.edu -- > > hm, my application has also WOLA ... > &g

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Message Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "gm" Date: Fri, November 9, 2018 4:19 pm To: music-dsp@music.columbia.edu -

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

be an incorrect historical impression. Original Message -------------------- Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

>> DFT. >>>> >>>> (And I don't know anything about the historical question!) >>>> >>>> -Ethan >>>> >>>> >>>> >>>> On Mon, Nov 5, 2018 at 2:18 PM, robert bristow-johnson < >>>> r...@audioimagination.

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Original Message -------- Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "Ethan Fenn" mailto:et...@polyspectral.com>> Date: Mon, No

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

;>> r...@audioimagination.com> wrote: >>> >>>> >>>> >>>> Ethan, that's just the difference between Decimation-in-Frequency FFT >>>> and Decimation-in-Time FFT. >>>> >>>> i guess i am not entirely certainly o

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

No matter how you go about this, the the Fast Fourier will in almost every case act as some sort of ensemble measurement over it's length, and maybe do some filtering between consecutive transform steps. Maybe you even continuously average in the frequency domain, using per sample sliding FFT

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

cy FFT >>> and Decimation-in-Time FFT. >>> >>> i guess i am not entirely certainly of the history, but i credited both >>> the DIT and DIF FFT to Cooley and Tukey. that might be an incorrect >>> historical impression. >>> >>> >>&g

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

I think I figured it out. I use 2^octave * SR/FFTsize -> toERBscale -> * log2(FFTsize)/42 as a scaling factor for the windows. Means the window of the top octave is about 367 samples at 44100 SR - does that seem right? Sounds better but not so different, still pretty blurry and somewhat

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Further tests let me assume that you can do it on a log2 scale but that appropriate window sizes are crucial. But how to derive these optmal window sizes I am not sure. I could calculate the bandwitdh of the octave band (or an octave/N band) in ERB for instance but then what? How do I derive a

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

At the moment I am using decreasing window sizes on a log 2 scale. It's still pretty blurred, and I don't know if I just don't have the right window parameters, and if a log 2 scale is too coarse and differs too much from an auditory scale, or if if I don't have enough overlaps in resynthesis

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

On 7/11/2018 12:03 AM, gm wrote: A similar idea would be to do some basic wavelet transfrom in octaves for instance and then do smaller FFTs on the bands to stretch and shift them but I have no idea if you can do that - if you shift them you exceed their bandlimit I assume? and if you stretch

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

at's just the difference between Decimation-in-Frequency FFT >>> and Decimation-in-Time FFT. >>> >>> i guess i am not entirely certainly of the history, but i credited both >>> the DIT and DIF FFT to Cooley and Tukey. that might be an incorrect >>> histor

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

>> the DIT and DIF FFT to Cooley and Tukey. that might be an incorrect >> historical impression. >> >> >> >> ------------ Original Message >> Subject: Re: [music-dsp] 2-point DFT Matrix for sub

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

lumbia.edu Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? I don't think that's correct -- DIF involves first doing a single stage of butterfly operations over the input, and then doing two smaller DFTs on that preprocessed data. I don't think there is any

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

n-Time FFT. > > i guess i am not entirely certainly of the history, but i credited both > the DIT and DIF FFT to Cooley and Tukey. that might be an incorrect > historical impression. > > > > Original Message ---------------- > Subject:

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

. Original Message Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? From: "Ethan Fenn" Date: Mon, November 5, 2018 10:17 am To: music-dsp@music.co

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Am 05.11.2018 um 16:17 schrieb Ethan Fenn: Of course it's possible you'll be able to come up with a clever frequency estimator using this information. I'm just saying it won't be exact in the way Cooley-Tukey is. Maybe, but not the way I laid it out. Also it seems wiser to interpolate

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

It's not exactly Cooley-Tukey. In Cooley-Tukey you take two _interleaved_ DFT's (that is, the DFT of the even-numbered samples and the DFT of the odd-numbered samples) and combine them into one longer DFT. But here you're talking about taking two _consecutive_ DFT's. I don't think there's any

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Am 05.11.2018 um 01:56 schrieb gm: so you do the "radix 2 algorithm" if you will on a subband, and now what? the bandlimits are what? the neighbouring upper and lower bands? how do I get a frequency estimate "in between" out of these two real values that describe the upper and lower limit

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

Am 05.11.2018 um 01:39 schrieb robert bristow-johnson: mr. g, I think what you're describing is the Cooley-Tukey Radix-2 FFT algorithm. yes that seems kind of right, though I am not describing something but posting a question actually and the "other thing" was an answer to a question

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

8:00) To: music-dsp@music.columbia.edu Subject: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? bear with me, I am a math illiterate.I understand you can do a Discrete Fourier Transform in matrix form,and for 2-point case it is simply[ 1, 1 1,-1]like the Haa

### Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?

music-dsp@music.columbia.edu Subject: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis? bear with me, I am a math illiterate.I understand you can do a Discrete Fourier Transform in matrix form,and for 2-point case it is simply[ 1, 1 1,-1]like the Haar transfor