The system is memoryless just because it is based on the DFT and nothing else, which is also why it's time-invariant. unless you alter certain parameters in real-time like the window size or hop size or windowing function, etc, any input gives you the same output at any given time, which is the definition of time-invariance.
well, you're RBJ and I see that you used to work at Kurzweil until 2008. that's cool and what have you been up to since then? incidentally i was in California until 2008. As you might be able to tell, i don't care too much about the fact that time domain filtering theory is brought up often because I did my master's thesis with this frequency domain FFT filter, which I believe was rather novel at the time of completion. I do know that the field is steeped in tradition, which might be why I'm writing to the mailing list and to you in particular. but bringing up traditional FIR/IIR filtering terminology to describe FFT filtering doesn't make sense in my mind. I'm not in the audio field. but yes, I do believe that the system is time invariant, but I don't have time to prove myself to you on this forum at this time, nor do I have any interest in meeting Dr Bosi at AES. -ez On Sun, Mar 8, 2020 at 4:42 PM robert bristow-johnson < r...@audioimagination.com> wrote: > > > > On March 8, 2020 3:07 PM zhiguang zhang <zhiguangezh...@gmail.com> > wrote: > > > > > > Well I believe the system is LTI just because the DFT is LTI by > definition. > > TI is nowhere in the definition of the DFT. L is a consequence of the > definition of the DFT, but the DFT is not an LTI system. it is an > operation done to a finite segment of samples of a discrete-time signal. > > > The impulse response of a rectangular window I believe is that of a sinc > function, > > window functions do not have impulse responses. > > both window functions and impulse responses can be Fourier transformed. > the Fourier transform of the latter is what we call the "frequency > response" of the system. i am not sure what they call the fourier > transform of a window function. what is done with the frequency response > (multiplication) is *not* what is done with the fourier transform of a > window function (convolution). > > > which has ripple artifacts. > > there are no ripple artifacts in fast convolution using a rectangular > window. you need to learn what that is. > > > Actually, the overlap-add method (sorry I don't have time to dig into > the differences between overlap-add and overlap-save right now) > > what you need is time to learn the basics and learn the proper terminology > of things so that confusion in communication is minimum. > > > minimizes artifacts depending on the windowing function. > > again, there are no ripple artifacts in fast convolution using a > rectangular window. none whatsoever. > > > A sine window ... > > i think you might mean the "Hann window" (sometimes misnamed "Hanning", > but that is an old misnomer). i have never heard of a "sine window" and i > have been doing this for 45 years. perhaps the classic Fred Harris paper > on windows has a "sine window". > > > ... actually sums to 1, > > that's what we mean by "complementary". > > > the proof of which can be found in audio coding theory. I suggest you > check out the book by Bosi. > > i didn't even know Marina did a book, but i am not surprized. i've known > (or been acquainted with) Marina since she was with Digidesign back in the > early 90s. before the Dolby Lab days. before her injury at the New York > Hilton in 1993. would you like me to introduce you to her at the next AES? > > Eric, you gotta get the basics down right and you gotta learn the correct > terminology if you're going to communicate with other people about this > topic matter. Neologisms are frowned on but people do them anyway. > However you just cannot change the meanings of terms that have existed > since the 1960s (and some as far back as the 1930s). > > -- > > r b-j r...@audioimagination.com > > "Imagination is more important than knowledge." >
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