I wrote an article a few years back surveying common windows and discussing their pros and cons for different measurement goals. AudioXpress put it on line here.
I wrote an article a few years back surveying common windows and discussing their pros and cons for different measurement goals. AudioXpress put it on line here.
Just a minor gripe. "Hanning" is the process of applying a Hann window (proposed by Dr. von Hann) to a stream of data. Since it adds to 1 exactly with a 1/2 overlap, that process acquired a name. But the name of the window is "Hann" window.
Not some old, grumpy, grey-haired curmudgeon????
hann(N)= sin( 2*pi* (2n+1)/4/N))^2 (0<=n<N) You may see other expressions that go to zero at the ends. That is making the window unnecessarily short for analysis. It can also be written as .5 - .5 cos(...) Same thing.
To answer your question about Hamming window, the + centers the window around zero.
Whilst we're on this windows business, how about a discussion on FIR filter impulse response windowing...
(I've mostly used Kaiser.)
One often does not have that choice in the real world of audio, so yes, windows are then necessary. For test signals, there is often a good reason to have a prime wrt analysis length, too. Depends on what you're doing.
Rectangular/no window is great when you can perfectly match the FFT size to the signal period (aside from low-level noise). Sometimes that's possible, but often it's not, and then the best choice, as JJ said, depends on what you need.
I often use Dolph-Chebyshev since it easily allows pushing the side lobes below the noise level, even when there's very little noise. If you're only interested in features above the level of the side lobes, another window may do just as well or better.
I used Kaiser in DeltaWave filter calculations.
Forgive me if I've missed something, but isn't DeltaWave used for measuring signals rather than filter design? (i.e. For high quality audio processing applications, where the output signal will be ultimately "received" by the human auditory system.)
Assume we have a signal of unknown origin... price, temperature, coordinate of some movement, index of happiness in population...
...does anybody apply dither, say, before rounding financial data, which is a type of quantization?)...
If I wanted to treat financial data like an analog signal that I needed to digitize, and I was limited to a certain number of bits to represent each sample, then yes I would want to apply dither.
For test signals, there is often a good reason to have a prime wrt analysis length, too. Depends on what you're doing.
If you rip the discs and post the tracks, we can perhaps figure something out.Perhaps you can clarify why certain test discs (CD) of mine use different (to one another) digitally generated (not from analog sign gen) prime frequencies for the high precision THD testing tracks?
The Denon uses (small excerpts- not complete) 1001/3149/6301/9999/15999Hz etc. The CBS-CD1 uses 997/4001/7993/19997Hz etc The Philips test disc 3 uses 997/10007/16001Hz etc. My Sony test discs use even figures (1KHz,10KHz etc)
I've seen and read various explanations about hitting absolute 16 bit values or correlation with the sampling frequency but the only one that lines up with that is the Denon disc (1982) and it would have been a 44,056 sample rate on a Umatic based source (via a PCM-xxxx adapter at the time I assume), which makes no sense as the frequencies are spot on at 44,100.
Way back in 1984, Louis Challis compared the Sony YEDs with the Denon 99 track test disc and found a big difference in the 5th harmonic. Were/are digitally generated sines synthesized from lookup tables? Is the difference in 5th to do with the chosen frequency or a flaw in the generated sine itself?
(The Sony is a misprint, the frequency is 1000Hz)
View attachment 48940
I tried 997,8,9 1000 and 1001,2,3 generated sines on loopback (ARTA) and could repeatedly get better (very tiny amount) residual THD than the 1KHz. That was with either 24/44.1 or 24/48. I couldn't do 16/44.
Anyway, I'll be perfectly honest, I'm confused about it all and have been for years.
And the Denon disc gives lower THD than the CBS CD-1 test disc (which was the test standard for years at all the audio magazines) on many of its high precision tracks too. Not only that, the Denon is balls accurate (benchtop freq counter) on all the spot frequencies, whereas the CD-1 isn't.
Why you choose truncation and not rounding? May I ask you to repeat your example with rounding?For example, here is a 1kHz sine wave at -40dBr, truncated to 16-bits: (rescaled so that the 1kHz sine wave is at 0dBr in the plots.)
The question is whether the human auditory system can perform that statistical analysis for the detection.Yes, one could do wider band noise, but I'm pretty sure that the statistical approach to detection will require endless explanations.
Then probably rounding operation, routinely used everywhere, is not the most correct and we should use some more sophisticated method for that?It does work universally. My first exposure to dithering was in the 1970s in capturing photoacoustic interferograms, decidedly nonperiodic.
Then probably rounding operation, routinely used everywhere, is not the most correct and we should use some more sophisticated method for that?
Why you choose truncation and not rounding? May I ask you to repeat your example with rounding?
Please, try your demonstration with "round" not "floor".floor function is used, i.e. toward negative.