At 05:30, the formula for the triangle waveform is incorrect. It should not be "square root" but "square". The correct formula is: 1/harmo-index^2
@TheSlyProfessor
10 ай бұрын
What makes these waves bandlimited? Wouldn't you still get aliasing if the fundamental of these sinesum tones approaches the nyquist limit?
@SoundCodex
4 ай бұрын
Sorry for laaaaaate reply! For a tone to be bandlimited, all of its frequency components must be within a certain range (well below the Nyquist number). These signals are called “band-limited” because the spectral content is limited (one can literally count the harmonics written within sinesum, 12 for the sawtooth wave in the video). If the fundamental (or some harmonics) approaches Nyquist, aliasing occurs. There are some techniques used to mitigate aliasing in these cases, such as anti-aliasing filtering (it will not eliminate aliasing but will reduce its effect).
@atwork22
Жыл бұрын
With a sr of 48000 can't hear any thing with a freq of 25000, according to your formula there should be a Tone 1 at 25000 and a Tone 2 at 1000?! The blue line should rather be the sr itself: If I play a 49000 Hz I hear a 1000 Hz tone.
@SoundCodex
Жыл бұрын
I think the misunderstanding is at minute 00:49 when I say that Tone2 is “the exact difference between the Nyquist number and Tone1”. That sentence is wrong and partially explained but the graphic and formula are correct. Tone1 - Nyquist = the absolute change (Δf) in Hertz of Tone2 in relation to the Nyquist number (obviously if Tone1 > SR/2). Following the video example: with SR at 44.100 Hz (Nyquist number is 22.050 Hz), Tone1 at 23.050 Hz, the absolute variation between the aliased frequency and Nyquist is 1000 Hz. The complete formula to calculate the aliased frequency (Tone 2) is: Nyquist - (f1 - Nyquist) = f2 Referring to your example with SR at 48.000 Hz and Tone1 at 25.000 Hz, Tone2 will be (24.000 - (25.000 - 24.000)) = 23.000 Hz. That’s why you can’t hear anything… 23 KHz is impossible to be perceived by human ear. And finally, if Tone1 is at 49.000 Hz the full formula gives -1000 as result. You exceeded two times + 1000 Hz the Nyquist number. The descending aliased frequency has bounced in the lower end of the spectrum (at 0 Hertz) and kept raising up to 1000 Hertz. I recommend you watch this video kzitem.info/news/bejne/1Z6tmWaPr36jjKQ where this same phenomenon is explained very clearly at minute 04:26. I hope I made myself clear. Thanks for your comment, you gave me the opportunity to point out some significant steps.
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