I am asking specifically about discrete sound signal, non dithered 16 bit 48000 Hz pcm/wav format.
My question is, how fast can you change sinewave frequency before it distort? Imagine a frequency sweep,it starts at 3000 Hz and ends at 6000 Hz, 3000 Hz full cycle sinewave at 48k sampling frequency is 16 samples long, 6000 Hz is half that, so 8 samples long...
If we do the sweep from 3k to 6K long duration,lets say one second,it will cleanly sweep from one point to another,but what is the precise limit,the threshold of how fast/short we can do this sweep before it becomes distorted?
Obviously we know its at least as long as single cycle of the lowest frequency we want to sweep,so its 16 minimum becose remember 16 samples is minimum lenght of single 3000hz cycle,but is it precisely 16 or is it longer? maybe one full cycle of starting frequency sample length(16) + same for final highest frequency(6000hz = 8) so 16 + 8?
I believe its also called "sweep rate",and sinewave frequency sweep is called "chirp",I want to know precisely the mathematics behind this to figure out where exactly this threshold is.
Also does this change depending on loudness/amplitude level? if we do the 3000 Hz to 6000 Hz sweep -6 db instead of maximum amplitude,would it make difference? considering signed 16 bit is 32768 amplitude levels,-6 db would be 16384.
I want some kind o mathematical formula that would precisely tell me exactly how many samples do I need to make shortest sweep possible at specific loudness and frequency points.So for example 3000 -> 6000 full amplitude sweep? atleast XXX samples needed! 375hz to 12000hz -12db? that be XXXXX samples minimum,you get the idea...
remember,we are talking about sweeping sinewave,not waveforms like squarewave that contain harmonics
edit Definition of distortion,when the sinewave stops being sinewave,its simple as that.For example,if you module amplitude of sinewave slowly and only one way (up or down ) then it will always be just pure clean non-distorted sinewave,but if you start changing its amplitude too fast,so its going up and then changes direction downwards per single cycle of that sine,harmonic distortion will grow from that sine,so you will have multiple tones at same time for example 1000hz sine will get 2000hz,3000hz,4000hz... overtones/partials/harmonics all from amplitude changes
same things happens with freqency change instead of amplitude change,you do it too fast,and new sinewaves(hamonics) will appear at same moment on top of the original moduleted sine.