I have a rather strange but i thin interesting question. The idea is to gain a better understanding of sampling rate vs frequency shifting when playing audio. The idea is a little experiment:
%synthetic example T=1/(10*10^6);%period should be at least 1/(2*10^6Hz) => Nyquist freq if we want to be able to reproduce 10^5Hz max freq x=0:T:1-T; f=10^6;%frequency y=sin(2*pi*f*x); %i see visually that there is 11 samples constituting 1 period %plot(y(1:11)) %plot(y(100:111)) %etc nbPeriods=length(y)/11;%nbtotalsamples/nbsamplesOf1Period %y contains 10^6 oscillations each of 11 samples %therefore if i want to reproduce a 1Khz sound, I compute my sampling frequency : % Fs = nbPeriods/10^3 Fs=909.09; a=audioplayer(y,Fs) tic; play(a) toc;
my question is: is this reasoning correct? -> that Fs should be 909.09 to get a 1kHz sine wave from f=10^6;y=sin(2*pifx); when played at Fs=909.09 and considering of course the x range i have taken?
EDIT: following your answer would this (the comments!) be correct now:
clc;clear all; %synthetic example T=1/(10*10^6);% x=0:T:1-T;%my sampling rate is 1/T= 10*10^6 =10MHz f=10^6;%frequency %y: as if i had 1 period T of a sampled signal (sampled at 10MHz) y=sin(2*pi*f*x);%this signal has a freq of 1 MHz , according to %Nyquist Shannon sampling thm the MAX freq i could capture with %my sampling rate of 10MHz would be 5 MHz, %so i am a bit below that with my 1MHz %given that i want to create a 1KHz wave from y i must sample at % (10*10^6 samples)/(10^3 samples) = 10^4 10 KHz %idea: cutting my 10M samples into chunks of 10^3 oscillations Fs=10^4; a=audioplayer(2*y,Fs/4) tic; play(a) toc;
%indeed it plays now a sound that "sounds" like a reference 1KHz wave,