A320277 A digitized pure tuning tone, sampled at standard settings for consumer audio: a(n) = floor(sin(2*Pi*(440/44100)*n)*32767).

0, 2052, 4097, 6126, 8130, 10103, 12036, 13921, 15752, 17521, 19222, 20846, 22389, 23844, 25205, 26467, 27625, 28675, 29612, 30433, 31134, 31713, 32167, 32494, 32695, 32766, 32709, 32524, 32210, 31770, 31206, 30518, 29711, 28787, 27750, 26604, 25354, 24004, 22559, 21026, 19410

Offset: 0

Author

Jim Singh, Oct 08 2018

Keywords

• sign

Comments

This sequence represents sample values for the simplest sound: a pure tone with no harmonics (i.e., a sine wave) with 0 phase shift, of digital peak amplitude, pitched at the standard tuning frequency (A440), and sampled at the standard sampling rate and bit depth resolution for consumer audio: 44100 Hz and 16 bits, respectively.

Since the maximum signed integer value that can be stored in 16 bits is (2^15)-1=32767, the method used to convert the floats to integers is to multiply the floats by 32767 then cast to integer.

The numerator and the denominator of the g.f. have degrees respectively equal to 2204 and 2205. - Stefano Spezia, Nov 02 2018

References

• A. Davison, Killer Game Programming in Java, O'Reilly Media, 2005, page 254.

Links

• KVR, How to get each sample of a sine wave given sample rate, frequency, bit depth
• Wikipedia, Audio bit depth
• Wikipedia, Pulse-code modulation
• Wikipedia, Sampling

Programs

Mathematica

a[n_]:= Floor[Sin[2*Pi*(440/44100)*n]*32767]; Array[a, 50, 0] (* Stefano Spezia, Nov 02 2018 *)

Python

import math
for x in range(100):
    floatval = math.sin(2*math.pi*(440/44100)*x)*32767
    intval = int(floatval)
    print(intval, end=', ')