sumi, noise generation tool

This tool generates a time series of a noisy process. In particular, it may be used for generating flicker (1/f) noise. Random numbers with power-law spectrum are generated using the Timmer-Koenig algorithm.

J. Timmer, M. Koenig, "On generating power law noise", Astronomy and astrophysics (1995).

Command line options

Syntax: sumi [arguments]

-n 1: white noise [default]
-n 2: pink noise (flicker, 1/f)
-s SIGMA: standard deviation [default is 1.0]
-t: use a fixed seed value for the random number generator (to generate reproducible sequences)
-c: number of generated elements in the time series [default is 0 which stands for infinite length]
-b BS: sets the block size for performing Fourier transforms
-f 0: conversion of floating point to integer: round-off
-f 1: floor
-f 2: ceiling
-f 3: truncation
-ot -1: output: floating-point in ASCII
-ot 0: integer in ASCII
-ot 1: lowest-significant bit (lsb) in ASCII
-ot 8: binary packed with consecutive bits, 8-bit words
-ot 16: binary packed with consecutive bits, 16-bit words
-ot 32: binary packed with consecutive bits, 32-bit words
-ot 64: binary packed with consecutive bits, 64-bit words
-od 1: LSB to MSB bit order within words (default)
-od 2: MSB to LSB bit order within words
-ow: endianness conversion (e.g. little-endian to big-endian) for byte order in words
-v: increase verbosity (directed to stderr)

Note on floating-point to integer conversion

See (https://cplusplus.com/reference/cmath/trunc/) for details on rounding of floating point numbers.

Note the following:

value	round	floor	ceil	trunc
-----	-----	-----	----	-----
2.1 	2.0 	2.0 	3.0 	2.0
1.1 	1.0 	1.0 	2.0 	1.0
0.1 	0.0 	0.0 	1.0 	0.0
-0.9 	-1.0 	-1.0 	-0.0 	-0.0
-1.9 	-2.0 	-2.0 	-1.0 	-1.0

Truncation does not maintain the even/odd sequence across the zero point.

bitdump

bitdump is a tool for dumping time series of bit. It can also perform various bit-order (LSB to MSB vs. MSB to LSB), wordsize (between 8, 16, 32 and 64 bits) and byte-order (endianness) conversions.

bitent

bitent is a tool for calculating Shannon and minimal entropy for a bit series.

Sample outout:

nr=200000000000=10^11.3=2^37.54
P[000 ~    0]=0.12514958368         25029916736
P[001 ~    1]=0.12499761538         24999523076
P[010 ~    2]=0.124855502795        24971100559
P[011 ~    3]=0.124996685525        24999337105
P[100 ~    4]=0.124997615445        24999523089
P[101 ~    5]=0.1248545729          24970914580
P[110 ~    6]=0.124996685555        24999337111
P[111 ~    7]=0.12515173872         25030347744
mean=3.500004288195
var=5.2530018257816
stddev=2.2919428059578
Pmin=0.1248545729
Pmax=0.12515173872 Hmin=2.9982497605108
H=2.9999994952889 = 0.99999983176297 per bit
Hmin=2.9982497605108 = 0.99941658683692 per bit

Requirements

C++20 compiler (all testing done with GCC 11.3.0)
FFTW3 library

Contact information:

These codes were created in the scope of a Target research programme (Ciljni raziskovalni programi, CRP) V1-2119 "Cryptographically secure random number generator", funded by UVTP and ARIS, Slovenia.

Project home page

   Rok Zitko
   "Jozef Stefan" Institute
   F1 - Theoretical physics
   Jamova 39
   SI-1000 Ljubljana
   Slovenia

   rok.zitko@ijs.si