Audio Test File Generator Specifications
The goal was to produce a generator of audio frequency sine wave signals of the highest possible quality that may be used as a frequency standard for testing all components in the path of the signal. A very thorough specification follows, with the aim to increase the usefulness of the signal generator for sound engineers.
The sine wave generator
In the quest to create "the perfect wave", the floating point
calculations that produce the sine wave employ 80 bits of internal precision.
Each signal generated is a perfectly symmetrical series of whole waves so as to
end up with a negligible DC component. Whatever DC remains is removed,
so that for any given frequency of 10 seconds duration or less, the DC
level is guaranteed to be 0 before dithering is applied. Dithering will
add a minuscule amount. The actual DC level before correction is
pre-calculated on a sample by sample basis, so a slight delay may be noticed
when generating signals approaching 10 seconds in duration. Since DC correction
is not applied to signals of a duration greater than 10 seconds,
no delay is entailed in this case.
The following are details of distortion and noise readings taken on 10 second files at 44100 samples per second. It should be noted that these commonly used frequencies have significantly higher THD and noise than, for example, most of the musical notes because of aliasing due to the fact that they share a common denominator with the sampling rate. For example, a sine wave of C6 (1046.502261 Hz) at 0 dB, averaged over a 10 second test file and under the same test setup, has a THD+N of only 0.00011% and a SNR of about 114 dB. Compare that to the results below for 1000 Hz. As a testament to the effectiveness of dithering, simply average that same 1046.502261 Hz (C6) signal over 120 seconds and you will find the THD+N has now dropped to 0.00008% and SNR > 122 dB. (SNRs are for a bandwidth of 22kHz)
Samples are converted at the desired attenuation from floating point to 32 bit samples
and TPDF dithering is added to the lower 16 bits of each. This combination is then
downshifted to the final 16 bit output sample size. A separate dithering signal is applied
to each channel. (See images at bottom of page.)
Each sine wave signal generated begins and ends with a smooth linear taper of exact
multiples of the period to eliminate speaker pops and clicks. (See image above).
The taper length depends on the duration of the signal requested, with the maximum
duration set to approximately 0.01 seconds. The minimum taper length is equal to the
period of the requested frequency. [Update 28/01/2010: Version 1.06 of the
Audio Test File Generator employs a raised cosine (Blackman half-windows)
for the fade up/down to minimize distortion during fades.]
Signal duration is equal to exact multiples of the period at the requested frequency,
such that they add up to at least the duration requested in seconds.
Minimum signal duration is limited to the nearest exact multiple of the period
equal to or greater than 0.01 seconds, or the time it takes to play two whole waves
at the requested frequency - whichever is greater. The maximum permitted is 120 seconds.
Minimum frequency that can be generated is 10 Hz, and the maximum is 22050 Hz.
To avoid saturation while allowing room for dithering or DC correction
(should it be required), the initial maximum signal value is limited
to a maximum amplitude of +/- 0x7FFD (32765). The final signal
has a peak amplitude of -0.047 dB.
The minimum attenuation is 0 dB.
Maximum attenuation permitted is 90 dB.
If attenuation is applied, the signal level is calculated by
dBs = 20 x log10(amplitude). Attenuation is also calculated
with the highest precision possible.
File are generated in the form of 16 bit stereo Window's RIFF PCM Wave format files.
Each begins with a lead in of 512 samples of silence and a lead out of between 0 and 512
samples of silence (depending on how much room was left in the buffer).
The sweep wave generator
The sweep generator employs a swept sine wave function and does not include DC correction. (Significant DC can accumulate in a sweep signal but attempts to remove it would result in unacceptable distortion.) It can sweep up or down. The minimum and maximum frequencies and attenuation values allowed are the same as for the sine wave generator. The minimum sweep duration is 0.1 seconds and the maximum is 120 seconds. Duration is rounded up to the nearest multiple of 128 samples. A linear taper of 128 samples is applied to the end of the signal. During taper down, the frequency is held at the ending frequency requested. The default setting sweeps through 6 octaves from C2 to C8.
The white noise generator
The latest version (1.06) of the Audio Test File Generator has a white Gaussian noise generator. The pseudo-random number generator employs the "Mother-Of-All" generator invented by George Marsaglia and provides an excellent even distribution. The code for this can be found at http://www.agner.org/random/. The overlaid Gaussian window is a codification of the Box–Muller transform in its basic form to provide a zero-centered normal distribution of the samples. The output was thoroughly tested to ensure uniform distribution with a Gaussian curve.
The pink noise generator
The pink noise generator
employs an algorithm by Andrew Simper of Vellocet, a C++ implementation derived from the
code provided by the following people mainly from the music-dsp mailing list: Allan Herriman, James McCartney, Phil Burk and Paul Kellet and the web page by Robin Whittle: http://www.firstpr.com.au/dsp/pink-noise/.
Maximum signal level is nowhere near 0 dB, since considerable head room is given to ensure there can be no clipping. Determining the signal level of noise is problematic because of its random nature. However, if you employ attenuation you can be assured of accuracy of relative signal levels over the long term.
Its "peak" frequency is below 1 Hz, a thing you can verify by averaging a 120 second file using a very large FFT size.
Warning - pink noise contains frequencies below the range of hearing that may damage your speakers at very high levels. Turn down the bass if you want to pump up the sound, or watch your speaker cones for excessive movement.
From Wikipedia: "Pink noise, also known as 1/f noise, is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency. There is equal energy in all octaves (or similar log bundles). In terms of power at a constant bandwidth, 1/f noise falls off at 3 dB per octave. At high enough frequencies 1/f noise is never dominant. (White noise is equal energy per hertz.) 1/f noise occurs in many physical, biological and economic systems. Below are images showing spectral views of the signals produced by the Audio Test Signal Generator
Pink noise falls off at 3 dB per octave...
440 Hz sine wave without dithering...
Same signal with dithering applied...