# Psychoacoustic Roughness

### Sometimes audio signals are rough problems to analyze. Who knew that it was a parameter of acoustic roughness? Well there is and it's called the asper.

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Acoustic roughness is measured in aspers. An asper is the roughness of a 1 kHz tone, at 60 dB, 100% modulated at 70 Hz. That is, the signal

(1 + sin(140π*t*)) sin(2000π*t*)

where *t* is time in seconds.

Here’s what that sounds like (if you play this at 60 dB, about the loudness of a typical conversation at one meter):

http://www.johndcook.com/one_asper.wav

And here’s the Python code that made the file:

```
from scipy.io.wavfile import write
from numpy import arange, pi, sin, int16
def f(t, f_c, f_m):
# t = time
# f_c = carrier frequency
# f_m = modulation frequency
return (1 + sin(2*pi*f_m*t))*sin(2*f_c*pi*t)
def to_integer(signal):
# Take samples in [-1, 1] and scale to 16-bit integers,
# values between -2^15 and 2^15 - 1.
return int16(signal*(2**15 - 1))
N = 48000 # samples per second
x = arange(3*N) # three seconds of audio
# 1 asper corresponds to a 1 kHz tone, 100% modulated at 70 Hz, at 60 dB
data = f(x/N, 1000, 70)
write("one_asper.wav", N, to_integer(data))
```

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Published at DZone with permission of John Cook. See the original article here.

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