The equation to the left is a derivation of the normal
distribution function. My routine uses this to set the amplitude curve.
The free variable d controls the width of the curve.
From: Dan Kennedy
Date: 10/22/00
Time: 6:30:36 PM
I have made a routine that generates a test signal of specific parameters. It adds the signal to an existing WAV file.
The start frequency, frequency drift, peak amplitude and Gaussian half-power interval can be specified.
Gaussian Curve
The signal varies in amplitude on a normal curve centered in the WAV interval.
The equation to the left is a derivation of the normal
distribution function. My routine uses this to set the amplitude curve.
The free variable d controls the width of the curve.
Frequency Drift
It took me a while to figure out how to vary the frequency linearly. It turns out to be the same equation as accelerated motion.
s' = so + v t + ½ a t2
cycles = f t + ½ d t2
Where f is start frequency and d is the Doppler drift rate and t is the sample number divided by the sample rate.
Cycles can be converted to phase by multiplying by 2 p
phase = 2 p cycles
This same process can be used in reverse to dechirp a file without introducing the non-linear curves that my TDdechirp.exe file produces by successive approximation errors.
Peak Value
The sin value ranges ± 1 and the normal curve factor ranges 0 to 1. Another value is needed to set the peak signal amplitude. The data can range ± 128. The test below uses a peak amplitude of 3, or about 2.3%
The amplitude of the test signal is then sin(phase) multiplied by the gaussian equation above multiplied by the peak value desired.
My routine takes each sample from a normal WAV file, calculates the signal value as above and sums it in. This then preserves the original WAV file and provides a much better test signal than my previous attempts.
This is an example injection where the signal peaks
at a binary value of ± 3 or about 2.3%
Start freq = 1300 at the beginning of the file.
This file is here (7 Mb).
Here's the BASIC code that was used to sum in the signal.
Get #wavFile, , nChunkSize
' Set the Doppler drift rate.
d = 0.1 ' drift in hertz per second
freq = 1300 ' Initial frequency
dur = 3
' Now read the data bytes,
convert from PCM to ASCII values.
For i = 1 To nChunkSize: '
Just over 16 minutes.
' Get the original value from the WAV
file.
Get #wavFile, , value
' Calculate
the time index.
t = i / 8000
' Calculate
the phase angle at this time index.
phase = 2 * 3.14159 * (freq * t + 0.5 * d * t ^ 2)
' Figure
the normal curve value at this time index.
a = i / nChunkSize * dur - dur / 2
a = -((a ^ 2) / 0.4)
a = 2.718 ^ a
' Sum
in the signal scaled by phase, peak and normal factors.
value = value + Sin(phase) * 3.0 * a
' Write
an output value.
Print #rawFile, (value - 128) / 128
Next i
My next step will be to create a command line program in C that can inject signals into a WAV file. Another step would be to re-write the TDdechirp code to use these equations. That would make the dechirp more linear and presumably increase SETIEasy sensitivity.
- Dan