Multi-channel spatialization system for audio signals

Synthetic head related transfer functions (HRTFs) for imposing reprogrammable spatial cues to a plurality of audio input signals included, for example, in multiple narrow-band audio communications signals received simultaneously are generated and stored in interchangeable programmable read only memories (PROMs) which store both head related transfer function impulse response data and source positional information for a plurality of desired virtual source locations. The analog inputs of the audio signals are filtered and converted to digital signals from which synthetic head related transfer functions are generated in the form of linear phase finite impulse response filters. The outputs of the impulse response filters are subsequently reconverted to analog signals, filtered, mixed and fed to a pair of headphones.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates generally to the field of three dimensional audio 
technology and more particularly to the use of head related transfer 
functions (HRTF) for separating and imposing spatial cues to a plurality 
of audio signals in order to generate local virtual sources thereof such 
that each incoming signal is heard at a different location about the head 
of a listener. 
2. Description of the Prior Art 
Three dimensional or simply 3-D audio technology is a generic term 
associated with a number of new systems that have recently made the 
transition from the laboratory to the commercial audio world. Many of the 
terms have been used both commercially and technically to describe this 
technique, such as, dummy head synthesis, spatial sound processing, etc. 
All these techniques are related in their desired result of providing a 
psychoacoustically enhanced auditory display. 
Much in the same way that stereophonic and quadraphonic signal processing 
devices have been introduced in the past as improvements over their 
immediate predecessors, 3-D audio technology can be considered as the most 
recent innovation for both mixing consoles and reverberation devices. 
Three dimensional audio technology utilizes the concept of digital 
filtering based on head related transfer functions (HRTF). The role of the 
HRTF was first summarized by Jens Blauert in "Spatial Hearing: the 
psychophysics of human sound localization" MIT Press, Cambridge, 1983. 
This publication noted that the pinnae of the human ears are shaped to 
provide a transfer function for received audio signals and thus have a 
characteristic frequency and phase response for a given angle of incidence 
of a source to a listener. This characteristic response is convolved with 
sound that enters the ear and contributes substantially to our ability to 
listen spatially. 
Accordingly, this spectral modification imposed by an HRTF on an incoming 
sound has been established as an important cue for auditoryspatial 
perception, along with interaural level and amplitude differences. The 
HRTF imposes a unique frequency response for a given sound source position 
outside of the head, which can be measured by recording the impulse 
response in or at the entrance of the ear canal and then examining its 
frequency response via Fourier analysis. This binaural impulse response 
can be digitally implemented in a 3-D audio system by convolving the input 
signal in the time domain with the impulse response of two HRTFs, one for 
each ear, using two finite impulse response filters. This concept was 
taught, for example, in 1990 by D. R. Begault et al in "Technical Aspects 
of a Demonstration Tape for Three-Dimensional Sound Displays" (TM 102826), 
NASA--Ames Research Center and also in U.S. Pat. No. 5,173,944, "Head 
Related Transfer Function Pseudo-Stereophony", D. R. Begault, Dec. 22, 
1992. 
The primary application of 3-D sound, however, has been made towards the 
field of entertainment and not towards improving audio communications 
systems involving intelligibility of multiple streams of speech in a noisy 
environment. Thus the focus of recent research and development for 3-D 
audio technology has centered on either commercial music recording, 
playback and playback enhancement techniques or on utilizing the 
technology in advanced human-machine interfaces such as computer work 
stations, aeronautics and virtual reality systems. The following cited 
literature is typically illustrative of such developments: D. Griesinger, 
(1989), "Equalization and Spatial Equalization of Dummy Head Recordings or 
Loudspeaker Reproduction", Journal of Audio Engineering Society, 37 (1-2), 
20-29; L. F. Ludwig et al (1990), "Extending the Notion of a Window System 
To Audio", Computer, 23 (8), 66-72; D. R. Begault et al (1990), 
"Techniques and Application For Binaural Sound Manipulation in 
Human-Machine Interfaces" (TM102279), NASA-Ames Research Center; and E. M. 
Wenzel et al (1990), "A System for Three-Dimensional Acoustic 
Visualization in a Virtual Environment Work Station", Visualization '90, 
IEEE Computer Society Press, San Francisco, Calif. (pp. 329-337). 
The following patented art is also directed to 3-D audio technology and is 
worthy of note: U.S. Pat. No. 4,817,149, "Three Dimensional Auditory 
Display Apparatus And Method Utilizing Enhanced Bionic Emulation Of Human 
Binaural Sound Localization", Peter H. Meyers, Mar. 28, 1989; U.S. Pat. 
No. 4,856,064, "Sound Field Control Apparatus", M. Iwamatsu, Aug. 8, 1989; 
and U.S. Pat. No. 4,774,515, "Attitude Indicator", B. Gehring, Sep. 27, 
1988. The systems disclosed in these references simulate virtual source 
positions for audio inputs either with speakers, e.g. U.S. Pat. No. 
4,856,064 or with headphones connected to magnetic tracking devices, e.g. 
U.S. Pat. No. 4,774,515 such that the virtual position of the auditory 
source is independent of head movement. 
SUMMARY 
Accordingly, it is an object of the invention to provide a method and 
apparatus for producing three dimensional audio signals. 
And it is another object of the invention is to provide a method and 
apparatus for deriving synthetic head related transfer functions for 
imposing spatial cues to a plurality of audio inputs in order to generate 
virtual sources thereof. 
It is a further object of the invention to provide a method and apparatus 
for producing three dimensional audio signals which appear to come from 
separate and discrete positions from about the head of a listener. 
It is still yet another object to separate multiple audio signal streams 
into discrete selectively changeable external spatial locations about the 
head of a listener. 
And still yet a further object of the invention is to reprogrammably 
distribute simultaneous incoming audio signals at different locations 
about the head of a listener wearing headphones. 
The foregoing and other objects are achieved by generating synthetic head 
related transfer functions (HRTFs) for imposing reprogrammable spatial 
cues to a plurality of audio input signals received simultaneously by the 
use of interchangeable programmable read only memories (PROMs) which store 
both head related transfer function impulse response data and source 
positional information for a plurality of desired virtual source 
locations. The analog inputs of the audio signals are filtered and 
converted to digital signals from which synthetic head related transfer 
functions are generated in the form of linear phase finite impulse 
response filters. The outputs of the impulse response filters are 
subsequently reconverted to analog signals, filtered, mixed and fed to a 
pair of headphones. Another aspect of the invention is employing a 
simplified method for generating the synthetic HRTFs so as to minimize the 
quantity of data necessary for HRTF generation.

DETAILED DESCRIPTION OF THE INVENTION 
Referring now to the drawings and more particularly to FIG. 1, shown 
thereat is an electronic block diagram generally illustrative of the 
preferred embodiment of the invention. As shown, reference numerals 
10.sub.1, 10.sub.2, 10.sub.3 and 10.sub.4 represent discrete simultaneous 
analog audio outputs of a unitary device or a plurality of separate 
devices capable of receiving four separate audio signals, for example, 
four different radio communications channel frequencies f.sub.1, f.sub.2, 
f.sub.3 and f.sub.4. Such apparatus is well known and includes, for 
example, the operational intercom system (OIS) used for space shuttle 
launch communications at the NASA Kennedy Space Center. Although radio 
speech communications is illustrated herein for purposes of illustration, 
it should be noted that this invention is not meant to be limited thereto, 
but is applicable to other types of electrical communications systems as 
well, typical examples being wire and optical communications systems. 
Each of the individual analog audio inputs is fed to respective lowpass 
filters 12.sub.1, 12.sub.2, 12.sub.3, and 12.sub.4 whose outputs are fed 
to individual analog to digital (A/D) converters 14.sub.1, 14.sub.2, 
14.sub.3, and 14.sub.4. Such apparatus is also well known to those skilled 
in the art. 
Conventionally, the cutoff frequency f.sub.c of the lowpass filters is set 
so that the stopband frequency is at one half or slightly below one half 
the sampling rate, the Nyquist rate f.sub.c N of the analog to digital 
converters 14.sub.1 . . . 14.sub.4. Typically, the filter is designed so 
that the passband is as close to f.sub.c N as possible. In the present 
invention, however, another stopband frequency f.sub.c J is utilized and 
is shown in FIGS. 5A and 5B. F.sub.c J is specifically chosen to be much 
lower than f.sub.c N. Further, f.sub.c J is set to the maximum usable 
frequency for speech communication and is therefore set at 10 kHz, 
although it can be set as low as 4 kHz depending upon the maximum 
frequency obtainable from audio signal devices 10.sub.1, 10.sub.2, 
10.sub.3 and 10.sub.4. 
In FIG. 1, the lowpass filters 12.sub.1, 12.sub.2, 12.sub.3 and 12.sub.4 
have a passband up to f.sub.c J and include a stopband attenuation of at 
least 60 dB at 16 kHz. It should be noted, however, that the closer the 
f.sub.c J is to 16 kHz, the more expensive the filter implementation 
becomes and thus cost considerations may influence the design 
considerations. In no case, however, is f.sub.c J chosen to be below 3.5 
kHz. 
Reference numerals 16.sub.1, 16.sub.2, 16.sub.3 and 16.sub.4 denote four 
discrete digital filters for generating pairs of synthetic head related 
transfer functions (HRTF), for the left and right ear from the respective 
outputs of the A/D converter 14.sub.1 . . . 14.sub.4. The details of one 
of the filters, 16.sub.1, is shown in FIG. 2 and will be referred to 
subsequently. Each filtering operation implemented by the four filters 
16.sub.1 . . . 16.sub.4 is designed to impart differing spatial auditory 
cues to each radio communication channel output, four of which are shown 
in FIG. 1. As shown, the cues are related to head related transfer 
functions measured at 0.degree. elevation and at 60.degree. left, 
150.degree. left, 150.degree. right and 60.degree. right for the audio 
signals received, for example, on radio carrier frequencies f.sub.1, 
f.sub.2, f.sub.3, and f.sub.4. 
Outputted from each of the digital filters 16.sub.1 . . . 16.sub.4 are two 
synthetic digital outputs HRTF.sub.L and HRTF.sub.R for left and right 
ears, respectively, which are fed to two channel digital to analog 
converters 20.sub.1, 20.sub.2, 20.sub.3 and 20.sub.4. The outputs of each 
of the D/A converters is then coupled to respective low-pass smoothing 
filters 22.sub.1, 22.sub.2, 22.sub.3, 22.sub.4. The cut-off frequencies of 
the smoothing filters 22.sub.1 . . . 22.sub.4 can be set to either f.sub.c 
J or f.sub.c N, depending upon the type of devices which are selected for 
use. 
The pair of outputs from each of the filters 22.sub.1 . . . 22.sub.4 are 
next fed to left and right channel summing networks 24.sub.1 and 24.sub.2 
which typically consist of a well known circuit including electrical 
attenuations and summing points, not shown. The left and right channel 
outputs of the filters 22.sub.1 . . . 22.sub.4 are summed and scaled to 
provide a sound signal level below that which provides distortion. 
The summed left and right channel outputs from the networks 24.sub.1 and 
24.sub.2 are next fed to a stereo headphone amplifier 26, the output of 
which is coupled to a pair of headphones 18. The user or listener 28 
listening over the stereo headphones 18 connected to the amplifier 26 is 
caused to have a separate percept of the audio signals received, for 
example, but not limited to, by the four radio channels, as shown in FIG. 
1, so that they seem to be coming from different spatial locations about 
the head, namely at or near left 60.degree., left 150.degree., right 
150.degree. and right 60.degree. and at 0.degree. elevation. Referring now 
to FIG. 2, shown thereat are the details of one of the digital filters, 
i.e. filter 16.sub.1 shown in FIG. 1. This circuit element is used to 
generate a virtual sound source at 60.degree. left as shown in FIGS. 3A 
and 3B. The digital filter 16.sub.1 thus receives the single digital input 
from the A/D converter 14.sub.1 where it is split into two channels, left 
and right, where individual left and right ear synthetic HRTFs are 
generated and coupled to the digital to analog converter 20.sub.1. Each 
synthetic HRTF, moreover, is comprised of two parts, a time delay and an 
impulse response that give rise to a particular spatial location percept. 
Each HRTF has a unique configuration such that a different spatial image 
for each channel frequency f.sub.1 . . . f.sub.4 results at a 
predetermined different position relative to the listener 28 when wearing 
the pair of headphones as shown in FIG. 1. 
It is important to note that both interaural time delay and interaural 
magnitude of the audio signals function as primary perceptual cues to the 
location of sounds in space, when convolved, for example, with monaural 
speech or audio signal sound sources. Accordingly, the digital filter 
16.sub.1 as well as the other digital filters 16.sub.2, 16.sub.3 and 
16.sub.4 are comprised of digital signal processing chips, e.g. Motorola 
type 56001 DSPs that access interchangeable PROMs, such as type 27C64-150 
EPROMs manufactured by National Semiconductor Corp. The PROMs are 
programmed with two types of information: (a) time delay difference 
information regarding the difference in time delays TD.sub.L and TD.sub.R 
for sound to reach the left and right ears for a desired spatial position 
as depicted by reference numerals 30.sub.1 and 30.sub.2, and (b) sets of 
filter coefficients used to implement finite impulse response (FIR) 
filtering, as depicted by reference numerals 32.sub.1 and 32.sub.2, over a 
predetermined audio frequency range to provide suitable frequency 
magnitude shaping for left and right channel synthetic HRTF outputs. 
The time delays for each channel TD.sub.L and TD.sub.R to the left ear and 
right ear, respectively, are based on the sinewave path lengths from the 
simulated sound source at left 60.degree. to the left and right ears as 
shown in FIGS. 3A and 3B. A working value for the speed of sound in normal 
air is 345 meters per second, which can be used to calculate the effect of 
a spherical modeled head on interaural time differences. The values for 
TD.sub.L and TD.sub.R are in themselves less relevant than the path length 
difference between the two values. Rather than using path lengths to a 
spherically modeled head as a model, it is also possible to use the 
calculated mean group delay difference between each channel of a measured 
binaural head related transfer function. The latter is employed in the 
subject invention, although either technique, i.e. modeling based on a 
spherical head or derivation from actual measurements, is adequate for 
implementing a suitable time delay for each virtual sound position. The 
mean group delay is calculated within the primary region of energy for 
speech frequencies such as shown in FIG. 4 in the region 100 Hz-6 kHz for 
azimuths ranging between 0.degree. and 90.degree.. The "mirror image" can 
be used for rearward azimuths, for example, the value for 30.degree. 
azimuth can be used for 150.degree. azimuth. The resulting delay actually 
used is the "far ear" channel while a value of zero is used in the "near 
ear" channel. 
Accordingly, when TD.sub.L &lt;TD.sub.R, as it is for a 60.degree. left 
virtual source S as shown in FIGS. 3A and 3B, a value for the mean time 
delay difference in block 30.sub.1 for the left ear is set at zero, while 
for the right ear, the mean time delay difference for a delay equivalent 
to the difference between TD.sub.R and TD.sub.L, is set in block 30.sub.2 
according to values shown in FIG. 4. 
For the other filters 16.sub.2, 16.sub.3 and 16.sub.4 which are used to 
generate percepts of 150.degree. left, 150.degree. right, and 60.degree. 
right, the same procedure is followed. 
With respect to finite impulse response filters 32.sub.1 and 32.sub.2 for 
the 60.degree. left spatial position, each filter is implemented from a 
set of coefficients obtained from synthetically generated magnitude 
response curves derived from previously developed HRTF curves made from 
actual measurements taken for the same location. A typical example 
involves the filter 16.sub.1 shown in FIG. 2, for a virtual source 
position of 60.degree. left. This involves selecting a predetermined 
number of points, typically 65, to represent the frequency magnitude 
response between 0 and 16 kHz of curve 36.sub.1 and 36.sub.2, with curves 
34.sub.1 and 34.sub.2 as shown in FIGS. 5A and 5B. 
The same method is used to derive the synthetic HRTF measurements of the 
other filter 16.sub.2, 16.sub.3 and 16.sub.4 in FIG. 1. To obtain the 
60.degree. right spatial position required for digital filters 16.sub.4, 
for example, the left and right magnitude responses for 60.degree. left as 
shown in FIGS. 5A and 5B are merely interchanged. To obtain the 
150.degree. right position for filter 16.sub.3, the left and right 
magnitude responses for 150.degree. left are interchanged. It should also 
be noted that the measured HRTF response curves 36.sub.1 and 36.sub.2 are 
utilized for illustrative purposes only inasmuch as any measured HRTF can 
be used, when desired. 
The upper limit of the number of coefficients selected for creating a 
synthetic HRTF is arbitrary; however, the number actually used is 
dependent upon the upper boundary of the selected DSP's capacity to 
perform all of the functions necessary in real time. In the subject 
invention, the number of coefficients selected is dictated by the 
selection of an interchangeable PROM accessed by a Motorola 56001 DSP 
operating with a clock frequency of 27 mHz. It should be noted that each 
of the other digital filters 16.sub.2, 16.sub.3 and 16.sub.4 also include 
the same DSP-removable PROM chip combinations respectively programmed with 
individual interaural time delay and magnitude response data in the form 
of coefficients for the left and right ears, depending upon the spatial 
position or percept desired, which in this case is 150.degree. left, 
150.degree. right and 60.degree. right as shown in FIG. 1. Other positions 
other than left and right 60.degree. and 150.degree. azimuth, 0.degree. 
elevation may be desirable. These can be determined through psychoacoustic 
evaluations for optimizing speech intelligibility, such as taught in D. R. 
Begault (1993), "Call sign intelligibility improvement using a spatial 
auditory display" (Technical Memorandum No. 104014), NASA Ames Research 
Center. 
Too few coefficients, e.g. less than 50, result in providing linear phase 
FIR filters which are unacceptably divergent from originally measured head 
related transfer functions shown, for example, by the curves 36.sub.1 and 
36.sub.2 in FIGS. 5A and 5B. It is only necessary that the synthetic 
magnitude response curves 34.sub.1 and 34.sub.2 closely match those of the 
corresponding measured head related transfer functions up to 16 kHz, which 
is to be noted includes within the usable frequency range between 0 Hz and 
f.sub.c J (10 kHz). With each digital filter 16.sub.1, 16.sub.2, 16.sub.3 
and 16.sub.4 being comprised of removable PROMs selectively programmed to 
store both time delay difference data and finite impulse response filter 
data, this permits changing of the spatial position for each audio signal 
by unplugging a particular interchangeable PROM and replacing it with 
another PROM suitably programmed. This has the advantage over known prior 
art systems where filtering coefficients and/or delays are obtained from a 
host computer which is an impractical consideration for many applications, 
e.g. multiple channel radio communications having different carrier 
frequencies f.sub.1 . . . f.sub.n. Considering now the method for deriving 
a synthetic HRTF in accordance with this invention, for example, the curve 
34.sub.1, from an arbitrary measured HRTF curve 36.sub. 1, it comprises 
several steps. First of all, it is necessary to derive the synthetic HRTF 
so that the number of coefficients is reduced to fit the real time 
capacity of the DSP chip-PROM combination selected for digital filtering. 
In addition, the synthetic filter must have a linear phase in order to 
allow a predictable and constant time shift vs. frequency. 
The following procedure demonstrates a preferred method for deriving a 
synthetic HRTF. First, the measured HRTFs for each ear and each position 
are first stored within a computer as separate files. Next, a 1024 point 
Fast Fourier Transform is performed on each file, resulting in an analysis 
of the magnitude of the HRTFs. 
Following this, a weighting value is supplied for each frequency and 
magnitude derived from the Fast Fourier Transform. The attached Appendix, 
which forms a part of this specification, provides a typical example of 
the weights and magnitudes for 65 discrete frequencies. The general scheme 
is to distribute three weight values across the analyzed frequency range, 
namely a maximum value of 1000 for frequencies greater than 0 and up to 
2250 Hz, an intermediate value of approximately one fifth the maximum 
value or 200 for frequencies between 2250 and 16,000 Hz, and a minimum 
value of 1 for frequencies above 16,000 Hz. It will be obvious to one 
skilled in the art of digital signal processing that the intermediate 
value weights could be limited to as low as f.sub.c J and that other 
variable weighting schemes could be utilized to achieve the same purpose 
of placing the maximal deviation in an area above f.sub.c J. 
Finally, the values of the table shown, for example, in the Appendix are 
supplied to a well known Parks-McClelland FIR linear phase filter design 
algorithm. Such an algorithm is disclosed in J. H. McClellend et al (1979) 
"FIR Linear Phase Filter Design Program", Programs For Digital Signal 
Processing, (pp.5.1-1-5.1-13), New York: IEEE Press and is readily 
available in several filter design software packages and permits a setting 
for the number of coefficients used to design a filter having a linear 
phase response. A Remez exchange program included therein is also utilized 
to further modify the algorithm such that the supplied weights in the 
weight column determine the distribution across frequency of the filter 
error ripple. 
The filter design algorithm meets the specification of the columns 
identified as FREQ, and MAG(dB) most accurately where the weights are the 
highest. The scheme of the weights given in the weighting step noted above 
reflects a technique whereby the resulting error is placed above f.sub.c, 
the highest usable frequency of the input, more specifically, the error is 
placed above the "hard limit" of 16 kHz. The region between f.sub.c J and 
15.5 kHz permits a practical lowpass filter implementation, i.e. an 
adequate frequency range between the pass band and stop band for the roll 
offs of the filters 16.sub.1 . . . 16.sub.4 shown in FIG. 1. 
Synthetic filters have been designed using the above outlined method and 
have been compared in a psychoacoustic investigation of multiple subjects 
who localize speech filtered using such filters and with measured HRTF 
filters. The results indicated that localization judgments obtained for 
measured and synthetic HRTFs were found to be substantially identical and 
reversing channels to obtain, for instance, 60.degree. right and 
60.degree. left as described above made no substantial perceptual 
difference. This has been documented by D. R. Begault in "Perceptual 
similarity of measured and synthetic HRTF filtered speech stimuli, Journal 
of the Acoustical Society of America, (1992), 92(4), 2334. 
The interchangeability of virtual source positional information through the 
use of interchangeable programmable read only memories (PROMs) obviates 
the need for a host computer which is normally required in a 3-D 
auditory display including a random access memory (RAM) which is 
down-loaded from a disk memory. 
Accordingly, thus what has been shown and described is a system of digital 
filters implemented using selectively interchangeable PROM-DSP chip 
combinations which generate synthetic head related transfer functions that 
impose natural cues to spatial hearing on the incoming signals, with a 
different set of cues being generated for each incoming signal such that 
each incoming stream is heard at a different location around the head of a 
user and more particularly one wearing headphones. 
Having thus shown and described what is at present considered to be the 
preferred embodiment and method of the subject invention, it should be 
noted that the same has been made by way of illustration and not 
limitation. Accordingly, all modifications, alterations and changes coming 
within the spirit and scope of the invention as set forth in the appended 
claims are herein meant to be included. 
______________________________________ 
APPENDIX 
SYNTHETIC HRTF MAG. RESPONSE 
FREQ. MAG (dB) WEIGHT 
______________________________________ 
1 0 28 1000 
2 250 28 1000 
3 500 28 1000 
4 750 28.3201742 1000 
5 1000 30.7059774 1000 
6 1250 32.7251318 1000 
7 1500 33.7176713 1000 
8 1750 34.9074494 1000 
9 2000 34.8472803 1000 
10 2250 42.8024473 200 
11 2500 45.6278461 200 
12 2750 42.0153019 200 
13 3000 43.1754388 200 
14 3250 44.1976273 200 
15 3500 42.2178506 200 
16 3750 39.4497855 200 
17 4000 33.7393717 200 
18 4250 33.7370408 200 
19 4500 33.3943621 200 
20 4750 33.5929666 200 
21 5000 30.5321917 200 
22 5250 31.8595491 200 
23 5500 30.2365342 200 
24 5750 26.4510162 200 
25 6000 23.6724967 200 
26 6250 25.7711753 200 
27 6500 26.7506029 200 
28 6750 26.7214031 200 
29 7000 25.7476349 200 
30 7250 25.8149831 200 
31 7500 27.7421324 200 
32 7750 28.3414934 200 
33 8000 27.4999637 200 
34 8250 26.0463004 200 
35 8500 20.0270081 200 
36 8750 17.917685 200 
37 9000 -3.8442713 200 
38 9250 10.077903 200 
39 9500 16.4291175 200 
40 9750 16.478697 200 
41 10000 15.5998639 200 
42 10250 13.7440975 200 
43 10500 10.9263854 200 
44 10750 9.65579861 200 
45 11000 6.94840601 200 
46 11250 6.51277426 200 
47 11500 5.00407516 200 
48 11750 6.98594207 200 
49 12000 8.66779983 200 
50 12250 8.51948656 200 
51 12500 6.05561633 200 
52 12750 3.43263396 200 
53 13000 2.03239314 200 
54 13250 0.67809805 200 
55 13500 -1.0820475 200 
56 13750 -2.7066935 200 
57 14000 -4.3344864 200 
58 14250 -3.8335688 200 
59 14500 -0.4265746 200 
60 14750 4.19244063 200 
61 15000 7.23285772 200 
62 15250 10.9713699 200 
63 15500 13.8831976 200 
64 15750 16.8619008 200 
65 16000 18.9512811 200 
66 17000 0 1 
67 20000 0 1 
68 25000 0 1 
______________________________________