Modules

Introduction

This Repository is a compilation of Cosine-Beamforming implementation in python.

Owner

Pranjall Kumar, Jr. Data Scientist @ Siemens Gamesa (DVL)

Aim

To find the exact position of the source of sound with the help of two microphone arrays in a 2D plane.

Experimental Setup:

Calculation of angular location (θ):

Calculation of source location (p):

Assumptions

1. There are 3 omnidirectional microphones in a linear array which are d distance apart.
2. There are 2 linear microphone arrays which are Δ distance apart.
3. All microphones are at a common fixed distance away from each other.
4. The position of the source of sound is unknown in a 2D plane.
5. There is only a single source of sound.
6. The souce of sound is to left of the normal to microphone array (minor change in code will fix this).
7. The source of sound is a point source.
8. The source of sound is sufficiently far away from the microphone array.
9. The source of sound is in a fixed position with respect to all the microphones.
10. The source of sound produces some sound for a very breif amount of time (max 0.2 seconds).
11. The source of sound is stationary.
12. There is minimal noise (max 0.5 units).
13. There is no echo.
14. There is minimal distortion.
15. The sound medium is dry air at 20 ^oC.
16. Microphones are of good quality.

Formulas

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Units

Metrics	Units
Distance	meters
Sampling	samples/seconds
Time	seconds
Angle	degrees
Speed	meters/second
Temperature	Celsius

Parameter List

Parameter	Value	Descripttion
Number of microphones (n+1)	3	Represents the number of microphones in the microphone array.
Number of microphone arrays	2	Represents the number of microphone arrays being used.
Reference Pulse	NA	The first sound pulse received by any microphone.
Resultant Pulse	NA	The final amplified sound pulse.
D	Unknown	Longitudinal distance of the source of sound from the microphone array.
θj	Unknown	Angle made by the source of sound from the normal to the jth microphone array.
d	0.1 meters	Distance between each microphone.
δ	Variable	Distance of the incident wavefront from the previous/subsequent incident microphone.
Δ	0.5 meters	Distance between the microphone arrays.
delayi	Variable	Delay in time for sound wavefront to reach the ith microphone.
mij	NA	ith microphone of jth microphone array.
px	Unknown	x-coordinate of the source of sound in meters with respect to microphone 2.
py	Unknown	y-coordinate of the source of sound in meters with respect to microphone 2.
S	343 meters/second	Speed of sound in dry air at 20 oC.
delay	Variable	Time taken by the incident wavefront to reach the previous/subsequent incident microphone.
Sampling Rate	44100 samples/second	The number of samples taken from a continuous signal to make a digital signal.
Scanning Window	0.2 seconds	The duration of signal considered for finding the source.
Shift	Variable	Represents the shift of signal in time from source to the closest microphone.
Offset	Variable	Represents the shift of signal in time from microphone to microphone (depends on d and θ).
Step	1	Represents the increments of shift in time for a signal.

Caution

• Verify the right value of d.
• Verify the right value of Δ.