3. Application techniques of Microphone Array
The fundamental techniques of microphone array are used to develop an acoustics based system according to the given requirement can be listed as
- Estimation of Direction of Arrival (DOA)
- Estimation of Time Difference of Arrival (TDOA)
- Beam-forming
3.1.Estimation of Direction of Arrival (DOA)
The Direction of Arrival (DOA) that is also sometimes referred to as Angle Of Arrival (AOA) estimation problem can be stated as “detect and locate N sources by using an array of i passive microphones”. This estimation is associated with the estimating the Time Difference of Arrival (TDOA) between the two adjacent microphones.
Microphone array is steered i.e. focused, in one direction after assuming the presence of a single source at a known time instant and output of the array is measured. The DOA estimate is found by getting the maximum output of array by changing the steering angle.
As shown, in the Fig.4 P unit vector points to the sound source with the angle θ with the normal direction (y-axis) of the microphone sensor array. Therefore, we can write
3.2.Estimation of Time Difference of Arrival (TDOA)
The Time Difference Of Arrival (TDOA) or Time-Delay-Estimation (TDE) is estimated by using following mathematical methods
- Time-domain computation based Cross-correlation
- The microphones of an array that has only two microphones, are expected to record two delayed copies of the source signal, along with some disturbs (environmental noise or reverberation)
- If the strength of the input signal is higher than noise magnitude, then TDOA can be estimate by cross-correlating the individual microphone signals. The cross-correlation of the microphone signals is given by the inverse Fourier Transform of the cross-spectrum:
III. The TDOA is estimated as the time-lag that maximizes the cross-correlation function, within a valid time interval:
The resolution of cross-correlation based method depends on both the sampling frequency and the distance between microphones.
