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Inside this VI, the complex frequency coefficient for the given frequency is extracted from the array for each microphone channel. These six values are then concantonated into a lengh six array. Next, the array is zeropadded to a user specified length (we used 256 in our simulation) so more resolution can be observed in the resulting spatial transform. Finally, the FFT is performed on these values transforming them into the spatial domain. With the data in the spatial domain we are easily able to figure out the magnitude of any frequency from any direction in our 180 degrees of interest. How to do this can be found in the magnitude VI.
Because this formula is dependent on the frequnecy of interest, we are required to run this VI for every frequency we are intereseted in. In order to do this, we put this VI inside a for loop that is controlled by our frequency range. Any coefficient for frequencies outside of this range are simply given a value of zero. The array modules ouside of this for loop are used to do just that. They append arrays with value zero on the front and back of the output of the for loop to return our vector to its original size. From here, we run this vector through a few multiplies to amplify the differnce between the coefficients with high and low magnitudes, and finally we inverse FFT it to get our output array. This array represents a signal in the time domain and is graphed on the front panel along with a graph of its frequency components. We also included a small VI that will play the output waveform on computer speakers. This VI uses a matlab script and requires the user to have matlab 6.5 or earlier.
Magnitude graph of coefficients after spatial fft
Magniutde calculation vi
The resulting vector of the previous six point FFT is immediately used as the input to the Magnitude Calculation VI. The vecor of spatial coefficients from the"six pt FFT"vis are complex, so this VI is used to calculate the magnitudes of the coefficients so the maximum coefficient can be found. The output of this VI is also used to create a visual representation of what direction the specified frequency is coming from. Below is a graph of the magnitude of the coefficients of the spatial FFT. As discussed before, we see the peak correspoinding to the incoming direction and the smaller ripples to each side.
Magnitude graph of coefficients after spatial fft
As we can see in the previous figure, the magnitude of the spatial FFT is greatest around coefficient 82. There are also smaller ripples that die off around each end. This graph tells us that the the direction that the given frequency is coming from corresponds to the angle represneted by coefficient 82. To figure out what angle this was, we would use our Coefficient to Angle VI.
Overall, the code involved in this method of array signal processing can be broken up into smaller parts that are easy to understand. By combining these smaller parts we are able to create an upper level VI that performs a complicated task that would be difficult to get working using other methods. The major problem with this VI is that it requires a large number of calculations. To increase performance (without upgrading computers) one could decrease the frequency range of interest, or they could lower the amount of zeropadding. They could aslo look at a smaller time period.
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