Now that the signals have been transformed to their spatial representations, the correct coefficients to construct the signal of interest must be computed. To do this we created the Coefficient Calculator VI.. This VI takes in the angle of interest, a frequency, the number of microphones, a constant factor (determined by the setup of the microphones and the amount of zero padding...in this example it is -93), and our original sampling frequency to compute the correct coefficient to look at for the given angle. Once this coefficient is found, we extract the value at that coefficient and append it to our ouptut array as the value at that given frequency. Below is the block diagram for this VI. It consists of a basic formula node and some logic on the front and back to make sure that the calculations are correct when working with angles from negative directions.

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.

If we go back to the branch in the pink wire immediatly after the signal generation VIs and move upwards instead of to the right, we come across the code that is used to calculate the angle at which the largest magnitude signal of a given frequency is approaching the array. Another "6 pt fft" VI is used, but this one is slightly modified. It also includes the initial FFTs of all 6 channels. We grouped these two VIs together because ony one spacial FFT is being computed (that at the frequeny of interest).

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.

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.

Finally, we isolate the index of the maximum angle and use it to compute the angle of incidence. Using the same formula used in the Coefficient Angle Calculator, the Coefficient to Angle VI deduces the angle of incidence. This VI uses the same formula found in the Coefficient Angle Calculator, but is arranged differently so that we can find the angle based on the coefficient instead of the coefficient based on the angle. Once the VI computes this value, the result is output on the front panel.