Minimum-Norm Solution for Robust Differential Arrays - Study and Design of Differential Microphone Arrays - page 116

this scenario, it is more appropriate to talk about a mixed first/second-order
cardioid (first order at low frequencies and second order at high frequencies).
Figure 6.4 gives plots of the white noise gain of the first-order cardioid, as
a function of frequency, for different values of M . As M increases, so is the
white noise gain. With 7 and 8 microphones and around 2 kHz and above,
we see that we reach the maximum white noise gain. Now, if we compare
the 2 and 5 microphone cases, we observe that at 1 kHz, the gain is above
0 dB with 5 microphones and around − 11 dB with 2 microphones, which
represents an improvement of more than 11 dB.
Figure 6.5 shows plots of the directivity factor of the first-order cardioid, as
a function of frequency, for different values of M . For M = 2, the directivity
factor is almost constant up to 4 kHz. As M increases, the frequency range for
which the directivity factor is constant decreases but at high frequencies, we
can get much better gains than at low frequencies, which is what we already
observed in the patterns.