Speech signals have a periodic envelope which can be used for speech separation. The choice of amplitude modulation spectrum (AMS) for speech separation is motivated by biological observations that variations in modulation frequency provides a long term window for characterizing speech information, especially in noisy and reverberant environments.
Suppose the received signal at the microphone is given as:

y[n]= s[n] + \nu[n]

where s[n] is the desired speech signal and \nu[n] is i.i.d zero mean Gaussian noise with variance \sigma_{\nu^2}. The short term spectrum of each frame is computed such that:

y(\omega)= s(\omega)+ \nu(\omega)

The negative frequency components of y(\omega) are set to zero to synthesize a signal \hat{y}(\omega) where:

\hat{y}(\omega)= \begin{cases}y(\omega) & \omega < \frac{F_s}{2}\\0 &\text{otherwise}\end{cases}

The inverse short term spectrum of \hat{y}(\omega) is the taken, denoted \hat{y}[n]. The AMS is then twice the amplitude of \hat{y}[n]. A sample performance of this algorithm is shown in Figure 1 below:

Speech amplitude modulation detection

Figure 1: Speech amplitude modulation detection

The AMS signal can also be used to detect the pitch of speech. However, this approach is very sensitive to noise.

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