## 4.3.1 Frequency Domain Conversion

06.943GPPTSVoice Activity Detector (VAD) for Adaptive Multi Rate (AMR) speech traffic channels

The input signal is pre-emphasised and windowed prior to frequency domain conversion. This process is defined as

, (4.1)

where *d*(*n*) is the pre-emphasised speech buffer, * _{p}* is the pre-emphasis factor, and

*L*is the subframe length. A rectangular window is then used to frame the speech prior to frequency domain conversion, which is expressed as:

, (4.2)

where *D* is the zero-padding offset into the DFT buffer, and *M* is the DFT length. The transformation of *g*(*n*) to the frequency domain is performed using the Discrete Fourier Transform (DFT) defined as:

(4.3)

where *e ^{j}*is a unit amplitude complex phasor with instantaneous radial position

**.