  Speech bandwidth extension (BWE) refers to widening the frequency bandwidth
range of speech signals, enhancing the speech quality towards brighter and
fuller. This paper proposes a generative adversarial network (GAN) based BWE
model with parallel prediction of Amplitude and Phase spectra, named AP-BWE,
which achieves both high-quality and efficient wideband speech waveform
generation. The proposed AP-BWE generator is entirely based on convolutional
neural networks (CNNs). It features a dual-stream architecture with mutual
interaction, where the amplitude stream and the phase stream communicate with
each other and respectively extend the high-frequency components from the input
narrowband amplitude and phase spectra. To improve the naturalness of the
extended speech signals, we employ a multi-period discriminator at the waveform
level and design a pair of multi-resolution amplitude and phase discriminators
at the spectral level, respectively. Experimental results demonstrate that our
proposed AP-BWE achieves state-of-the-art performance in terms of speech
quality for BWE tasks targeting sampling rates of both 16 kHz and 48 kHz. In
terms of generation efficiency, due to the all-convolutional architecture and
all-frame-level operations, the proposed AP-BWE can generate 48 kHz waveform
samples 292.3 times faster than real-time on a single RTX 4090 GPU and 18.1
times faster than real-time on a single CPU. Notably, to our knowledge, AP-BWE
is the first to achieve the direct extension of the high-frequency phase
spectrum, which is beneficial for improving the effectiveness of existing BWE
methods.
