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# System prepended metadata

title: Phase Response

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# Phase Response
Thank you for the prompt response!

We agree that phase is very important for a variety of tasks (including music synthesis and microphone-array direction estimation), and the phase recovered by Griffin-Lim may not be sufficiently faithful for the spatial impulse response in these applications. However, there are two reasons that we think using a neural implicit function to learn the magnitude alone is useful and meaningful.

- [**Qualitative results are good enough for game and VR applications**] For many widespread uses of spatial audio (gaming/VR), the goal is to provide a plausible representation of sound propagation and reverberation in a scene. For these use cases, the phase is not necessarily critical to providing a believable experience, and is often not modeled (notably Raghuvanshi's parametric coding, Drori's image2reverb). As we show on our website, we can still present a plausible spatial audio experience at continuous locations after trained on sparse samples, while using a magnitude less storage compared to the original dataset.

- [**Phase is hard to learn using neural implicit functions**] Following your suggestion, we did experiment with learning phase using an implicit function, however the naturally smooth nature of implicit functions and the spatially chaotic nature of phase meant that the network struggled to accurately generalize phase at unseen locations using the current parameter count. Attempting to learn the phase as an additional output to the current network led to degraded T60 and STFT MSE metrics. We speculate the reason is that phase changes too quickly as a function of spatial location, and is difficult to learn from sparse samples of a scene. We also added results that directly regress the waveform using an implicit function, however this approach struggles to model higher frequencies. We believe that as the first work in this field, our method of modeling magnitude is a valid initial step towards using a neural field to learn spatial reverberations.  

- [**Future work: NAF + neural vocoder**] We believe that a potential avenue for exploration would be to combine our implicit NAF STFT output with a principled neural vocoder (like Wavenet). While there are many possible approaches for recovering the phase, we believe they are orthogonal to the scope of our task. We are happy to clarify our goals more clearly, include a discussion of the limitations of our work, and describe possible avenues for future work in neural waveform recovery.

Thanks again for your insightful comments. We have gained much from your constructive suggestions, and have made a good faith effort to address your concerns in our revisions. We hope that we have been able to clarify our goals and limitations of this work. We believe this is the first study that tackles learning plausible spatial audio using a neural field. Indeed, completing this first step has not been trivial; more importantly, it lays the foundation for future exciting improvements that can fully address your suggestions. We hope that as an expert in the field, you will support our efforts of expanding the field and consider a more positive evaluation given to our work.

We are happy to answer any additional questions. 
