  Converting time domain waveforms to frequency domain spectrograms is
typically considered to be a prepossessing step done before model training.
This approach, however, has several drawbacks. First, it takes a lot of hard
disk space to store different frequency domain representations. This is
especially true during the model development and tuning process, when exploring
various types of spectrograms for optimal performance. Second, if another
dataset is used, one must process all the audio clips again before the network
can be retrained. In this paper, we integrate the time domain to frequency
domain conversion as part of the model structure, and propose a neural network
based toolbox, nnAudio, which leverages 1D convolutional neural networks to
perform time domain to frequency domain conversion during feed-forward. It
allows on-the-fly spectrogram generation without the need to store any
spectrograms on the disk. This approach also allows back-propagation on the
waveforms-to-spectrograms transformation layer, which implies that this
transformation process can be made trainable, and hence further optimized by
gradient descent. nnAudio reduces the waveforms-to-spectrograms conversion time
for 1,770 waveforms (from the MAPS dataset) from $10.64$ seconds with librosa
to only $0.001$ seconds for Short-Time Fourier Transform (STFT), $18.3$ seconds
to $0.015$ seconds for Mel spectrogram, $103.4$ seconds to $0.258$ for
constant-Q transform (CQT), when using GPU on our DGX work station with CPU:
Intel(R) Xeon(R) CPU E5-2698 v4 @ 2.20GHz Tesla v100 32Gb GPUs. (Only 1 GPU is
being used for all the experiments.) We also further optimize the existing CQT
algorithm, so that the CQT spectrogram can be obtained without aliasing in a
much faster computation time (from $0.258$ seconds to only $0.001$ seconds).
