Add configurable Pwelch scaling and improve performance#897
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…nel that performs better than CUB when in memory FFT bin powers are {batches, nfft}
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static_asserts for signal type
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This PR addresses concerns in issue #887:
Configurable scaling is supported. Density and Spectrum modes, similar to Matlab or scipy.signal, as well as fused dB modes frequently needed for spectrum-analyzer-like plotting
Custom reduction kernel is used instead of MatX sum() using CUB DeviceSegmentedReduce (DSR).
Three reasons why the custom reduction kernel is preferred:
In the nominal case where the input signal is a memory backed complex-valued tensor and the output power spectrum is a memory backed real-valued tensor, the intermediate overlapping signal is a 2D tensor {batches, nfft}. This is an optimal memory layout for the FFTs, but a very suboptimal layout for CUB DSR which would the permuted layout {nfft, batches} as CUB DSR uses one block of threads to read all the 'batches' of a single fft bin. To improve CUB performance, we'd either need to have the batched FFTs directly write to a permuted tensor (about 4x slower for the scenario considered) or permute the intermediate tensor after the FFT (extra round trip through global memory).
CUB currently needs begin/end indexes for each data segment, the generation of which takes around 50% longer than the custom reduction (ignoring the permutation issue)
The custom reduction allows for configurable scaling, such as fusing a dB conversion.