
A Fast Chebyshev Spectral Method for Nonlinear Fourier Transform
In this letter, we present a fast and wellconditioned spectral method b...
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Fast Partial Fourier Transform
Given a time series vector, how can we efficiently compute a specified p...
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The Number of Threshold Words on n Letters Grows Exponentially for Every n≥ 27
For every n≥ 27, we show that the number of n/(n1)^+free words (i.e., ...
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Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part II: Waveform Design and Experiment
The nonlinear Fourier transform has the potential to overcome limits on ...
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Fast Compressed Power Spectrum Estimation: Towards A Practical Solution for Wideband Spectrum Sensing
There has been a growing interest in wideband spectrum sensing due to it...
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Learning Kway Ddimensional Discrete Code For Compact Embedding Representations
Embedding methods such as word embedding have become pillars for many ap...
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A Comparison of SCFDE and UW DFTsOFDM for Millimeter Wave Communications
In this study, we compare the singlecarrier (SC) waveform adopted in IE...
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Is FFT Fast Enough for Beyond5G Communications?
In this work, we consider the complexity and throughput limits of the Fast Fourier Transform (FFT) algorithm having in mind the unprecedented number of points (subcarriers) N expected in future waveforms. Based on the spectrocomputational analysis, we verify that the FFT complexity to process an Nsubcarrier symbol grows faster than the number of bits in the symbol. Thus, the useful throughput of FFT nullifies as N grows. Also, because FFT demands N to be a power of two 2^i (for some i>0), the spectrum widening causes the FFT complexity to grow exponentially on i, i.e. O(2^ii). To overcome these limitations, we propose the Parameterized DFT (PDFT) algorithm, which builds on the parameterized complexity technique and the classic O(N^2) DFT algorithm to replace an Npoint DFT into N/n (n>0) smaller npoint DFTs. By setting n=Θ(1), we get a O(N) algorithm whose resulting waveform matches OFDM in its vectorized form (i.e., Vector OFDM) but with the N=2^i constraint relaxed. Besides, we also show that PDFT becomes multiplierless for n=2, requiring only Θ(N) complex sums. We believe our results constitute a relevant step towards the practical deployment of future extremely wide multicarrier signals.
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