In this work, we present two parallel algorithms for the large-scale discrete Fourier transform (DFT) on Tensor Processing Unit (TPU) clusters. The are associated with DFT formulations: one formulation, denoted as KDFT, is based Kronecker product; other famous Cooley-Tukey algorithm and phase adjustment, FFT. Both KDFT FFT formulations take full advantage of TPU's strength in matrix multiplicat...