IDFT - 2023.2 English

Vitis Tutorials: AI Engine (XD100)

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2023.2 English

The IDFT or IFFT must perform an M=16 point transform at the input sample rate Fs. Given the design adopts SSR = 8, it follows a complete transform must be performed once every M / SSR = 16/8 = 2 cycles. This is a very high throughput rate given the M=16 transform involves either four stages of Radix-2 butterflies (32 total) or two stages of Radix-4 butterflies (eight total). This is challenging to achieve at a sustained rate of two cycles per transform given the overhead of butterfly addressing required for FFT solutions.

In this case, a direct “matrix multiplication” approach to computing the IDFT directly provides a workable solution. For the “cint16” data types adopted in this design, the AI Engine is capable of performing a single [1x2] x [2x4] vector-matrix product “OP” per cycle. The IDFT for M=16 requires a [1x16] x [16x16] vector-matrix product, equivalent to 32 such OPs. It follows that 16 AI engine tiles are required to implement the IDFT matrix product in two cycles.

To support this 100% efficient compute bound, each tile must use two input streams and compute one OP every cycle without stalling. The final output tiles must deliver four samples every two cycles to meet the desired throughput. More design details are given below.