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First, we describe the decimation in frequency (DIF) algorithm.
Convolution is decomposed in a frequency domain using the decimation in frequency algorithm.
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Also, a recursive FFT can be implemented as in [6], and a combination between the decimation-in-frequency (DIF) and the decimation-in-time (DIT) FFT is proposed in [7].
The main principle of these algorithms is decomposing the computation of the discrete fourier transform of a sequence of length N into smaller discrete fourier transforms see Figure 2. Figure 2 Flow graph of the decimation-in-frequency decomposition of an N -point DFT computation into four (N/4 -point DFT computatioN/4 -point6).
We distinguish between two basic types of radix-4 algorithms: decimation-in-time (DIT) is the consequence of decomposing the input x[n], and decimation-in-frequency (DIF) when decomposing the output X[n].
The same storage requirements hold for a decimation-in-frequency FFT, bit-reversed input order, and consecutive data allocation.
A Decimation-In-Frequency implementation was used as it enabled the inputs to be ordered at the beginning of the calculation.
Recently, pipelined architectures consisting of only real datapaths for decimation-in-frequency (DIF) RFFT were proposed in [9].
Decimation in time (DIT) and decimation in frequency (DIF) are the two methods in grouping the N samples.
Furthermore, the [24] suggests, first, to perform decimation in frequency (DIF) and, second, a decimation in time (DIT).
After the synchronization process is done, the CFO compensated packets are transformed to the frequency domain by a 128-point radix- 23 decimation in frequency FFT block.
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