A Non-Feedback-Loop and Low-Computation- Complexity Algorithm Design for a Novel 2-D Sliding DFT Computation

Abstract

This paper presents a forward-path, novel, two-dimensional (2-D) sliding discrete Fourier transform (SDFT) algorithm based on the column-row 2-D DFT concept and the shifted window property. After applying a descending dimension method (DDM), a mixed-radix and butterfly-based structure can be further employed to effectively implement the proposed algorithm. Conceptually, it has many advantages, including greater stability, more accuracy, and less computational complexity because there are no extra feedback loops in the calculation. The evaluation results are based on the following conditions: (1) the window size (N ) to 16 × 16; (2) the test pattern is an SVC grayscale video, and the formats are CIF and 4CIF with 30fps; (3) one multiplication involves four real multiplications and two real additions. The proposed 2-D SDFT method clearly reduced the number of multiplications by 43.8% and only increased the number of additions by 33%, compared with the state-of-the-art Park's method. Additionally, for the first 100 frames of the CIF and 4CIF sequences, the proposed method saves 10.8% and 10.9% of the processing time, respectively, on average. Overall, the proposed DDM-based 2-D SDFT algorithm can be applied to calculate not only 1-D but also 2-D SDFT spectrum, and are especially appropriate for hybrid applications. INDEX TERMSSliding discrete Fourier transform (SDFT), two-dimension SDFT (2-D SDFT), column-row 2-D DFT, descending dimension method (DDM), DDM-based 2-D SDFT.

Hardware Accelerator Design of DCT Algorithm With Unique-Group Cosine Coefficients for Mel-Scale Frequency Cepstral Coefficients

“…The definition of the DCT conversion in MFCC is given in (1), where M and L are set as 13 and 32, respectively, in [10]. After substituting n=l-1 into (1), the equation can be written as (2), where n ranges from 0 to L-1.…”

“…Based on the above derivations, the proposed algorithm has a very simple computational kernel with the same multiplication of cosine function in (9) and (10). The number of the cosine coefficients can be completely shared with the preprocessing procedure and the computational kernel.…”

“…Moreover, some problems with sliding and hopping DFTs were developed in [10], [11], [12]. For DCT computation, most of the studies such as [13], [14] focused on the derivation of modified DCT (MDCT) and modified discrete sine transform (MDST) by converting the formula to the type IV of DCT in the applications of audio codec.…”