近年來，關於低功率的研究，已逐漸成為目前各個領域的研究焦點。先前關於Discrete Cosine Transform (DCT) 低功率的研究，大部份著重在如何降低電路的功率消耗，或是減少整體DCT的運算量以達到低功率的目的。然而，隨著時代的改變與技術的進步，為了滿足目前使用者對於的高水準影像品質的要求，兼顧低功率運算與高品質壓縮的研究設計逐漸成為近來關注的焦點。因此，在本論文中，我們提出了一個兼具低功率訊號處理以及高品質轉換的Cordic based Loeffler DCT架構。此架構只需要使用到38個加法器跟16個移位器運算就可以完成無乘法器的DCT轉換。

本論文使用TSMC 0.13-μm製程的技術來合成所提出的新架構，並且使用了Synopsys PrimePower來量測Gate Level的功率消耗。除此之外，也同時將所提出的架構崁入到JPEG和MPEG 4 Xvid內。根據模擬的數據結果，新架構除了只需原先Loeffler DCT 19%的面積和只消耗16%的功率之外，還同時可以維持跟Loeffer DCT相似的轉換品質。

最後，本論文所提出的Cordic based Loeffler DCT架構除了非常適合低功率高品質的CODECs外，同時也非常適合實現於VLSI設計之上。尤其是適合應用崁入式系統、高品質CODECs和低功率行動裝置。

In this master thesis, a low-power and high-quality preserving DCT architecture is presented. It is obtained by optimizing the Loeffler DCT based on the Cordic algorithm. The computational complexity is reduced significantly from 11 multiply and 29 add operations (Loeffler DCT) to 38 add and 16 shift operations (i.e., similar to
the complexity of the binDCT) without sacri‾cing the transformation accuracy. This implementation can also perform multiplierless DCT transformation as binDCT does.

In our experiments, we used different criteria to evaluate the proposed DCT architecture. After synthesizing with TSMC 0.13-um technology library, Synopsys PrimePower was used to estimate the power consumption at gate-level. Then we have embedded our DCT architecture into the JPEG and XVID CODECs to compare and analyze the quality of the compression results. The experimental results show that the proposed DCT architecture only occupies 19% of the area and consumes about 16% of the power of the Loe²er DCT. Moreover, it also retains the good transformation quality of the original Loeffler DCT.

As a result, the proposed Cordic based Loeffler DCT is not only very suitable for low-power and high-quality CODECs but also highly suited for VLSI-implementations since it only needs add and shift operations to carry out DCT transformation. Finally, it is worth noticing that the presented Cordic based Loeffler DCT architecture is especially suited for embedded systems, high-quality CODECs and mobile hand-held
devices due to its low power and small area properties.

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