A fast cosine transform in one and two dimensions 论文
1980IEEE Transactions on Acoustics Speech and Signal Processing引用 340
Digital Filter Design and ImplementationAdvancements in PLL and VCO TechnologiesNumerical Methods and Algorithms
详细信息
- 发表期刊/会议
- IEEE Transactions on Acoustics Speech and Signal Processing
- 发表日期
- 1980-02-01
- 发表年份
- 1980
关键词
Digital Filter Design and ImplementationAdvancements in PLL and VCO TechnologiesNumerical Methods and Algorithms
摘要
The discrete cosine transform (DCT) of an N-point real signal is derived by taking the discrete Fourier transform (DFT) of a 2N-point even extension of the signal. It is shown that the same result may be obtained using only an N-point DFT of a reordered version of the original signal, with a resulting saving of 1/2. If the fast Fourier transform (FFT) is used to compute the DFT, the result is a fast cosine transform (FCT) that can be computed using on the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \log_{2} N</tex> real multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.