Main ideas as follows : research of audio digital watermark algorithm based on fast fourier transforms and psychoacoustic auditory model 主要工作有:基于快速傅立叶变换与声学模型的音频数字水印算法研究。
Meschach computes fast fourier transforms , extracts columns and rows , and computes eigenvalues of symmetric matrices Meschach能计算快速傅立叶变换（ fast fourier transform ） 、提取列和行以及计算对称矩阵的特征值。
In addition , based on fast fourier transform ( fft ) , an effective and reliable carrier frequency detection method has also been designed in this thesis 此外，论文还设计了一种有效可靠的基于fft的载波频率测量方法。
Based of all , a method using fast fourier transform combining with wavelet transform is discussed , named eliminating singularity point and detecting harmonic 在此基础上，本文探讨了将快速傅立叶变换和小波变换相结合的方法，即剔除奇异点监测谐波。
The traditional beam propagation algorithm based on fast fourier transform fails to give right results due to the limitation of the sampling theorem 由于取样定理的限制，常规的基于快速傅里叶变换( fft )光束传输模拟算法不能进行任意焦距聚焦光束的传输过程的模拟。
The fields at any point , especially at the points in the middle field region , are reconstructed by using the theory of the plane wave and the inverse fast fourier transform in this thesis 论文根据平面波谱的展开理论和傅立叶反变换首次给出了在空间任意点，特别是中场区，的场分布。
Secondly , the sub - function blocks of fft ( fast fourier transform ) are finished in max + plus ii software platform , and each of them has been designed carefully and simulated in the software 然后用max + plus软件平台编程实现快速傅立叶变换的各个软件模块，并进行了大量的逻辑设计和软件仿真。
The author also ananlysises carefully the implement of fast fourier transform , the most classical application on the digital signal processment , based on the point - bit dsp processor 对数字信号处理中最经典的应用? ?快速傅立叶变换( fft )运算，在定点dsp芯片上的实现做了充分的分析和研究。
The concepts of filtering and sampling power system voltage and current signals for harmonic analysis using the fast fourier transform ( fft ) algorithm by a digital signal processor are introduced 软件算法方面，系统采用传统的快速付立叶变换( fft ) ，对采集的电压和电流信号进行频谱分析。
But the computing amount of dft is so large that its practical use is restricted , especially real - time processing . in fact , we use fast fourier transform ( fft ) in practical engineering 但庞大的运算量使得dft的实际应用，特别是实时处理难以实现，所以实际工程中用到的都是快速傅里叶变换( fft ) 。
