快速傅里叶算法的应用-中英文翻译.rar
快速傅里叶算法的应用-中英文翻译,introduction the symmetry and periodicity properties of the di screte fourier transform (dft) allow a variety of useful and interesting decompositions. in pa rt...
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Introduction
The symmetry and periodicity properties of the di screte Fourier transform (DFT) allow a variety of useful and interesting decompositions. In pa rticular, by clever groupin g and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation requi red). Many “fast” algorithms have been developed for computing the DFT, and collectively these are known as Fast Fourier Transform (FFT) algorithms. Always keep in mind that an FFT algorithm is not a different mathematical transform: it is simply an efficient means to compute the DFT. In this experiment you will use the Matlab fft() function to perform some frequency domain processing tasks. The concept of doing “real time” processing with an FFT algorithm is not really true, since the DFT requires an entire block of input samples to be available before processing can begin. So, rather than being able to run the processing algorithm on the fly as each waveform sample arrives as we might with a direct form digital filter, it will be necessary to buffer a block of samples and then start the first FFT while still re ceiving the new samples as they arrive from the A/D and providing the output samples to the D/A. This inherent delay, or processing latency , is separate from the time required to compute the FFT itself. The Matlab implementation will be run on stored dataanyway, so the real time proce ssing latency is not an issue for this particular lab experiment.
引言
离散傅立叶变换(DFT)的对称性和周期性允许有用和有趣的分解变换。特别地，当要获得DFT的精确解(非近似值)时，通过复指数乘法的灵活分组和重新排序可以达到实质的计算简化。许多快速算法的发展是为了计算处理DFT，它们也被公认为是快速傅里叶(FFT)算法。始终紧记FFT算法不是一种不同的数学变换：它是一种计算DFT简单有效的方法。本实验将利用Matlab fft功能去执行一些在处理任务的频域。
用FFT算法进行实时处理的观念是不正确的，因为在处理开始前DFT需要一个可利用的输入样本完整块。因此，当每个波形样值来到的时候，我们可以用直接型数字滤波器处理算法。当接收从A/D过来的新样本和提供输出样本到D/A时，我们有必要去缓存样本块并开始第一个FFT。这些固有延迟或反应时间与计算FFT它本身所需要的时间是分开的。总之，Matlab的执行将连续存储数据，因此，对于这个特殊的实验实时处理反应时间不是一个问题。
The symmetry and periodicity properties of the di screte Fourier transform (DFT) allow a variety of useful and interesting decompositions. In pa rticular, by clever groupin g and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation requi red). Many “fast” algorithms have been developed for computing the DFT, and collectively these are known as Fast Fourier Transform (FFT) algorithms. Always keep in mind that an FFT algorithm is not a different mathematical transform: it is simply an efficient means to compute the DFT. In this experiment you will use the Matlab fft() function to perform some frequency domain processing tasks. The concept of doing “real time” processing with an FFT algorithm is not really true, since the DFT requires an entire block of input samples to be available before processing can begin. So, rather than being able to run the processing algorithm on the fly as each waveform sample arrives as we might with a direct form digital filter, it will be necessary to buffer a block of samples and then start the first FFT while still re ceiving the new samples as they arrive from the A/D and providing the output samples to the D/A. This inherent delay, or processing latency , is separate from the time required to compute the FFT itself. The Matlab implementation will be run on stored dataanyway, so the real time proce ssing latency is not an issue for this particular lab experiment.
引言
离散傅立叶变换(DFT)的对称性和周期性允许有用和有趣的分解变换。特别地，当要获得DFT的精确解(非近似值)时，通过复指数乘法的灵活分组和重新排序可以达到实质的计算简化。许多快速算法的发展是为了计算处理DFT，它们也被公认为是快速傅里叶(FFT)算法。始终紧记FFT算法不是一种不同的数学变换：它是一种计算DFT简单有效的方法。本实验将利用Matlab fft功能去执行一些在处理任务的频域。
用FFT算法进行实时处理的观念是不正确的，因为在处理开始前DFT需要一个可利用的输入样本完整块。因此，当每个波形样值来到的时候，我们可以用直接型数字滤波器处理算法。当接收从A/D过来的新样本和提供输出样本到D/A时，我们有必要去缓存样本块并开始第一个FFT。这些固有延迟或反应时间与计算FFT它本身所需要的时间是分开的。总之，Matlab的执行将连续存储数据，因此，对于这个特殊的实验实时处理反应时间不是一个问题。
