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Review of Literature on Signal Transforms 2.1 Introduction 2.2 Dftifft
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | A review of the literature on signal transfonns would be helpful in realizing the depth and richness of the field of signal transforms. There is a multitude of transforms that have been developed over the years. The DFT is among the most popularly used transfonns in signal processing. Many methods have been proposed for efficient computation of the DFT. In Chapter I, some important transforms were described. In this chapter, the literature corresponding to these various transforms is reviewed. Many FFT methods have been developed to perform fast DFT computation. In [1], a procedure to compute the N-point DFT that requires a number of operations proportional to N log N rather than N 2 was presented. This paper proved to be a landmark in signal processing, and led to intensified research on other FFT methods. In [9], Yavne proposed a method that requires the least number of additions and multiplications for real and complex data for FFTs of length-2". An altemative form of the FFT was proposed in [10]. In contrast to earlier methods that required multiplication by complex constants, this algorithm requires either real or purely imaginary constants for multiplication, hence reducing the number of multiplications. However, this method requires a greater number of additions. A split-radix approach for length-2 n was proposed in [11], in which radix-2 is used for the even part of the transfonn and radix-4 for the odd part. This method has the same number of multiplications as [10], but much fewer additions. Rader [12] showed that the DFT of a sequence of N points, when N is a prime number, is circular correlation, and proposed an FFT based on this finding. In [l3], number theoretic transforms are developed for fast computation of digital convolution. Winograd proposed the Winograd Fourier Transform Algorithm [14]. This algorithm uses Winograd's theorems on computational complexity for small and large values of sequence lengths. For large lengths, the Chinese remainder theorem was proposed to be used as part of the algorithm. Theoretically, this method required lesser number of multiplications than the Cooley-Tukey method. However, Winograd's algorithm was found to be difficult for practical implementation. The prime factor algorithm for FFT was proposed in [15], in which Rader's idea of conversion of DFT into convolution and results on implementation of short convolutions with minimum 15 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://shodhganga.inflibnet.ac.in/bitstream/10603/3755/10/10_chapter%202.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
