Feature extraction is a fundamental operation of classification and pattern recognition. There are various strategies for one-and multi-dimensional feature extraction. The transform domain features are very effective when the patterns are characterized by their spectral properties. A wellknown successful example is the speech recognition. In this paper the feature extraction capability of discrete cosine transform (DCT), Walsh-Hadamard transform (WHT), discrete Hartley transform (DHT) and their sign transformations are investigated and compared for the recognition of two &-mensional binary patterns. It is shown, in this paper, that the noise immunity of the transform based feature extraction is rather promising. Selection of TransformsThe appliance of unitary transforms to feature extraction had been discussed in [1,2]. Since the characteristics of speech signals are represented by their spectral properties, the adoption of unitary transforms for speech recognition is very intuitive and effective [5].There are several ways to extract features of 2-D patterns, such as amplitude features, histogram fe& tures, transform domain features and shape features. Some comparisons of various properties among the discrete Fourier transform (DFT), the Karhunen-Ldve trans form (KLT), the WHT and the Haar transform (HT) were given in [l]. M is well known that KLT is the optimum choice for signal decorrelation in the sense of mean square error and the DCT performs closest to the KLT for highly correlated inputs. Hence, the feature extraction capability of the DCT is interesting.The DCT was first proposed in 1974 [3] and was proven to be of closest performance to the KLT for Markov-I signal class [4]. Thus it is natural to use DCT for feature extraction, classification and pattern recognition. The previous works [l] shown that the DFT performs better than other unitary tra.ns€orms in pattern classification applications. Since the transform kernel of DHT is very similar to that of DFT, the performance of the DHT is believed to be comparable to that of the DFT. Recently, Ersoy had proposed a new two -stage representation of the DFT [5]. In his work the computation of the DFT was decomposed into pre-and postprocessing stages by using MWius inversion formula [6].The pre-processing stage of the two-stage DFT consists of fl, ktj and their combinations; the postprocessing stage consists of several independent convolvers or correlators of smaller sizes. The two-stage representation of the DFT is not only a fast algorithm but also provides a new tool for feature extraction. The simple pre-processing stage can be treated as a new transform called discrete rectangular wave transform (DRWT). Ersoy et al. have used the DRWT in speech recognition [7] and image recognition [8,9] and the results are remarkable.From the derivation of the two-stage DFT (51, the sine and cosine function can be represented in numbertheoretic bases. It is clear from [5] that the DRWT is, in fact, the sign transformation of the DFT. Some similar works of the two-stage ...

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Since a new discrete rectan lar wave transform (DRWT) has been propcsef there are various applications which could be applied, such as real-time DFT implementation and ima e recognition. Although the DRWT possesses tfe property of easy-computation, there 19 no cost-effective algorithm for the implementation of DRWT. Most of the proposed architectures to implement this transform are systolic array, wavefront array, or algorithm based implementations with butterfly-like structures. Since these proposed architertiires have either the modular or high-throughput rate property, but not both; therefore, a same-geometry implementations B proposed in this paper.In this paper, a cost-effective algorithm for implementing DRWT is roposed, called the s a m T m e t r y DRWT. TKis newly proposed dgorit m provides a better procedure not merely in fast computation but also in the consideration of real implementation. In the sarne-geometry DRWT, power of two length is the cdnstraint. There are 21oaN-1 stages in the implementation of the DRWT with length N. Furthermore, logzN stages are identical and therefore only logzN st es demand circuit design in implementation phase.%he delay of each stage is merely one addition and the cells required to construct these stages are simple. Therefore, this algorithm is suitable for VLSI implementation.