Space/time/frequency methods in adaptive radar - New Jersey ...

APPENDIX ADISCRETE COSINE TRANSFORMIn discrete Wiener filtering, the filter is represented by G, an M x M matrix. Theestimate of the data vector 3C 1Swhere z = x N and N is the noise vector. The use of orthogonal transforms yielda G that contains a large number of elements that can be set to zero as they arerelatively small in magnitude.The Karhunen-Loeve transform (KLT) is optimal in respect to variance distribution[60] and estimation using the mean-square error [61]. There is no generalalgorithm that enables the fast computation of the KLT [60]. The KLT is aperformance basis to which many orthogonal transforms are compared, includingthe Walsh-Hadamard transform (WHT), discrete Fourier transform (DFT), andthe Haar transform (HT). The discrete cosine transform (DCT) is an orthogonaltransform that closely compares to the KLT [62].The DCT of a data sequence xm , m = 0, 1, • • • , (M — 1) is defined aswhere Gk is the kth DCT coefficient.The inverse discrete cosine transform (IDCT) is defined as109