... frequency.It is also possible to modify this transform to conserve the energy of the data vector. All that’s needed is to multiply the transformation matrix W by the scalefactor 1/2. Thus, the product ... changes along the basisvector) become higher. To illustrate how this matrix identifies the frequencies in a data vector, we mul-tiply it by the following test vectors (1, 0, 0, 1), (0, 0.33,−0.33,−1), ... transform.We use matrix W/2 to transform the (not very correlated) data vector d =(4, 6, 5, 2).The result is t =(8.5, 1.5,−2.5, 0.5). It’s easy to transform t back to d, but t itselfdoes not...