The definitions for the Fourier transform discussed earlier are not the only ones used. For example, the following definitions for the discrete Fourier transform and its inverse appear in Ronald Bracewell’s The Fourier Transform and Its Applications (McGraw- Hill, 1986)

• Instead of a factor of 1/ In in front of both forms, there is a factor of 1/n in front of the transform and no factor in front of the inverse.

• The minus sign appears in the exponent of the transform instead of in its inverse. The functions FFT, IFFT, CFFT, and ICFFT are used in exactly the same way as the functions discussed in the previous section

**Wavelet transforms**

Mathcad Professional includes two wavelet transforms for performing the one-dimensional discrete wavelet transform and its inverse. The transform is performed using the Daubechies four-coefficient wavelet basis.

wave(v) Returns the discrete wavelet transform of v, a 2m element vector containing real data. The vector returned is the same size as v.

Returns the inverse discrete wavelet transform of v, a 2m element vector containing real data. The vector returned is the same size as v.

**Sorting functions**

Mathcad includes three functions shown in Figure 13-4 for sorting arrays and one for reversing the order of their elements:

The above sorting functions accept matrices and vectors with complex elements. However in sorting them, Mathcad ignores the imaginary part

To sort a vector or matrix in descending order, first sort in ascending order, then use reverse. For example, reversetsortiv) returns the elements of v sorted in descending order.

Unless you change the value of ORIGIN, matrices are numbered starting with row zero and column zero. If you forget this, it’s easy to make the error of sorting a matrix on the wrong row or column by specifying an incorrect n argument for rsort and csort. To sort on the first column of a matrix, for example, you must use csort(A, 0)