TMtx.DCT Method — Dew Math

TMtxVec DCT(TMtxVec Vec, Int32 VecIndex, Int32 Index, Int32 Len)

The forward discrete cosine transform (DCT).

#	Name	Type	Description
1	Vec	TMtxVec	source TVec or TMtx
2	VecIndex	Int32
3	Index	Int32	start index
4	Len	Int32	element count

Result: stored in self (calling object), returns self for chaining

Remarks:

Calculates the forward discrete cosine transform (DCT) of the Vec and writes the result in the calling vector. If Vec.Length is a power of 2, the function uses an efficient algorithm that is significantly faster than the direct computation of DCT. For other values of Vec Length, this function uses the direct formulas given below; however, the symmetry of cosine function is taken into account, which allows to perform about half of the multiplication operations in the formulas. In the following definition of DCT, N=Vec.Length and V is the calling vector:

\begin{aligned} C(k) &= \begin{cases} \sqrt{\frac{1}{N}} & k=0 \\ \sqrt{\frac{2}{N}} & k > 0 \end{cases} \\ \text{V}[k] &= C(k)\cdot \sum _{n=0} ^{N-1} \text{Vec}[n]\cdot \cos \left( \frac{(2n+1)k\pi}{2N}\right) \end{aligned}

Examples

Matrix a;
Matrix b;
a.SetIt(1,4,false,new double[] {1,-2,3,4});
b.DCT(a,0,0,4);