Question

How to find value of i in dTf formula

Answer 1

All DFT's use this formula:

DFT equation

X(k) is transformed sample value (complex domain)

x(n) is input data sample value (real or complex domain)

N is number of samples/values in your dataset

This whole thing is usually multiplied by normalization constant c. As you can see for single value you need N computations so for all samples it is O(N^2) which is slow.

Here mine Real<->Complex domain DFT/IDFT in C++ you can find also hints on how to compute 2D transform with 1D transforms and how to compute N-point DCT,IDCT by N-point DFT,IDFT there.