DFT, DCT, MDCT, DST and signal Fourier spectrum analysis

DFT, DCT, DST and MDCT are compared in terms of their resolution power for signal Fourier spectrum analysis and energy compaction properties. For test sinusoidal signals with random frequency it was shown by computer simulation that the resolution power of the transforms is not uniform within the frequency band and that on average over the frequency range, DFT, DCT and DST have almost the same resolution power, while MDCT slightly remises them in this respect.