Improved Frequency Resolution DFT Eases Teaching FFT Analysis and Provides Better Amplitude Accuracy

For a signal extension T, DFT and FFT calculate the transform at frequencies 1/T apart. Due to this, amplitude of the transform can show more than 36% of discrepancy relatively to exact analytical Fourier transform and this disagreement looks random. Calculating the transform with a frequency resolution 7 times thinner lowers this difference to within 1%. As a result, obtained spectrums are easier to explain. This high resolution spectrum can be obtained either directly from time file or by interpolating frequency file that results from standard calculation. Both algorithms are supplied and spectrums of simple signals, obtained with standard and improved resolution, are compared