|X(k)|_dB (k=0...N/2-1) = 20log₁₀|SUM(w(n)x(n)e^-jk(2π/N)n)|, n=0...N-1. Signal x(n) = x_a(nT), n=0...N-1, T is the sample period, x_a= analog signal. If x_a is the voltage signal of the microphone, then x_a(nT) = kP_a(nT), where P_a is the pressure and k is the constant factor.

The computation uses the decimation-in-time (DIT) computation method. Over the years, I have coded as a DSP man FFT spectrum of the Intelligent Speech Analyser™ (ISA) program
(1) for the Texas 16-bit TMS320 signal processor family in machine language,
(2) for Motorola's 16 and 32-bit M68000 microprocessor families in machine language and C language,
(3) for IBM 600 Series 32-bit PowerPC Microprocessor Family in machine language and C language,
(4) for Intel 32-bit and 64-bit microprocessor families in C++ language.

Signal windowing is done with a Hamming window, a rectangular window or a Blackman-Harris window with more than 90 dB.

Analysis pictures I have coded from the very beginning in Neon object-oriented programming language.

Hamming-window w(n) = 0.54-0.46cos(2πn/(N-1)).

Blackman-Harris-window w(n) = 0.35875-0.48829cos(2πn/(N-1))+0.14128cos(4πn/(N-1))-0.01168 cos(6πn/(N-1)).

Hz is converted to Bark by the formula x/Bark=7ln[f/650+√(1+(f/650)²)] and Barks are converted to Hz by the formula f/Hz=650sinh(x/7).

Hz is converted to ERBs by the formula x/ERB=21,3log₁₀(1+f/228,7) and ERBs are converted to Hz by the formula f/Hz=228,7(10^x/21,3-1).

Hz is converted to mel by the formula x/mel=2595log₁₀(1+f/700) and mels are converted to Hz by the formula f/Hz=700(10^x/2595-1).



Harmooninen FFT dB/Hz/Bark-asteikolla ja S/N-analyysi