©copyright Raimo Olavi Toivonen 1985-2023. All rights reserved. Last updated on Jan 8, 2023.

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Home  Signal displays 1985-  Multi-envelope displays 1998-  Cepstrum displays 1983-   LPC displays 1992-   Auditory displays 1983-   Loudness displays 1995-   Loudness Curves 1998-   Timbre spectrum 1983-  LTAS displays 1982-   Harmonic FFT displays 1989-  Waterfall displays 1983-   F0 displays 1983-   F0 histograms in semitone scale 1989-  Jitter/shimmer 1990-  Computer Voice Fields 1983-  FFT spectrogram displays 1985-  LPC spectrogram displays 1998-  Auditory spectrogram displays 1985-  Formant charts in Bark, ERB, mel, semitone and Hz scales 1988-   Synte 2 demo video speech on 8.8.1977 analyzed 2018-   Formant charts of world languages in Bark scale 2018-   Other links Works   Works before ISA FFT spectra in dB/Hz/Bark scale

|X(k)|_dB (k=0...N/2-1) = 20log₁₀|Σ(w(n)x(n)e^-jk(2π/N)n)|, n=0... 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.

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

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

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/(N1))-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).

FTT and LPC spectrum of the vowel a:

FTT and LPC spectrum of the vowel e:

FTT and LPC spectrum of the vowel i:

FTT and LPC spectrum of the vowel o:

FTT and LPC spectrum of the vowel u:

FTT and LPC spectrum of the vowel y:

FTT and LPC spectrum of the vowel ä:

FTT and LPC spectrum of the vowel ö: