Cepstrum of the Intelligent Speech Analyser™

Home Signal displays 1985- Multi-envelope displays 1998- FFT displays 1985- 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 in Hz scale 1983- FFT spectrogram displays 1985- LPC spectrogram displays 1998- Auditory spectrogram displays 1985- Bark, ERB, mel, semitone and Hz scales formant charts 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

Cepstra in lin/Hz scale

|X(k)|_dB (k=0...N/2-1) = 20log₁₀|SUM(w(n)x(n)e^-jk(2π/N)n)|, n=0...N-1. |Y(k)|_dB (k=0...N/4-1) = |SUM(|X(n)|_dBe^-jk(2π/N)n)|, n=0...N/2-1. 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.

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)).

The calculation uses a decimation-in-time (DIT) algorithm.

Over the years, I have coded as a DSP man cepstrum
(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.

Cepstrum on the lin/Hz scale.

YIN on the lin/Hz scale.

FFT on the dB/Hz/Bark scale.