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### BE2M31ZRE seminar LPC spectrum and formant estimation

• LPC spectrum and formant estimation
• For voiced short-time frame muz1-AA-frame.CS0 (raw data without header, fs=16000 Hz, for download into MATLAB use loadbin.m) estimate formant frequencies in the following steps:
• apply weighting by Hamming window to analyzed frame,
• compute and observe DFT-based power spectrum in dBs,
• compute LPC coefficients and LPC power spectrum in dBs (parameters of AR model compute on the basis of autocorrelation method using MATLAB function lpc or aryule. You can use also Burg algorithm using MATLAB function arburg,
• HOME PREPARATION Display for voiced frame : muz1-AA-frame.CS0:
- waveform of the signal
- DFT and LPC spectrum in dBs

• observe the positions of zeros and poles of AR model transfer function,
• observe impact of preemphasis to zero and pole position and computed LPC spectrum respectively, (further apply always preemphasis for an estimation of formants),
• for related poles (p_1 up to p_4) compute values of formant frequencies (F1, F2, F3, and F4), see lecture slides EZRE_pr2_spectral_char_lpc_HANDOUT.pdf.
• display the values of formant frequencies in a figure and proove that they correspond to peaks of smoothed LPC spectrum.
• Result: Display for voiced frame muz1-AA-frame.CS0:
- the diagram of zeros and poles for computed AR model,
- formant frequencies F1 and F2 in LPC spectrum.

• Analysis of formants of basic vowels
• Compute the first four formants for all 5 basic vowels (F1 - F4) in particular short-time frames of the length of 32 ms taken with 50% overlap. Apply preemphasis with the coefficient m=0.97 before the segmentation, then realize centering of each short-time frame as well as the weighting using Hamming window.
• Work with signals of the speaker T16204 - signals are available in the directory K:\ZRE\data\zreratdb\BLOCK162\T16204 or in the following archive zrerat_T16204_vowels_cs0.zip.
• Result: For speaker T16204 draw:
• time dependancy of concatenated vowels a-e-i-o-u for the 1st realizations of all 5 vowels,
• time dependancy of the first 4 formants for concatenated vowels a-e-i-o-u for the 1st realizations of all 5 vowels,
• for all vowel realizations A1,A2,A3,....,U1,U2,U3 of speaker T16204 draw formant triangle, i.e. computed values of the first and the second formats draw into the graph F1 = f ( F2 ). Point related to each particular vowel resolve by different colour.

• Repeat previous step also with other signals, mainly with your own records. Signals resampled to 16 kHz (files *.CS0) from the database zreratdb are available for direct usage in the lab 802 at CTU FEE at the directory K:\ZRE\data\zreratdb or within the following archive zrerat_blocken_2024_cs0.zip.
• Result:
- formant traingle for all available short-time frames for your realizations of 5 basic vowels.

• Observe formant estimation in Praat (i.e. time dependacy of formants in signal spectrogram).

• Repeat for your own records and on the basis of formant triangle for vowels pronounced by you correct the potentionally bad recordings of 5 basic vowels, i.e. remove possibly long pause at the beginning and the end of a record or rerecord possibly completely bad vowel realizations.