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**Spectral Analysis & Spectrogram**

SASPL Cheolwoo Jo

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**Contents Spectral Analysis Spectrogram Analysis of Spectrogram**

Narrow Band Wide Band Analysis of Spectrogram AR, MA, ARMA model of Speech

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Spectral Analysis

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**Spectrogram in matlab [B,F,T] = SPECGRAM(A,NFFT,Fs,WINDOW,NOVERLAP)**

A: Speech Signal NFFT: Number of samples Fs: Sampling Frequency Window: Type of Window NOVERLAP: Number of Overlapping signal

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**Spectrogram in auditory toolbox**

function [array,raw] = spectrogram(wave,segsize,nlap,ntrans); %function array = spectrogram(wave,segsize,nlap,ntrans); % defaults spectrogram(wave,128,8,4) % nlap is number of hamming windows overlapping a point; % ntrans is factor by which transform is bigger than segment; % returns a spectrogram 'array' with fourth root of power, % filter smoothed and formatted for display. % Added option to return raw spectrogram.... Malcolm 5/26/95 % Added code so that input could be any direction ... Malcolm 5/26/95 % (c) 1998 Interval Research Corporation if nargin < 4; ntrans=4; end if nargin < 3; nlap=8; end if nargin < 2; segsize=128; end [r c] = size(wave); if (r < c) wave = filter([ ],[1],wave'); else wave = filter([ ],[1],wave); end

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s = length(wave); nsegs = floor(s/(segsize/nlap))-nlap+1; array = zeros(ntrans/2*segsize,nsegs); window = *cos(2*pi/(segsize+1)*(1:segsize)'); for i = 1:nsegs seg = zeros(ntrans*segsize,1); % leave half full of zeroes seg(1:segsize) = ... window.*wave(((i-1)*segsize/nlap+1):((i+nlap-1)*segsize/nlap)); seg = abs(fft(seg)); % reverse for image display array(:,i) = seg(((ntrans/2*segsize)+1):(ntrans*segsize)); end if nargout > 1 raw = array;

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**array = array .* array; % back into power domain for smoothing**

for i=1:nsegs % smooth the spectral slices array(:,i) = filter([ ],[1],array(:,i)); end for i=1:ntrans/2*segsize % smooth the channels array(i,:) = filter([ ],[1],array(i,:)); % compress with square root of amplitude (fourth root of power) off = *max(max(array)); % low end stabilization offset, array = (off+array).^0.25-off^0.25; % better than a threshold hack! array = 255/max(max(array))*array;

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**Spectrogram level scaling**

Log|x[k]|2 Gray Intensity Black Log Energy(dB) White 60dB

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**Specgram SPECGRAM(A,F,Fs,WINDOW) Matlab A: Speech**

F: Vector of Frequencies Fs: Sampling Frequency Window: Type of Window Function

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