1. Spectral Analysis & Spectrogram
SASPL
Cheolwoo Jo

2. Contents Spectral Analysis Spectrogram Analysis of Spectrogram
Narrow Band
Wide Band
Analysis of Spectrogram
AR, MA, ARMA model of Speech

3. Spectral Analysis

4. 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

5. 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

6. 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;

7. 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;

8. Spectrogram level scaling
Log|x[k]|2
Gray Intensity
Black
Log Energy(dB)
White
60dB

9. Specgram SPECGRAM(A,F,Fs,WINDOW) Matlab A: Speech
F: Vector of Frequencies
Fs: Sampling Frequency
Window: Type of Window Function