Digital Representation of Audio InformationIntroduction Kevin D. Donohue
Question!
If a tree falls in the forest and nobody is there to hear it, will it make a sound?
Sound provided by http://www.therecordist.com/downloads.html
• Merriam-Webster Dictionary: • Sound a : a particular auditory impression
b : the sensation perceived by the sense of hearing c : mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium (as air) and is the objective cause of hearing.
Electronic Audio Systems
Amplification, Signal
Synthetic Audio: Imitating Nature
1780 Wolfgang von Kemplen’s Speaking Machine Mid 1800’s Charles Wheatstone Late 1800’s Alexander Graham Bell 1939 Homer Dudley’s Voder http://www.acoustics.hut.fi/~slemmett/wave/track01f.wav
1898 Thaddeus Cahill’s Telharmonium (First Music Synthesizer) 1919 Lev Theremin’s Theremin
Communication channels (acoustic and electric) 1874/1876 (Antonio Meucci’s) Alexander Graham Bell’s Telephone. 1940’s Homer Dudley’s Channel Vocoder first analysis-synthesis system
Voice-Coding Models The general speech model:
Speech sounds can be analyzed by determining the states of the vocal system components (vocal chords, track, lips, tongue … ) for each fundamental sound of speech (phoneme).
Unvoiced Speech
Voiced Speech
Spectral Analysis Voiced Speech Spectral envelop => vocal tract formants Harmonic peaks => vocal chord pitch
Time Analysis Voiced Speech Time envelop => Volume dynamics Oscillations => Vocal chord motion
Spectrogram Analysis
0 5 10 15
1920’s Radio Rex 1950’s (Bell Labs) Digit Recognition
Spectral/Formant analysis Filter Banks
1960’s Neural Networks 1970’s ARPA Project for Speech Understanding
Applications of spectral analysis methods FFT, Cepstral/homomorphic, LPC 1970’s Application of pattern matching methods DTW, and HMM
Speech Recognition
1980’s Standardize Training and Test with Large Corpora (TIMIT) (RM) (DARPA) New Front Ends (feature extractors) more perceptually based Dominance/Development of HMM Backpropagation and Neural Networks Rule-Base AI systems
Specification of Speech Recognition
Speaker dependent or independent Recognize isolated, continuous, or spot speech Vocabulary Size, Grammar Perplexity, Speaking style Recording conditions
Components of Speech Recognition
Input Speech Detected Speech String
Matlab Examples %% Create and play a 2 second 440 Hz tone in Matlab: fs = 8000; % Set a sampling frequency fq = 440; % frequency to play t = [0:round(2*fs)-1]/fs; % Sampled time axis sig = cos(2*pi*fq*t); % Create sampled signal soundsc(sig,fs) % Play it plot(t,sig); xlabel('Seconds'); ylabel('Amplitude') wavwrite(sig,fs,'t440.wav') clear % Remove all variables from work space
%% Reload tone and weight it with a decaying exponential of time constant .6 seconds tc = .6; % Set time constant [y, fs] = wavread('t440.wav'); % read in wave file t =[0:length(y)-1]'/fs; % Create sampled time axis dw = exp(-t/tc); % Compute sampled decaying exponential dsig = y.*dw; % Multiply sinusoid with decaying exponential soundsc(dsig,fs) plot(t,dsig); xlabel('Seconds'); ylabel('Amplitude')
Matlab Examples Explore demo and help files >> help script SCRIPT About MATLAB scripts and M-files.
A SCRIPT file is an external file that contains a sequence of MATLAB statements. By typing the filename, subsequent MATLAB input is obtained from the file. SCRIPT files have a filename extension of ".m" and are often called "M-files". To make a SCRIPT file into a function, see FUNCTION. See also type, echo. Reference page in Help browser
doc script In the help window (click on question mark) Go through section on
programming and then go to the demo tab and view a few of the demo.
Matlab Examples
• In class examples …
Matlab Exercise Use the sine/cosine function in Matlab to write a function that generates a minor scale (for testing the function use start tones between 100 and 440 Hz with a sampling rate of 8 kHz). Let the Matlab function input arguments be the starting frequency and the time interval for each scale tone in seconds. Let the output be a vector of samples that can be played with Matlab command “soundsc(v,8000)” (where v is the vector output of your function).
The frequency range of a scale covers one octave, which implies the last frequency is twice the starting frequency. On most fixed pitch instruments, 12 semi-tones or half steps make up the notes within an octave. A minor scale sequentially increases by a whole, half, whole, whole, half, whole, and whole (8 notes altogether – including the starting note).
Matlab Exercise - Scales Just Pythagorean Equal Temperament
Interval - 0 (1) 1/1 = 1 1 = 1 2^(0)=1
Interval - 1 16/15 256/243 2^(1/12)
Interval - 2 (2) 10/9 (or 9/8) 9/8 2^(2/12)
Interval - 3 (3) 6/5 32/27 2^(3/12)
Interval - 4 5/4 81/64 2^(4/12)
Interval - 5 (4) 4/3 4/3 2^(5/12)
Interval - 6 45/32 (or 64/45) 1024/729 (or 729/512) 2^(6/12)
Interval - 7 (5) 3/2 3/2 2^(7/12)
Interval - 8 (6) 8/5 128/81 2^(8/12)
Interval - 9 5/3 27/16 2^(9/12)
Interval - 10 (7) 7/4 (or 16/19 or 9/5) 16/9 2^(10/12)
Interval - 11 15/8 243/128 2^(11/12)
Interval - 12 (8) 2/1 = 2 2/1 = 2 2^(12/12) = 2
Matlab Exercise – Famous Notes Middle C = 261.626 Hz (standard tuning)
Concert A (A above middle C) = 440 Hz
Middle C = 256 Hz (Scientific tuning)
Lowest note on piano A=27.5 Hz
Highest note on piano C= 4186.009
EE513Audio Signals and Systems
Question!
Ambiguity!