EE513Audio Signals and Systems

Introduction

Kevin D. DonohueElectrical and Computer Engineering

University of Kentucky

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

Ambiguity!

• 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

Sound Sources – Vibrations at 20Hz-20kHz

Amplification, Signal

Conditioning

Electoacoustic Transducer

Processing for Intended

Application

Transmission Media

Storage

Information Extraction /

Measurement

Playback

Natural Audio Systems

Generation

Propagation

Amplification

Transduction

Information

Understa

nding

Synthetic Audio: Imitating Nature

1780 Wolfgang von Kemplen’s Speaking Machine U2B Mid 1800’s Charles Wheatstone MR Late 1800’s Alexander Graham Bell 1939 Homer Dudley’s Voder U2B

http://www.acoustics.hut.fi/~slemmett/wave/track01f.wav

1898 Thaddeus Cahill’s Telharmonium (First Music Synthesizer)

1919 Lev Theremin’s Theremin U2B1 and U2B2

Speech Analysis and Synthesis

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 ModelsThe 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

Quasi-Periodic

Pulsed Air

Air Burst or

Continuous flow

Voiced Speech

Vocal TractFilter

Vocal Radiator

Spectral Analysis Voiced Speech Spectral envelop => vocal tract formantsHarmonic peaks => vocal chord pitch

0 1000 2000 3000 4000-120

-100

-80

-60

-40Spectrum of Speech Segment - ah

Hertz

dB

Time Analysis Voiced Speech Time envelop => Volume dynamicsOscillations => Vocal chord motion

0 50 100 150 200 250-0.1

-0.05

0

0.05

0.1

Milliseconds

Am

plit

ud

e

Waveform of Speech Segment - ah

12 ms 83 Hz

0.5 1 1.5 2 2.5 3 3.5 4 4.50

1000

2000

3000

4000

-50

-40

-30

-20

-10

0

10

20

Spectrogram Analysis

Time

Fre

qu

ency

There shoeold

doShelived

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

0

1

Spectogram of CD sound

2 4 6 8 10 12 140

2000

4000

6000

8000

10000

-20

-15

-10

-5

0

5

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25

0 2 4 6 8 10 12 14 16 18-2

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Time

Fre

qu

ency

Speech Recognition

1920’s Radio Rex1950’s (Bell Labs) Digit Recognition

Spectral/Formant analysisFilter Banks

1960’s Neural Networks1970’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’sStandardize Training and Test with Large

Corpora (TIMIT) (RM) (DARPA)New Front Ends (feature extractors) more

perceptually basedDominance/Development of HMMBackpropagation and Neural Networks U2BRule-Base AI systems

Specification of Speech Recognition

Speaker dependent or independentRecognize isolated, continuous, or spot

speechVocabulary Size, Grammar Perplexity,

Speaking styleRecording conditions

Components of Speech Recognition

Speech Transduction Acoustic/Electronic

Front End

Local Match

Global Detector Language Model

Input SpeechDetected SpeechString

Matlab Examples%% Create and play a 2 second 440 Hz tone in Matlab:fs = 8000; % Set a sampling frequencyfq = 440; % frequency to playt = [0:round(2*fs)-1]/fs; % Sampled time axissig = cos(2*pi*fq*t); % Create sampled signalsoundsc(sig,fs) % Play itplot(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 secondstc = .6; % Set time constant[y, fs] = wavread('t440.wav'); % read in wave filet =[0:length(y)-1]'/fs; % Create sampled time axisdw = exp(-t/tc); % Compute sampled decaying exponentialdsig = y.*dw; % Multiply sinusoid with decaying exponentialsoundsc(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 scriptIn 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 Dorian 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 - ScalesJust 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