Lab 6: Sound Analysis Fourier Synthesis Fourier Analysis

Slides:



Advertisements
Similar presentations
For more ppt’s, visit Fourier Series For more ppt’s, visit
Advertisements

DCSP-3: Fourier Transform (continuous time) Jianfeng Feng
DCSP-3: Fourier Transform Jianfeng Feng Department of Computer Science Warwick Univ., UK
IntroductionIntroduction Most musical sounds are periodic, and are composed of a collection of harmonic sine waves.Most musical sounds are periodic, and.
Fourier Series 主講者:虞台文.
Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 8 Harmonic Series Unit 1 Session 8 Harmonic Series.
Fourier Transform – Chapter 13. Image space Cameras (regardless of wave lengths) create images in the spatial domain Pixels represent features (intensity,
Harmonic Series and Spectrograms 220 Hz (A3) Why do they sound different? Instrument 1 Instrument 2Sine Wave.
Math Review with Matlab:
Wave Physics PHYS 2023 Tim Freegarde 2 Spectrum periodic waveform can be expressed as a superposition of harmonics amplitude or intensity commonly represented.
Sound waves and Perception of sound Lecture 8 Pre-reading : §16.3.
A.Diederich– International University Bremen – USC – MMM Spring Sound waves cont'd –Goldstein, pp. 331 – 339 –Cook, Chapter 7.
Pressure waves in open pipe Pressure waves in pipe closed at one end.
Dr. Jie ZouPHY Chapter 8 (Hall) Sound Spectra.
Intro to Fourier Analysis Definition Analysis of periodic waves Analysis of aperiodic waves Digitization Time-frequency uncertainty.
Signals Processing Second Meeting. Fourier's theorem: Analysis Fourier analysis is the process of analyzing periodic non-sinusoidal waveforms in order.
S. Mandayam/ ECOMMS/ECE Dept./Rowan University Signals & Systems & Music ECE Spring 2010 Shreekanth Mandayam ECE Department Rowan University March.
Fourier Analysis D. Gordon E. Robertson, PhD, FCSB School of Human Kinetics University of Ottawa.
Waveform and Spectrum A visual Fourier Analysis. String with fixed ends.
Fourier Series. is the “fundamental frequency” Fourier Series is the “fundamental frequency”
Transmitting Signals First Meeting. Signal Processing: Sinewaves Sinewave is a fundamental tool in many areas of science, engineering and mathematics.
Square wave Fourier Analysis + + = Adding sines with multiple frequencies we can reproduce ANY shape.
CH#3 Fourier Series and Transform
Chapter 25 Nonsinusoidal Waveforms. 2 Waveforms Used in electronics except for sinusoidal Any periodic waveform may be expressed as –Sum of a series of.
EGR 1101 Unit 6 Sinusoids in Engineering (Chapter 6 of Rattan/Klingbeil text)
Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.
Physics 1200 Review Questions Tuning and Timbre May 14, 2012.
EE2010 Fundamentals of Electric Circuits Lecture 13 Sinusoidal sources and the concept of phasor in circuit analysis.
Harmonic Series and Spectrograms
Fourier Concepts ES3 © 2001 KEDMI Scientific Computing. All Rights Reserved. Square wave example: V(t)= 4/  sin(t) + 4/3  sin(3t) + 4/5  sin(5t) +
Fourier series. The frequency domain It is sometimes preferable to work in the frequency domain rather than time –Some mathematical operations are easier.
Fundamentals of Electric Circuits Chapter 17
Chapter 17 The Fourier Series
CH. 21 Musical Sounds. Musical Tones have three main characteristics 1)Pitch 2) Loudness 3)Quality.
ENE 208: Electrical Engineering Mathematics Fourier Series.
WELCOME to Physics is Phun. Please be Seated Physics Lecture-Demonstration Web Site Summer Programs for Youth Physics Olympics Physics Question of the.
Periodic driving forces
Signals & Systems Lecture 13: Chapter 3 Spectrum Representation.
Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 7 Good Vibrations Unit 1 Session 7 Good Vibrations.
12/2/2015 Fourier Series - Supplemental Notes A Fourier series is a sum of sine and cosine harmonic functions that approximates a repetitive (periodic)
Sinusoid Seventeenth Meeting. Sine Wave: Amplitude The amplitude is the maximum displacement of the sine wave from its mean (average) position. Simulation.
Harmonic Series and Spectrograms BY JORDAN KEARNS (W&L ‘14) & JON ERICKSON (STILL HERE )
Sin & Cos with Amplitude and Phase.. In the equation, 2 is a multiplier and called an amplitude. Amplitude describes the “height” of the trigonometric.
3.3 Waves and Stuff Science of Music 2007 Last Time  Dr. Koons talked about consonance and beats.  Let’s take a quick look & listen at what this means.
The Spectrum n Jean Baptiste Fourier ( ) discovered a fundamental tenet of wave theory.
Basic Acoustics. Sound – your ears’ response to vibrations in the air. Sound waves are three dimensional traveling in all directions. Think of dropping.
EEE 332 COMMUNICATION Fourier Series Text book: Louis E. Frenzel. Jr. Principles of Electronic Communication Systems, Third Ed. Mc Graw Hill.
FCI. Faculty of Computer and Information Fayoum University FCI.
Intro to Fourier Series BY JORDAN KEARNS (W&L ‘14) & JON ERICKSON (STILL HERE )
Fourier analysis Periodic function: Any (“reasonable”) periodic function, can be written as a series of sines and cosines “vibrations”, whose frequencies.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
Electrical Circuits Dr inż. Agnieszka Wardzińska Room: 105 Polanka
Signal Fndamentals Analogue, Discrete and Digital Signals
Fourier’s Theorem.
Things that make strange noises. October 27, 2004
Continuous-Time Signal Analysis
For a periodic complex sound
Standing waves standing waves on a string: RESONANCE:
Intro to Fourier Series
Lecture 35 Wave spectrum Fourier series Fourier analysis
Speech Pathologist #10.
Wavetable Synthesis.
Digital Signal Processing
7.2 Even and Odd Fourier Transforms phase of signal frequencies
Lecture 5: Phasor Addition & Spectral Representation
Graphs of Sine and Cosine: Sinusoids
C H A P T E R 21 Fourier Series.
Discrete Fourier Transform
Linear Combinations of Sinusoids
Complex Waveforms HNC/D Engineering.
Presentation transcript:

Lab 6: Sound Analysis Fourier Synthesis Fourier Analysis Two Sine Waves of the Same Frequency Building a Square Wave from Sine Waves Does One Hear Phase? Fourier Analysis Fourier Analysis of Sine Waves Fourier Spectrum of the Square Wave Fourier Analysis of Your Voice online manual printed manual Red – use tabletop devises Magenta – use tabletop devises and java applet Blue – use java applet

Waveform (Wave Shape) Is it voice or musical instrument?

Sound of Musical Instruments Waveform superposition of harmonics amplitude (A) and period (T) quality of sound indiscernible Fourier spectrum Fourier components (harmonics) amplitude (A) and frequency ( f ) unique to each instrument

Fourier Theorem “Any periodic function of period T can be expressed as a sum of sine curves whose frequencies are multiples of f = 1/T and whose amplitude and phase are suitably chosen.” (textbook)

Concepts Superposition Phase Periodic non-sinusoidal wave Fourier Spectrum

Superposition (1) t S 1 -1 2 -2 3 -3 A B

Superposition (2) A B S t 3 2 1 -1 -2 0 + (-2) = -2 -3 1 -1 2 -2 3 -3 A B 0 + (-2) = -2 (+1.4) + (-1.4) = 0

Superposition (3) t S 1 -1 2 -2 3 -3 A B

Sine function: S = sin(360 · f · t) Phase of Sine Wave t S 90 180 270 0 1 -1 Sine function: S = sin(360 · f · t) Phase angle “(360 · f · t)” 0 90 180 270 360 or 0 Value of sine S 1 -1

Phase Shift Phase shift  : phase of sine curve at t = 0 180 0 90 A 270 0 Phase shift  : phase of sine curve at t = 0 t S A 0 t S 180 t S 90

Two Sine Waves of Same Frequency In phase t S 1 -1 180° out of phase t S 1 -1 180°

Fourier Synthesis + + + Superposition (Fourier synthesis) S: A periodic wave having the frequency f1 and period T fn: Frequency of the nth mode that is an integer multiple of f1 (= n·f1) fn: Phase of the nth mode at t = 0 t t t t + + + t Superposition (Fourier synthesis) Fourier analysis

t = 0 t=0