Analyzing Musical Sound
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Lab 12. Vibrating Strings
Lab 12. Vibrating Strings Goals • To experimentally determine the relationships between the fundamental resonant frequency of a vibrating string and its length, its mass per unit length, and the tension in the string. • To introduce a useful graphical method for testing whether the quantities x and y are related by a “simple power function” of the form y = axn. If so, the constants a and n can be determined from the graph. • To experimentally determine the relationship between resonant frequencies and higher order “mode” numbers. • To develop one general relationship/equation that relates the resonant frequency of a string to the four parameters: length, mass per unit length, tension, and mode number. Introduction Vibrating strings are part of our common experience. Which as you may have learned by now means that you have built up explanations in your subconscious about how they work, and that those explanations are sometimes self-contradictory, and rarely entirely correct. Musical instruments from all around the world employ vibrating strings to make musical sounds. Anyone who plays such an instrument knows that changing the tension in the string changes the pitch, which in physics terms means changing the resonant frequency of vibration. Similarly, changing the thickness (and thus the mass) of the string also affects its sound (frequency). String length must also have some effect, since a bass violin is much bigger than a normal violin and sounds much different. The interplay between these factors is explored in this laboratory experi- ment. You do not need to know physics to understand how instruments work. In fact, in the course of this lab alone you will engage with material which entire PhDs in music theory have been written. -
Enhance Your DSP Course with These Interesting Projects
AC 2012-3836: ENHANCE YOUR DSP COURSE WITH THESE INTER- ESTING PROJECTS Dr. Joseph P. Hoffbeck, University of Portland Joseph P. Hoffbeck is an Associate Professor of electrical engineering at the University of Portland in Portland, Ore. He has a Ph.D. from Purdue University, West Lafayette, Ind. He previously worked with digital cell phone systems at Lucent Technologies (formerly AT&T Bell Labs) in Whippany, N.J. His technical interests include communication systems, digital signal processing, and remote sensing. Page 25.566.1 Page c American Society for Engineering Education, 2012 Enhance your DSP Course with these Interesting Projects Abstract Students are often more interested learning technical material if they can see useful applications for it, and in digital signal processing (DSP) it is possible to develop homework assignments, projects, or lab exercises to show how the techniques can be used in realistic situations. This paper presents six simple, yet interesting projects that are used in the author’s undergraduate digital signal processing course with the objective of motivating the students to learn how to use the Fast Fourier Transform (FFT) and how to design digital filters. Four of the projects are based on the FFT, including a simple voice recognition algorithm that determines if an audio recording contains “yes” or “no”, a program to decode dual-tone multi-frequency (DTMF) signals, a project to determine which note is played by a musical instrument and if it is sharp or flat, and a project to check the claim that cars honk in the tone of F. Two of the projects involve designing filters to eliminate noise from audio recordings, including designing a lowpass filter to remove a truck backup beeper from a recording of an owl hooting and designing a highpass filter to remove jet engine noise from a recording of birds chirping. -
The Physics of Sound 1
The Physics of Sound 1 The Physics of Sound Sound lies at the very center of speech communication. A sound wave is both the end product of the speech production mechanism and the primary source of raw material used by the listener to recover the speaker's message. Because of the central role played by sound in speech communication, it is important to have a good understanding of how sound is produced, modified, and measured. The purpose of this chapter will be to review some basic principles underlying the physics of sound, with a particular focus on two ideas that play an especially important role in both speech and hearing: the concept of the spectrum and acoustic filtering. The speech production mechanism is a kind of assembly line that operates by generating some relatively simple sounds consisting of various combinations of buzzes, hisses, and pops, and then filtering those sounds by making a number of fine adjustments to the tongue, lips, jaw, soft palate, and other articulators. We will also see that a crucial step at the receiving end occurs when the ear breaks this complex sound into its individual frequency components in much the same way that a prism breaks white light into components of different optical frequencies. Before getting into these ideas it is first necessary to cover the basic principles of vibration and sound propagation. Sound and Vibration A sound wave is an air pressure disturbance that results from vibration. The vibration can come from a tuning fork, a guitar string, the column of air in an organ pipe, the head (or rim) of a snare drum, steam escaping from a radiator, the reed on a clarinet, the diaphragm of a loudspeaker, the vocal cords, or virtually anything that vibrates in a frequency range that is audible to a listener (roughly 20 to 20,000 cycles per second for humans). -
4 – Synthesis and Analysis of Complex Waves; Fourier Spectra
4 – Synthesis and Analysis of Complex Waves; Fourier spectra Complex waves Many physical systems (such as music instruments) allow existence of a particular set of standing waves with the frequency spectrum consisting of the fundamental (minimal allowed) frequency f1 and the overtones or harmonics fn that are multiples of f1, that is, fn = n f1, n=2,3,…The amplitudes of the harmonics An depend on how exactly the system is excited (plucking a guitar string at the middle or near an end). The sound emitted by the system and registered by our ears is thus a complex wave (or, more precisely, a complex oscillation ), or just signal, that has the general form nmax = π +ϕ = 1 W (t) ∑ An sin( 2 ntf n ), periodic with period T n=1 f1 Plots of W(t) that can look complicated are called wave forms . The maximal number of harmonics nmax is actually infinite but we can take a finite number of harmonics to synthesize a complex wave. ϕ The phases n influence the wave form a lot, visually, but the human ear is insensitive to them (the psychoacoustical Ohm‘s law). What the ear hears is the fundamental frequency (even if it is missing in the wave form, A1=0 !) and the amplitudes An that determine the sound quality or timbre . 1 Examples of synthesis of complex waves 1 1. Triangular wave: A = for n odd and zero for n even (plotted for f1=500) n n2 W W nmax =1, pure sinusoidal 1 nmax =3 1 0.5 0.5 t 0.001 0.002 0.003 0.004 t 0.001 0.002 0.003 0.004 £ 0.5 ¢ 0.5 £ 1 ¢ 1 W W n =11, cos ¤ sin 1 nmax =11 max 0.75 0.5 0.5 0.25 t 0.001 0.002 0.003 0.004 t 0.001 0.002 0.003 0.004 ¡ 0.5 0.25 0.5 ¡ 1 Acoustically equivalent 2 0.75 1 1. -
Lecture 1-10: Spectrograms
Lecture 1-10: Spectrograms Overview 1. Spectra of dynamic signals: like many real world signals, speech changes in quality with time. But so far the only spectral analysis we have performed has assumed that the signal is stationary: that it has constant quality. We need a new kind of analysis for dynamic signals. A suitable analogy is that we have spectral ‘snapshots’ when what we really want is a spectral ‘movie’. Just like a real movie is made up from a series of still frames, we can display the spectral properties of a changing signal through a series of spectral snapshots. 2. The spectrogram: a spectrogram is built from a sequence of spectra by stacking them together in time and by compressing the amplitude axis into a 'contour map' drawn in a grey scale. The final graph has time along the horizontal axis, frequency along the vertical axis, and the amplitude of the signal at any given time and frequency is shown as a grey level. Conventionally, black is used to signal the most energy, while white is used to signal the least. 3. Spectra of short and long waveform sections: we will get a different type of movie if we choose each of our snapshots to be of relatively short sections of the signal, as opposed to relatively long sections. This is because the spectrum of a section of speech signal that is less than one pitch period long will tend to show formant peaks; while the spectrum of a longer section encompassing several pitch periods will show the individual harmonics, see figure 1-10.1. -
The Musical Kinetic Shape: a Variable Tension String Instrument
The Musical Kinetic Shape: AVariableTensionStringInstrument Ismet Handˇzi´c, Kyle B. Reed University of South Florida, Department of Mechanical Engineering, Tampa, Florida Abstract In this article we present a novel variable tension string instrument which relies on a kinetic shape to actively alter the tension of a fixed length taut string. We derived a mathematical model that relates the two-dimensional kinetic shape equation to the string’s physical and dynamic parameters. With this model we designed and constructed an automated instrument that is able to play frequencies within predicted and recognizable frequencies. This prototype instrument is also able to play programmed melodies. Keywords: musical instrument, variable tension, kinetic shape, string vibration 1. Introduction It is possible to vary the fundamental natural oscillation frequency of a taut and uniform string by either changing the string’s length, linear density, or tension. Most string musical instruments produce di↵erent tones by either altering string length (fretting) or playing preset and di↵erent string gages and string tensions. Although tension can be used to adjust the frequency of a string, it is typically only used in this way for fine tuning the preset tension needed to generate a specific note frequency. In this article, we present a novel string instrument concept that is able to continuously change the fundamental oscillation frequency of a plucked (or bowed) string by altering string tension in a controlled and predicted Email addresses: [email protected] (Ismet Handˇzi´c), [email protected] (Kyle B. Reed) URL: http://reedlab.eng.usf.edu/ () Preprint submitted to Applied Acoustics April 19, 2014 Figure 1: The musical kinetic shape variable tension string instrument prototype. -
Analysis of EEG Signal Processing Techniques Based on Spectrograms
ISSN 1870-4069 Analysis of EEG Signal Processing Techniques based on Spectrograms Ricardo Ramos-Aguilar, J. Arturo Olvera-López, Ivan Olmos-Pineda Benemérita Universidad Autónoma de Puebla, Faculty of Computer Science, Puebla, Mexico [email protected],{aolvera, iolmos}@cs.buap.mx Abstract. Current approaches for the processing and analysis of EEG signals consist mainly of three phases: preprocessing, feature extraction, and classifica- tion. The analysis of EEG signals is through different domains: time, frequency, or time-frequency; the former is the most common, while the latter shows com- petitive results, implementing different techniques with several advantages in analysis. This paper aims to present a general description of works and method- ologies of EEG signal analysis in time-frequency, using Short Time Fourier Transform (STFT) as a representation or a spectrogram to analyze EEG signals. Keywords. EEG signals, spectrogram, short time Fourier transform. 1 Introduction The human brain is one of the most complex organs in the human body. It is considered the center of the human nervous system and controls different organs and functions, such as the pumping of the heart, the secretion of glands, breathing, and internal tem- perature. Cells called neurons are the basic units of the brain, which send electrical signals to control the human body and can be measured using Electroencephalography (EEG). Electroencephalography measures the electrical activity of the brain by recording via electrodes placed either on the scalp or on the cortex. These time-varying records produce potential differences because of the electrical cerebral activity. The signal generated by this electrical activity is a complex random signal and is non-stationary [1]. -
AN INTRODUCTION to MUSIC THEORY Revision A
AN INTRODUCTION TO MUSIC THEORY Revision A By Tom Irvine Email: [email protected] July 4, 2002 ________________________________________________________________________ Historical Background Pythagoras of Samos was a Greek philosopher and mathematician, who lived from approximately 560 to 480 BC. Pythagoras and his followers believed that all relations could be reduced to numerical relations. This conclusion stemmed from observations in music, mathematics, and astronomy. Pythagoras studied the sound produced by vibrating strings. He subjected two strings to equal tension. He then divided one string exactly in half. When he plucked each string, he discovered that the shorter string produced a pitch which was one octave higher than the longer string. A one-octave separation occurs when the higher frequency is twice the lower frequency. German scientist Hermann Helmholtz (1821-1894) made further contributions to music theory. Helmholtz wrote “On the Sensations of Tone” to establish the scientific basis of musical theory. Natural Frequencies of Strings A note played on a string has a fundamental frequency, which is its lowest natural frequency. The note also has overtones at consecutive integer multiples of its fundamental frequency. Plucking a string thus excites a number of tones. Ratios The theories of Pythagoras and Helmholz depend on the frequency ratios shown in Table 1. Table 1. Standard Frequency Ratios Ratio Name 1:1 Unison 1:2 Octave 1:3 Twelfth 2:3 Fifth 3:4 Fourth 4:5 Major Third 3:5 Major Sixth 5:6 Minor Third 5:8 Minor Sixth 1 These ratios apply both to a fundamental frequency and its overtones, as well as to relationship between separate keys. -
Improved Spectrograms Using the Discrete Fractional Fourier Transform
IMPROVED SPECTROGRAMS USING THE DISCRETE FRACTIONAL FOURIER TRANSFORM Oktay Agcaoglu, Balu Santhanam, and Majeed Hayat Department of Electrical and Computer Engineering University of New Mexico, Albuquerque, New Mexico 87131 oktay, [email protected], [email protected] ABSTRACT in this plane, while the FrFT can generate signal representations at The conventional spectrogram is a commonly employed, time- any angle of rotation in the plane [4]. The eigenfunctions of the FrFT frequency tool for stationary and sinusoidal signal analysis. How- are Hermite-Gauss functions, which result in a kernel composed of ever, it is unsuitable for general non-stationary signal analysis [1]. chirps. When The FrFT is applied on a chirp signal, an impulse in In recent work [2], a slanted spectrogram that is based on the the chirp rate-frequency plane is produced [5]. The coordinates of discrete Fractional Fourier transform was proposed for multicompo- this impulse gives us the center frequency and the chirp rate of the nent chirp analysis, when the components are harmonically related. signal. In this paper, we extend the slanted spectrogram framework to Discrete versions of the Fractional Fourier transform (DFrFT) non-harmonic chirp components using both piece-wise linear and have been developed by several researchers and the general form of polynomial fitted methods. Simulation results on synthetic chirps, the transform is given by [3]: SAR-related chirps, and natural signals such as the bat echolocation 2α 2α H Xα = W π x = VΛ π V x (1) and bird song signals, indicate that these generalized slanted spectro- grams provide sharper features when the chirps are not harmonically where W is a DFT matrix, V is a matrix of DFT eigenvectors and related. -
Attention, I'm Trying to Speak Cs224n Project: Speech Synthesis
Attention, I’m Trying to Speak CS224n Project: Speech Synthesis Akash Mahajan Management Science & Engineering Stanford University [email protected] Abstract We implement an end-to-end parametric text-to-speech synthesis model that pro- duces audio from a sequence of input characters, and demonstrate that it is possi- ble to build a convolutional sequence to sequence model with reasonably natural voice and pronunciation from scratch in well under $75. We observe training the attention to be a bottleneck and experiment with 2 modifications. We also note interesting model behavior and insights during our training process. Code for this project is available on: https://github.com/akashmjn/cs224n-gpu-that-talks. 1 Introduction We have come a long way from the ominous robotic sounding voices used in the Radiohead classic 1. If we are to build significant voice interfaces, we need to also have good feedback that can com- municate with us clearly, that can be setup cheaply for different languages and dialects. There has recently also been an increased interest in generative models for audio [6] that could have applica- tions beyond speech to music and other signal-like data. As discussed in [13] it is fascinating that is is possible at all for an end-to-end model to convert a highly ”compressed” source - text - into a substantially more ”decompressed” form - audio. This is a testament to the sheer power and flexibility of deep learning models, and has been an interesting and surprising insight in itself. Recently, results from Tachibana et. al. [11] reportedly produce reasonable-quality speech without requiring as large computational resources as Tacotron [13] and Wavenet [7]. -
Time-Frequency Analysis of Time-Varying Signals and Non-Stationary Processes
Time-Frequency Analysis of Time-Varying Signals and Non-Stationary Processes An Introduction Maria Sandsten 2020 CENTRUM SCIENTIARUM MATHEMATICARUM Centre for Mathematical Sciences Contents 1 Introduction 3 1.1 Spectral analysis history . 3 1.2 A time-frequency motivation example . 5 2 The spectrogram 9 2.1 Spectrum analysis . 9 2.2 The uncertainty principle . 10 2.3 STFT and spectrogram . 12 2.4 Gabor expansion . 14 2.5 Wavelet transform and scalogram . 17 2.6 Other transforms . 19 3 The Wigner distribution 21 3.1 Wigner distribution and Wigner spectrum . 21 3.2 Properties of the Wigner distribution . 23 3.3 Some special signals. 24 3.4 Time-frequency concentration . 25 3.5 Cross-terms . 27 3.6 Discrete Wigner distribution . 29 4 The ambiguity function and other representations 35 4.1 The four time-frequency domains . 35 4.2 Ambiguity function . 39 4.3 Doppler-frequency distribution . 44 5 Ambiguity kernels and the quadratic class 45 5.1 Ambiguity kernel . 45 5.2 Properties of the ambiguity kernel . 46 5.3 The Choi-Williams distribution . 48 5.4 Separable kernels . 52 1 Maria Sandsten CONTENTS 5.5 The Rihaczek distribution . 54 5.6 Kernel interpretation of the spectrogram . 57 5.7 Multitaper time-frequency analysis . 58 6 Optimal resolution of time-frequency spectra 61 6.1 Concentration measures . 61 6.2 Instantaneous frequency . 63 6.3 The reassignment technique . 65 6.4 Scaled reassigned spectrogram . 69 6.5 Other modern techniques for optimal resolution . 72 7 Stochastic time-frequency analysis 75 7.1 Definitions of non-stationary processes . -
On the Use of Time–Frequency Reassignment in Additive Sound Modeling*
PAPERS On the Use of Time–Frequency Reassignment in Additive Sound Modeling* KELLY FITZ, AES Member AND LIPPOLD HAKEN, AES Member Department of Electrical Engineering and Computer Science, Washington University, Pulman, WA 99164 A method of reassignment in sound modeling to produce a sharper, more robust additive representation is introduced. The reassigned bandwidth-enhanced additive model follows ridges in a time–frequency analysis to construct partials having both sinusoidal and noise characteristics. This model yields greater resolution in time and frequency than is possible using conventional additive techniques, and better preserves the temporal envelope of transient signals, even in modified reconstruction, without introducing new component types or cumbersome phase interpolation algorithms. 0INTRODUCTION manipulations [11], [12]. Peeters and Rodet [3] have developed a hybrid analysis/synthesis system that eschews The method of reassignment has been used to sharpen high-level transient models and retains unabridged OLA spectrograms in order to make them more readable [1], [2], (overlap–add) frame data at transient positions. This to measure sinusoidality, and to ensure optimal window hybrid representation represents unmodified transients per- alignment in the analysis of musical signals [3]. We use fectly, but also sacrifices homogeneity. Quatieri et al. [13] time–frequency reassignment to improve our bandwidth- propose a method for preserving the temporal envelope of enhanced additive sound model. The bandwidth-enhanced short-duration complex acoustic signals using a homoge- additive representation is in some way similar to tradi- neous sinusoidal model, but it is inapplicable to sounds of tional sinusoidal models [4]–[6] in that a waveform is longer duration, or sounds having multiple transient events.