Spectral Analysis – Fourier Decomposition
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Effect of Moisture Distribution on Velocity and Waveform of Ultrasonic-Wave Propagation in Mortar
materials Article Effect of Moisture Distribution on Velocity and Waveform of Ultrasonic-Wave Propagation in Mortar Shinichiro Okazaki 1,* , Hiroma Iwase 2, Hiroyuki Nakagawa 3, Hidenori Yoshida 1 and Ryosuke Hinei 4 1 Faculty of Engineering and Design, Kagawa University, 2217-20 Hayashi, Takamatsu, Kagawa 761-0396, Japan; [email protected] 2 Chuo Consultants, 2-11-23 Nakono, Nishi-ku, Nagoya, Aichi 451-0042, Japan; [email protected] 3 Shikoku Research Institute Inc., 2109-8 Yashima, Takamatsu, Kagawa 761-0113, Japan; [email protected] 4 Building Engineering Group, Civil Engineering and Construction Department, Shikoku Electric Power Co., Inc., 2-5 Marunouchi, Takamatsu, Kagawa 760-8573, Japan; [email protected] * Correspondence: [email protected] Abstract: Considering that the ultrasonic method is applied for the quality evaluation of concrete, this study experimentally and numerically investigates the effect of inhomogeneity caused by changes in the moisture content of concrete on ultrasonic wave propagation. The experimental results demonstrate that the propagation velocity and amplitude of the ultrasonic wave vary for different moisture content distributions in the specimens. In the analytical study, the characteristics obtained experimentally are reproduced by modeling a system in which the moisture content varies between the surface layer and interior of concrete. Keywords: concrete; ultrasonic; water content; elastic modulus Citation: Okazaki, S.; Iwase, H.; 1. Introduction Nakagawa, H.; Yoshida, H.; Hinei, R. Effect of Moisture Distribution on As many infrastructures deteriorate at an early stage, long-term structure management Velocity and Waveform of is required. If structural deterioration can be detected as early as possible, the scale of Ultrasonic-Wave Propagation in repair can be reduced, decreasing maintenance costs [1]. -
Introduction to Noise Radar and Its Waveforms
sensors Article Introduction to Noise Radar and Its Waveforms Francesco De Palo 1, Gaspare Galati 2 , Gabriele Pavan 2,* , Christoph Wasserzier 3 and Kubilay Savci 4 1 Department of Electronic Engineering, Tor Vergata University of Rome, now with Rheinmetall Italy, 00131 Rome, Italy; [email protected] 2 Department of Electronic Engineering, Tor Vergata University and CNIT-Consortium for Telecommunications, Research Unit of Tor Vergata University of Rome, 00133 Rome, Italy; [email protected] 3 Fraunhofer Institute for High Frequency Physics and Radar Techniques FHR, 53343 Wachtberg, Germany; [email protected] 4 Turkish Naval Research Center Command and Koc University, Istanbul, 34450 Istanbul,˙ Turkey; [email protected] * Correspondence: [email protected] Received: 31 July 2020; Accepted: 7 September 2020; Published: 11 September 2020 Abstract: In the system-level design for both conventional radars and noise radars, a fundamental element is the use of waveforms suited to the particular application. In the military arena, low probability of intercept (LPI) and of exploitation (LPE) by the enemy are required, while in the civil context, the spectrum occupancy is a more and more important requirement, because of the growing request by non-radar applications; hence, a plurality of nearby radars may be obliged to transmit in the same band. All these requirements are satisfied by noise radar technology. After an overview of the main noise radar features and design problems, this paper summarizes recent developments in “tailoring” pseudo-random sequences plus a novel tailoring method aiming for an increase of detection performance whilst enabling to produce a (virtually) unlimited number of noise-like waveforms usable in different applications. -
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). -
Tracking of High-Speed, Non-Smooth and Microscale-Amplitude Wave Trajectories
Tracking of High-speed, Non-smooth and Microscale-amplitude Wave Trajectories Jiradech Kongthon Department of Mechatronics Engineering, Assumption University, Suvarnabhumi Campus, Samuthprakarn, Thailand Keywords: High-speed Tracking, Inversion-based Control, Microscale Positioning, Reduced-order Inverse, Tracking. Abstract: In this article, an inversion-based control approach is proposed and presented for tracking desired trajectories with high-speed (100Hz), non-smooth (triangle and sawtooth waves), and microscale-amplitude (10 micron) wave forms. The interesting challenge is that the tracking involves the trajectories that possess a high frequency, a microscale amplitude, sharp turnarounds at the corners. Two different types of wave trajectories, which are triangle and sawtooth waves, are investigated. The model, or the transfer function of a piezoactuator is obtained experimentally from the frequency response by using a dynamic signal analyzer. Under the inversion-based control scheme and the model obtained, the tracking is simulated in MATLAB. The main contributions of this work are to show that (1) the model and the controller achieve a good tracking performance measured by the root mean square error (RMSE) and the maximum error (Emax), (2) the maximum error occurs at the sharp corner of the trajectories, (3) tracking the sawtooth wave yields larger RMSE and Emax values,compared to tracking the triangle wave, and (4) in terms of robustness to modeling error or unmodeled dynamics, Emax is still less than 10% of the peak to peak amplitude of 20 micron if the increases in the natural frequency and the damping ratio are less than 5% for the triangle trajectory and Emax is still less than 10% of the peak to peak amplitude of 20 micron if the increases in the natural frequency and the damping ratio are less than 3.2 % for the sawtooth trajectory. -
Verified Design Analog Pulse Width Modulation
John Caldwell TI Precision Designs: Verified Design Analog Pulse Width Modulation TI Precision Designs Circuit Description TI Precision Designs are analog solutions created by This circuit utilizes a triangle wave generator and TI’s analog experts. Verified Designs offer the theory, comparator to generate a pulse-width-modulated component selection, simulation, complete PCB (PWM) waveform with a duty cycle that is inversely schematic & layout, bill of materials, and measured proportional to the input voltage. An op amp and performance of useful circuits. Circuit modifications comparator generate a triangular waveform which is that help to meet alternate design goals are also passed to the inverting input of a second comparator. discussed. By passing the input voltage to the non-inverting comparator input, a PWM waveform is produced. Negative feedback of the PWM waveform to an error amplifier is utilized to ensure high accuracy and linearity of the output Design Resources Ask The Analog Experts Design Archive All Design files WEBENCH® Design Center TINA-TI™ SPICE Simulator TI Precision Designs Library OPA2365 Product Folder TLV3502 Product Folder REF3325 Product Folder R4 C1 VCC R3 - VPWM + VIN VREF R1 + ++ + U1A - U2A V R2 C2 CC VTRI C3 R7 - ++ U1B VREF VCC VREF - ++ U2B VCC R6 R5 An IMPORTANT NOTICE at the end of this TI reference design addresses authorized use, intellectual property matters and other important disclaimers and information. TINA-TI is a trademark of Texas Instruments WEBENCH is a registered trademark of Texas Instruments SLAU508-June 2013-Revised June 2013 Analog Pulse Width Modulation 1 Copyright © 2013, Texas Instruments Incorporated www.ti.com 1 Design Summary The design requirements are as follows: Supply voltage: 5 Vdc Input voltage: -2 V to +2 V, dc coupled Output: 5 V, 500 kHz PWM Ideal transfer function: V The design goals and performance are summarized in Table 1. -
Music Synthesis
MUSIC SYNTHESIS Sound synthesis is the art of using electronic devices to create & modify signals that are then turned into sound waves by a speaker. Making Waves: WGRL - 2015 Oscillators An oscillator generates a consistent, repeating signal. Signals from oscillators and other sources are used to control the movement of the cones in our speakers, which make real sound waves which travel to our ears. An oscillator wiggles an audio signal. DEMONSTRATE: If you tie one end of a rope to a doorknob, stand back a few feet, and wiggle the other end of the rope up and down really fast, you're doing roughly the same thing as an oscillator. REVIEW: Frequency and pitch Frequency, measured in cycles/second AKA Hertz, is the rate at which a sound wave moves in and out. The length of a signal cycle of a waveform is the span of time it takes for that waveform to repeat. People generally hear an increase in the frequency of a sound wave as an increase in pitch. F DEMONSTRATE: an oscillator generating a signal that repeats at the rate of 440 cycles per second will have the same pitch as middle A on a piano. An oscillator generating a signal that repeats at 880 cycles per second will have the same pitch as the A an octave above middle A. Types of Waveforms: SINE The SINE wave is the most basic, pure waveform. These simple waves have only one frequency. Any other waveform can be created by adding up a series of sine waves. In this picture, the first two sine waves In this picture, a sine wave is added to its are added together to produce a third. -
Airspace: Seeing Sound Grades
National Aeronautics and Space Administration GRADES K-8 Seeing Sound airspace Aeronautics Research Mission Directorate Museum in a BO SerieXs www.nasa.gov MUSEUM IN A BOX Materials: Seeing Sound In the Box Lesson Overview PVC pipe coupling Large balloon In this lesson, students will use a beam of laser light Duct tape to display a waveform against a flat surface. In doing Super Glue so, they will effectively“see” sound and gain a better understanding of how different frequencies create Mirror squares different sounds. Laser pointer Tripod Tuning fork Objectives Tuning fork activator Students will: 1. Observe the vibrations necessary to create sound. Provided by User Scissors GRADES K-8 Time Requirements: 30 minutes airspace 2 Background The Science of Sound Sound is something most of us take for granted and rarely do we consider the physics involved. It can come from many sources – a voice, machinery, musical instruments, computers – but all are transmitted the same way; through vibration. In the most basic sense, when a sound is created it causes the molecule nearest the source to vibrate. As this molecule is touching another molecule it causes that molecule to vibrate too. This continues, from molecule to molecule, passing the energy on as it goes. This is also why at a rock concert, or even being near a car with a large subwoofer, you can feel the bass notes vibrating inside you. The molecules of your body are vibrating, allowing you to physically feel the music. MUSEUM IN A BOX As with any energy transfer, each time a molecule vibrates or causes another molecule to vibrate, a little energy is lost along the way, which is why sound gets quieter with distance (Fig 1.) and why louder sounds, which cause the molecules to vibrate more, travel farther. -
33600A Series Trueform Waveform Generators Generate Trueform Arbitrary Waveforms with Less Jitter, More Fidelity and Greater Resolution
DATA SHEET 33600A Series Trueform Waveform Generators Generate Trueform arbitrary waveforms with less jitter, more fidelity and greater resolution Revolutionary advances over previous generation DDS 33600A Series waveform generators with exclusive Trueform signal generation technology offer more capability, fidelity and flexibility than previous generation Direct Digital Synthesis (DDS) generators. Use them to accelerate your development Trueform process from start to finish. – 1 GSa/s sampling rate and up to 120 MHz bandwidth Better Signal Integrity – Arbs with sequencing and up to 64 MSa memory – 1 ps jitter, 200x better than DDS generators – 5x lower harmonic distortion than DDS – Compatible with Keysight Technologies, DDS Inc. BenchVue software Over the past two decades, DDS has been the waveform generation technology of choice in function generators and economical arbitrary waveform generators. Reduced Jitter DDS enables waveform generators with great frequency resolution, convenient custom waveforms, and a low price. <1 ps <200 ps As with any technology, DDS has its limitations. Engineers with exacting requirements have had to either work around the compromised performance or spend up to 5 times more for a high-end, point-per-clock waveform generator. Keysight Technologies, Inc. Trueform Trueform technology DDS technology technology offers an alternative that blends the best of DDS and point-per-clock architectures, giving you the benefits of both without the limitations of either. Trueform technology uses an exclusive digital 0.03% -
The Oscilloscope and the Function Generator: Some Introductory Exercises for Students in the Advanced Labs
The Oscilloscope and the Function Generator: Some introductory exercises for students in the advanced labs Introduction So many of the experiments in the advanced labs make use of oscilloscopes and function generators that it is useful to learn their general operation. Function generators are signal sources which provide a specifiable voltage applied over a specifiable time, such as a \sine wave" or \triangle wave" signal. These signals are used to control other apparatus to, for example, vary a magnetic field (superconductivity and NMR experiments) send a radioactive source back and forth (M¨ossbauer effect experiment), or act as a timing signal, i.e., \clock" (phase-sensitive detection experiment). Oscilloscopes are a type of signal analyzer|they show the experimenter a picture of the signal, usually in the form of a voltage versus time graph. The user can then study this picture to learn the amplitude, frequency, and overall shape of the signal which may depend on the physics being explored in the experiment. Both function generators and oscilloscopes are highly sophisticated and technologically mature devices. The oldest forms of them date back to the beginnings of electronic engineering, and their modern descendants are often digitally based, multifunction devices costing thousands of dollars. This collection of exercises is intended to get you started on some of the basics of operating 'scopes and generators, but it takes a good deal of experience to learn how to operate them well and take full advantage of their capabilities. Function generator basics Function generators, whether the old analog type or the newer digital type, have a few common features: A way to select a waveform type: sine, square, and triangle are most common, but some will • give ramps, pulses, \noise", or allow you to program a particular arbitrary shape. -
Interference: Two Spherical Sources Superposition
Interference: Two Spherical Sources Superposition Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase Superposition Traveling waves move through each other, interfere, and keep on moving! Pulsed Interference Superposition Waves ADD in space. Any complex wave can be built from simple sine waves. Simply add them point by point. Simple Sine Wave Simple Sine Wave Complex Wave Fourier Synthesis of a Square Wave Any periodic function can be represented as a series of sine and cosine terms in a Fourier series: y() t ( An sin2ƒ n t B n cos2ƒ) n t n Superposition of Sinusoidal Waves • Case 1: Identical, same direction, with phase difference (Interference) Both 1-D and 2-D waves. • Case 2: Identical, opposite direction (standing waves) • Case 3: Slightly different frequencies (Beats) Superposition of Sinusoidal Waves • Assume two waves are traveling in the same direction, with the same frequency, wavelength and amplitude • The waves differ in phase • y1 = A sin (kx - wt) • y2 = A sin (kx - wt + f) • y = y1+y2 = 2A cos (f/2) sin (kx - wt + f/2) Resultant Amplitude Depends on phase: Spatial Interference Term Sinusoidal Waves with Constructive Interference y = y1+y2 = 2A cos (f/2) sin (kx - wt + f /2) • When f = 0, then cos (f/2) = 1 • The amplitude of the resultant wave is 2A – The crests of one wave coincide with the crests of the other wave • The waves are everywhere in phase • The waves interfere constructively Sinusoidal Waves with Destructive Interference y = y1+y2 = 2A cos (f/2) -
The Differential Pair As a Triangle-Sine Wave Converter V - ROBERT G
418 IEEE JOURNAL OF SOLID-STATE CIRCUITS, JUNE 1976 Correspondence The Differential Pair as a Triangle-Sine Wave Converter v - ROBERT G. MEYER, WILLY M. C. SANSEN, SIK LUI, AND STEFAN PEETERS R~ R~ 1 / Abstract–The performance of a differential pair with emitter degen- eration as a triangle-sine wave converter is analyzed. Equations describ- ing the circuit operation are derived and solved both analytically and by computer. This allows selection of operating conditions for optimum performance such that total harmonic distortion as low as 0.2 percent “- has been measured. -vEE (a) I. INTRODUCTION The conversion of ttiangle waves to sine waves is a function I ---- I- often required in waveshaping circuits. For example, the oscil- lators used in function generators usually generate triangular output waveforms [ 1] because of the ease with which such oscillators can operate over a wide frequency range including very low frequencies. This situation is also common in mono- r v, Zr t lithic oscillators [2] . Sinusoidal outputs are commonly de- sired in such oscillators and can be achieved by use of a non- linear circuit which produces an output sine wave from an input triangle wave. — — — — The above circuit function has been realized in the past by -I -I ----- means of a piecewise linear approximation using diode shaping J ‘“b ‘M VI networks [ 1] . However, a simpler approach and one well M suited to monolithic realization has been suggested by Grebene [3] . This is shown in Fig. 1 and consists simply of a differen- 77 tial pair with an appropriate value of emitter resistance R. -
Chapter 1 Waves in Two and Three Dimensions
Chapter 1 Waves in Two and Three Dimensions In this chapter we extend the ideas of the previous chapter to the case of waves in more than one dimension. The extension of the sine wave to higher dimensions is the plane wave. Wave packets in two and three dimensions arise when plane waves moving in different directions are superimposed. Diffraction results from the disruption of a wave which is impingent upon an object. Those parts of the wave front hitting the object are scattered, modified, or destroyed. The resulting diffraction pattern comes from the subsequent interference of the various pieces of the modified wave. A knowl- edge of diffraction is necessary to understand the behavior and limitations of optical instruments such as telescopes. Diffraction and interference in two and three dimensions can be manipu- lated to produce useful devices such as the diffraction grating. 1.1 Math Tutorial — Vectors Before we can proceed further we need to explore the idea of a vector. A vector is a quantity which expresses both magnitude and direction. Graph- ically we represent a vector as an arrow. In typeset notation a vector is represented by a boldface character, while in handwriting an arrow is drawn over the character representing the vector. Figure 1.1 shows some examples of displacement vectors, i. e., vectors which represent the displacement of one object from another, and introduces 1 CHAPTER 1. WAVES IN TWO AND THREE DIMENSIONS 2 y Paul B y B C C y George A A y Mary x A x B x C x Figure 1.1: Displacement vectors in a plane.