Getting Started with Smaartlive: Basic Measurement Setup and Procedures
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J-DSP Lab 2: the Z-Transform and Frequency Responses
J-DSP Lab 2: The Z-Transform and Frequency Responses Introduction This lab exercise will cover the Z transform and the frequency response of digital filters. The goal of this exercise is to familiarize you with the utility of the Z transform in digital signal processing. The Z transform has a similar role in DSP as the Laplace transform has in circuit analysis: a) It provides intuition in certain cases, e.g., pole location and filter stability, b) It facilitates compact signal representations, e.g., certain deterministic infinite-length sequences can be represented by compact rational z-domain functions, c) It allows us to compute signal outputs in source-system configurations in closed form, e.g., using partial functions to compute transient and steady state responses. d) It associates intuitively with frequency domain representations and the Fourier transform In this lab we use the Filter block of J-DSP to invert the Z transform of various signals. As we have seen in the previous lab, the Filter block in J-DSP can implement a filter transfer function of the following form 10 −i ∑bi z i=0 H (z) = 10 − j 1+ ∑ a j z j=1 This is essentially realized as an I/P-O/P difference equation of the form L M y(n) = ∑∑bi x(n − i) − ai y(n − i) i==01i The transfer function is associated with the impulse response and hence the output can also be written as y(n) = x(n) * h(n) Here, * denotes convolution; x(n) and y(n) are the input signal and output signal respectively. -
SR1 — Dual-Domain Audio Analyzer
Audio Analyzer SR1 — Dual-domain audio analyzer SR1 Audio Analyzer Introducing SR1 Dual-Domain Audio Analyzer — high · Analog/digital domain measurements performance audio analysis at a very affordable price. SR1 is a stand-alone instrument that delivers cutting edge · −112 dB THD + N (at 1 kHz, 20 kHz BW) performance in a wide variety of audio measurements. With a versatile high-performance generator, an array of analyzers · 200 kHz frequency range that operate symmetrically in both the analog and digital domains, and digital audio carrier measurements at sampling · −118 dBu analyzer noise (20 kHz BW) rates up to 192 kHz, SR1 is the right choice for the most demanding analog and digital audio applications. · ±0.008 dB flatness (20 Hz to 20 kHz) User Interface · −140 dB input crosstalk SR1 uses an integrated computer running the Windows XP embedded operating system, so operation will be immediately · −125 dB output crosstalk familiar and intuitive. Depending on the application, SR1 can be operated with an external mouse and keyboard, or by using · <600 ps jitter (50 Hz to 100 kHz) the front-panel knob, keypad and touchpad. Seven on-screen tabbed pages are available for arranging · Dual-channel FFT measurements panels, graphs, and displays. Screen setups, data, and instrument configurations can be quickly saved and recalled to either the internal hard disk or to a flash drive connected to one of the two front-panel USB connectors. An optional 1024 × 768 XVGA monitor (opt. 02) provides better resolution and allows more information to be displayed. (U.S. list) · SR1 ... $12,400 While SR1’s configuration panels offer total flexibility in setting up every detail of the analyzer, at times it is useful to get a measurement going quickly, without worrying Stanford Research Systems phone: (408)744-9040 www.thinkSRS.com SR1 Audio Analyzer about infrequently used parameters. -
Control Theory
Control theory S. Simrock DESY, Hamburg, Germany Abstract In engineering and mathematics, control theory deals with the behaviour of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain ref- erence over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. Rapid advances in digital system technology have radically altered the control design options. It has become routinely practicable to design very complicated digital controllers and to carry out the extensive calculations required for their design. These advances in im- plementation and design capability can be obtained at low cost because of the widespread availability of inexpensive and powerful digital processing plat- forms and high-speed analog IO devices. 1 Introduction The emphasis of this tutorial on control theory is on the design of digital controls to achieve good dy- namic response and small errors while using signals that are sampled in time and quantized in amplitude. Both transform (classical control) and state-space (modern control) methods are described and applied to illustrative examples. The transform methods emphasized are the root-locus method of Evans and fre- quency response. The state-space methods developed are the technique of pole assignment augmented by an estimator (observer) and optimal quadratic-loss control. The optimal control problems use the steady-state constant gain solution. Other topics covered are system identification and non-linear control. System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. -
The Scientist and Engineer's Guide to Digital Signal Processing Properties of Convolution
CHAPTER 7 Properties of Convolution A linear system's characteristics are completely specified by the system's impulse response, as governed by the mathematics of convolution. This is the basis of many signal processing techniques. For example: Digital filters are created by designing an appropriate impulse response. Enemy aircraft are detected with radar by analyzing a measured impulse response. Echo suppression in long distance telephone calls is accomplished by creating an impulse response that counteracts the impulse response of the reverberation. The list goes on and on. This chapter expands on the properties and usage of convolution in several areas. First, several common impulse responses are discussed. Second, methods are presented for dealing with cascade and parallel combinations of linear systems. Third, the technique of correlation is introduced. Fourth, a nasty problem with convolution is examined, the computation time can be unacceptably long using conventional algorithms and computers. Common Impulse Responses Delta Function The simplest impulse response is nothing more that a delta function, as shown in Fig. 7-1a. That is, an impulse on the input produces an identical impulse on the output. This means that all signals are passed through the system without change. Convolving any signal with a delta function results in exactly the same signal. Mathematically, this is written: EQUATION 7-1 The delta function is the identity for ( ' convolution. Any signal convolved with x[n] *[n] x[n] a delta function is left unchanged. This property makes the delta function the identity for convolution. This is analogous to zero being the identity for addition (a%0 ' a), and one being the identity for multiplication (a×1 ' a). -
2913 Public Disclosure Authorized
WPS A 13 POLICY RESEARCH WORKING PAPER 2913 Public Disclosure Authorized Financial Development and Dynamic Investment Behavior Public Disclosure Authorized Evidence from Panel Vector Autoregression Inessa Love Lea Zicchino Public Disclosure Authorized The World Bank Public Disclosure Authorized Development Research Group Finance October 2002 POLIcy RESEARCH WORKING PAPER 2913 Abstract Love and Zicchino apply vector autoregression to firm- availability of internal finance) that influence the level of level panel data from 36 countries to study the dynamic investment. The authors find that the impact of the relationship between firms' financial conditions and financial factors on investment, which they interpret as investment. They argue that by using orthogonalized evidence of financing constraints, is significantly larger in impulse-response functions they are able to separate the countries with less developed financial systems. The "fundamental factors" (such as marginal profitability of finding emphasizes the role of financial development in investment) from the "financial factors" (such as improving capital allocation and growth. This paper-a product of Finance, Development Research Group-is part of a larger effort in the group to study access to finance. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Kari Labrie, room MC3-456, telephone 202-473-1001, fax 202-522-1155, email address [email protected]. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at [email protected] or [email protected]. October 2002. (32 pages) The Policy Research Working Paper Series disseminates the findmygs of work mn progress to encouirage the excbange of ideas about development issues. -
Keysight U8903A Audio Analyzer
Keysight U8903A Audio Analyzer Data Sheet Make an audible difference Whether listening to mono, stereo or surround, the human ear knows what sounds good. Measuring “how good,” however, can be a challenge. Now, with a two-in-one digital audio interface card that provides AES3/ SPDIF and Digital Serial Interface digital audio formats, Keysight Technologies, Inc. U8903A offers you the flexibility to measure and quantify both analog and digital U8903A audio analyzer key features audio performance in applications such as analog and digital IC compo- – Customize your unit with flexible – Characterize signal-to-noise nents and module design, wireless digital audio interface options, ratios, SINAD, IMD, DFD, THD+N audio and consumer audio. offering AES3/SPDIF or DSI ratio, THD+N level, crosstalk and standard digital audio formats, or more. The U8903A contains the full both in a convenient two-in-one – Apply weighting functions, functions of analog domain and card. standard filters and custom digital domain audio measurement – Test a variety of current filters. in one box, allowing you to perform components and applications – Stimulate the device with quick and convenient complex with a logic level input range of high-quality signals and arbitrary cross-domain measurements. 1.2 V to 3.3 V (DSI). waveforms. – Analyze a wide range of – View numerical and graphical The U8903A audio analyzer com- applications with multiple DSI displays of measurement results. bines the functionality of a distortion formats: I2S, Left Justified, Right – Connect to a PC through GPIB, meter, SINAD meter, frequency Justified and DSP. LAN/LXI C and USB interfaces. counter, AC voltmeter, DC voltmeter – Select generator, analyzer, graph – Eliminate the need to rewrite and FFT analyzer with a low-distor- and sweep modes with one- programs into SCPI command tion audio source. -
Design of Ultralow Noise and THD Low Pass Filter for Audio Analyzer By
Design of ultralow noise and THD low pass filter for audio analyzer by Justin Lee Kung Wen 16073 Dissertation submitted in partial fulfillment of the requirements for the Bachelor of Engineering (Hons) (Electrical and Electronic) January 2016 Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Perak Darul Ridzuan CERTIFICATION OF APPROVAL DESIGN OF ULTRALOW NOISE AND THD LOW PASS FILTER FOR AUDIO ANALYZER by Justin Lee Kung Wen 16073 A project dissertation submitted to the Electrical & Electronic Engineering Programme Universiti Teknologi PETRONAS In partial fulfillment of the requirement for the BACHELOR OF ENGINEERING (Hons) (ELECTRICAL & ELECTRONIC) Approved by, _________________ Dr Wong Peng Wen UNIVERSITI TEKNOLOGI PETRONAS TRONOH, PERAK January 2016 i CERTIFICATION OF ORIGINALITY This is to certify that I am responsible for the work submitted in this project, that the original work is my own except as specified in the references and acknowledgements, and the original work contained herein have not been undertaken or done by unspecified sources or persons. __________________ Justin Lee Kung Wen ii Abstract An ultralow noise and THD low pass filter is required to design for Keysight Technologies audio analyzer model U8903B. The company provides the required specifications for the filter. There are two different filters required based on the installed option. Passive low pass Chebyshev ladder network is constructed due to its characteristics. It is constructed by cascading capacitor and inductor. Air core inductor is used to minimize THD. iii Acknowledgement Firstly, I would like to thank my supervisor, Dr Wong Peng Wen and co-supervisor, Dr Lee Yen Cheong for helping, guiding and sharing their knowledge and experiences with me. -
Audio Analyzer Type 2012 (Bp1503)
Product Data Audio Analyzer — Type 2012 Version 4.0 including Special Calculation Software Type 7661 USES: ❍ Automated measurements of individual Harmonic, ❍ Development and quality control testing of Intermodulation and Difference Frequency distortion electroacoustic and vibration transducers: components and total RMS loudspeakers, telephones, headphones, ❍ 1600 line FFT spectrum microphones, hearing-aids, hydrophones, ❍ User-definable Auto Sequences accelerometers ❍ Extensive post-processing facilities: +, –, ×, /, 1/x, ❍ Linear and non-linear system analysis x2, √x, |x|, poles, zeros, windowing, editing, ❍ Propagation path identification smoothing ❍ Acoustical measurements in rooms and vehicles ❍ On-screen help in English, French or German ❍ Preamplifier (microphone) and balanced or single- ended direct inputs FEATURES: ❍ Two separate built-in sine generators ❍ Transducer workstation combining the most ❍ 1 ″ Built-in 3 /2 , 1.44Mbyte, PC/MS-DOS compatible advanced sine sweep and FFT techniques floppy disk drive for storage of data, setups, and ❍ 12″ high-resolution colour monitor displays up to 36 Auto Sequences and simple loading of complete curves simultaneously applications ❍ Frequency range: 1Hz to 40kHz ❍ Screen copy facility for plotters and printers, both ❍ Distortion and noise: <–80 dB re full scale input colour and monochrome, direct or via disk ❍ ❍ Fast time selective measurement of complex Upgrade kit from Version 3.0 to Version 4.0 frequency and impulse response available ❍ Steady-state response measurements as a function of swept frequency or level The Type 2012 Audio Analyzer is a powerful instrument for transducer measurements and system analysis. It 1 ″ features a colour screen, built-in 3 /2 floppy disk drive, IEEE-488 and RS- 232-C interfaces, three measurement modes and an Auto Sequence facility. -
Time Alignment)
Measurement for Live Sound Welcome! Instructor: Jamie Anderson 2008 – Present: Rational Acoustics LLC Founding Partner & Systweak 1999 – 2008: SIA Software / EAW / LOUD Technologies Product Manager 1997 – 1999: Independent Sound Engineer A-1 Audio, Meyer Sound, Solstice, UltraSound / Promedia 1992 – 1997: Meyer Sound Laboratories SIM & Technical Support Manager 1991 – 1992: USC – Theatre Dept Education MFA: Yale School of Drama BS EE/Physics: Worcester Polytechnic University Instructor: Jamie Anderson Jamie Anderson [email protected] Rational Acoustics LLC Who is Rational Acoustics LLC ? 241 H Church St Jamie @RationalAcoustics.com Putnam, CT 06260 Adam @RationalAcoustics.com (860)928-7828 Calvert @RationalAcoustics.com www.RationalAcoustics.com Karen @RationalAcoustics.com and Barb @RationalAcoustics.com SmaartPIC @RationalAcoustics.com Support @RationalAcoustics.com Training @Rationalacoustics.com Info @RationalAcoustics.com What Are Our Goals for This Session? Understanding how our analyzers work – and how we can use them as a tool • Provide system engineering context (“Key Concepts”) • Basic measurement theory – Platform Agnostic Single Channel vs. Dual Channel Measurements Time Domain vs. Frequency Domain Using an analyzer is about asking questions . your questions Who Are You?" What Are Your Goals Today?" Smaart Basic ground rules • Class is informal - Get comfortable • Ask questions (Win valuable prizes!) • Stay awake • Be Courteous - Don’t distract! TURN THE CELL PHONES OFF NO SURFING / TEXTING / TWEETING PLEASE! Continuing -
Mathematical Modeling of Control Systems
OGATA-CH02-013-062hr 7/14/09 1:51 PM Page 13 2 Mathematical Modeling of Control Systems 2–1 INTRODUCTION In studying control systems the reader must be able to model dynamic systems in math- ematical terms and analyze their dynamic characteristics.A mathematical model of a dy- namic system is defined as a set of equations that represents the dynamics of the system accurately, or at least fairly well. Note that a mathematical model is not unique to a given system.A system may be represented in many different ways and, therefore, may have many mathematical models, depending on one’s perspective. The dynamics of many systems, whether they are mechanical, electrical, thermal, economic, biological, and so on, may be described in terms of differential equations. Such differential equations may be obtained by using physical laws governing a partic- ular system—for example, Newton’s laws for mechanical systems and Kirchhoff’s laws for electrical systems. We must always keep in mind that deriving reasonable mathe- matical models is the most important part of the entire analysis of control systems. Throughout this book we assume that the principle of causality applies to the systems considered.This means that the current output of the system (the output at time t=0) depends on the past input (the input for t<0) but does not depend on the future input (the input for t>0). Mathematical Models. Mathematical models may assume many different forms. Depending on the particular system and the particular circumstances, one mathemati- cal model may be better suited than other models. -
Finite Impulse Response (FIR) Digital Filters (I) Types of Linear Phase FIR Filters Yogananda Isukapalli
Finite Impulse Response (FIR) Digital Filters (I) Types of linear phase FIR filters Yogananda Isukapalli 1 Key characteristic features of FIR filters 1. The basic FIR filter is characterized by the following two equations: N -1 N -1 y(n) = å h(k)x(n - k) (1) H (z) = å h(k)z -k (2) k =0 k =0 where h(k), k=0,1,…,N-1, are the impulse response coefficients of the filter, H(z) is the transfer function and N the length of the filter. 2. FIR filters can have an exactly linear phase response. 3. FIR filters are simple to implement with all DSP processors available having architectures that are suited to FIR filtering. 2 Linear phase response • Consider a signal that consists of several frequency components passing through a filter. 1. The phase delay (T p ) of the filter is the amount of time delay each frequency component of the signal suffers in going through the filter. 2. The group delay (T g ) is the average time delay the composite signal suffers at each frequency. 3. Mathematically, T p = -q (w) / w (3) Tg = -dq (w) / dw (4) where q(w) is the phase angle. 3 • A filter is said to have a linear phase response if, J(w) = -aw (5) J(w) = b -aw (6) where a and b are constants. Example) Ideal Lowpass filter k Magnitude 0 wc p w Phase 0 a wc p w 4 k e-jwa passband jw H(e ) = 0 otherwise Magnitude response = |H(ejw)| = k Phase response (q(w)) = < H(ejw) = -wa Follows: y[n] = kx[n-a] : Linear phase implies that the output is a replica of x[n] {LPF} with a time shift of a - p -wu -wl 0 wl wu p w - p -wu -wl 0 wl wu p w 5 Linear phase FIR filters • Symmetric impulse response will yield linear phase FIR filters. -
Vector Autoregressions
Vector Autoregressions • VAR: Vector AutoRegression – Nothing to do with VaR: Value at Risk (finance) • Multivariate autoregression • Multiple equation model for joint determination of two or more variables • One of the most commonly used models for applied macroeconometric analysis and forecasting in central banks Two‐Variable VAR • Two variables: y and x • Example: output and interest rate • Two‐equation model for the two variables • One‐Step ahead model • One equation for each variable • Each equation is an autoregression plus distributed lag, with p lags of each variable VAR(p) in 2 riablesaV y=t1μ 11 +α yt− 1+α 12 yt− +L 2 +αp1 y t− p +11βx +t− 1 β 12t x− +L 1 βp +1x t− p1 e t + x=t 2μ 21+α yt− 1+α 22 yt− +L 2 +αp2 y t− p +β21x +t− 1 β 22t x− +L 1 β +p2 x t− p e2 + t Multiple Equation System • In general: k variables • An equation for each variable • Each equation includes p lags of y and p lags of x • (In principle, the equations could have different # of lags, and different # of lags of each variable, but this is most common specification.) • There is one error per equation. – The errors are (typically) correlated. Unrestricted VAR • An unrestricted VAR includes all variables in each equation • A restricted VAR might include some variables in one equation, other variables in another equation • Old‐fashioned macroeconomic models (so‐called simultaneous equations models of the 1950s, 1960s, 1970s) were essentially restricted VARs – The restrictions and specifications were derived from simplistic macro theory, e.g.