DOCSLIB.ORG

FIR Filter Approximations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
FIR Filter Approximations Diniz, da Silva and Netto FIR Filter Approximations Paulo S. R. Diniz Eduardo A. B. da Silva Sergio L. Netto diniz,eduardo,[email protected] September 2010 1 Diniz, da Silva and Netto Contents Ideal characteristics of standard filters • – Lowpass, highpass, bandpass, and bandstop filters – Differentiators – Hilbert transformers FIR filter approximation by frequency sampling • FIR filter approximation by window functions • – Rectangular window – Tr iangular windows – Hamming and Hann windows – Blackman window – Kaiser window – Dolph-Chebyshev window 2 Diniz, da Silva and Netto Contents (cont.) Maximally-flat FIR filter approximation • FIR filter approximation by optimization • – Weighted-least-squares method – Chebyshev method – WLS-Chebyshev method Do-it-yourself: FIR filter approximations • 3 Diniz, da Silva and Netto Ideal characteristics of standard filters As seen in Section 2.8, the relationship between H(e jω) and h(n) is given by the • following pair of equations: jω − jωn H(e )= ∞ h(n)e (2) n"=− 1 ∞π h(n)= H(e jω)e jωndω (3) 2π #−π In what follows, we determine H(e jω) and h(n) related to ideal standard filters. • 8 Diniz, da Silva and Netto Lowpass, highpass, bandpass, and bandstop filters The ideal magnitude responses of some standard digital filters are depicted below. • j! j! |H(e )| |H(e )| 1 1 2 0 (a) !c " " ! (b) !c " 2" ! j! j! | H(e )| | H(e ) | 1 1 0 !c !c " 2" ! 0 ! !c " 2" ! (c) 1 2 (d) c1 2 Figure 1: Ideal magnitude responses: (a) lowpass; (b) highpass; (c) bandpass; (d) band- stop filters. 9 Diniz, da Silva and Netto Lowpass, highpass, bandpass, and bandstop filters For instance, the lowpass filter, as seen in Figure 1a, is described by • 1, for |ω| ωc |H(e jω)| = ≤ (4) 0, for ωc < |ω| π ≤ Using (3), the impulse response for the ideal lowpass filter is • ωc , for n = 0 ωc 1 jωn π h(n)= e dω = (5) 2π #−ω sin(ωcn) c , for n = 0 πn " One should note that in the above inverse transform calculations we have supposed • that the phase of the filter is zero. 10 Diniz, da Silva and Netto Lowpass, highpass, bandpass, and bandstop filters From Section 4.2.3, we have that the phase of an FIR filter must be of the form • − jω M e 2 ,whereM is an integer. M Therefore, for M even, it suffices to shift the above impulse response by 2 • M samples. However, for M odd, 2 is not an integer, and the impulse response must be computed as ωc 1 − jω M jωn h(n)= e 2 e dω 2π #−ωc ωc 1 jω n− M = e ( 2 )dω 2π #−ωc M sin ωc n − = 2 (6) π n − M ! " 2 #$ " # 11 Diniz, da Silva and Netto Lowpass, highpass, bandpass, and bandstop filters Likewise, for bandstop filters, the ideal magnitude response, depicted in Figure 1d, is • given by 1, for 0 |ω| ωc1 ≤ ≤ |H(e jω)| = | | (7) 0, for ωc1 < ω < ωc2 1, for ωc2 |ω| π ≤ ≤ Then, using (3), the impulse response for such an ideal filter is • ω π −ω 1 c1 c2 h(n)= e jωndω + e jωndω + e jωndω 2π # # # % −ωc1 ωc2 −π & ωc − ωc 1 + 1 2 , for n = 0 = π (8) 1 [sin(ωc n) − sin(ωc n)] , for n = 0 πn 1 2 " 12 Diniz, da Silva and Netto Differentiators An ideal discrete-time differentiator is a linear system that, when samples of a • band-limited continuous signal are used as input, the outputsamplesrepresentthe derivative of the continuous signal. π π More precisely, given a continuous-time signal xa(t) band-limited to − , , • T T when its corresponding sampled version x(n)=x (nT) is input to an ideal a ! # differentiator, it produces the output signal, y(n),suchthat dxa(t) y(n)= (9) dt 't=nT ' ' If the Fourier transform of the continuous-time signal' is denoted by Xa(jΩ),we • have that the Fourier transform of its derivative is jΩXa(jΩ). 14 Diniz, da Silva and Netto Differentiators Therefore, an ideal discrete-time differentiator is characterized by a frequency • response, up to a multiplicative constant, of the form H(e jω)=jω, for −π ω < π (10) ≤ The magnitude and phase responses of a differentiator are depicted in Figure 2. • 15 Diniz, da Silva and Netto Differentiators | H (e j ! ) | ... ... (a) – 2" – " " 2" ! # (! ) _" 2 ... ... – 2 " – " " 2 " ! – _" 2 (b) Figure 2: Characteristics of an ideal discrete-time differentiator: (a) magnitude response; (b) phase response. 16 Diniz, da Silva and Netto Differentiators Using equation (3), the corresponding impulse response is given by • 1 π h(n)= jωe jωndω 2π#−π 0, for n = 0 = π 1 ω 1 (−1)n e jωn − = , for n = 0 2π n jn2 n " ( ) *+'−π ' ' (11) ' One should note that if a differentiator is to be approximatedbyalinear-phaseFIR • filter, one should necessarily use either a Type-III or a Type-IV form. 17 Diniz, da Silva and Netto Hilbert transformers These equations provide a relation between the Fourier transforms of the real and • imaginary parts of a signal whose Fourier transform is null for −π ω <0.Itthus ≤ implies that the ideal Hilbert transformer has the followingtransferfunction: −j, for 0 ω < π H(e jω)= ≤ (17) j, for − π ω <0 ≤ The magnitude and phase components of such a frequency response are depicted in • Figure 3. 22 Diniz, da Silva and Netto Hilbert transformers | H (e j ! ) | ... ... (a) –2 " – " " 2 " ! #(!) _" ... 2 −2" −" " 2" ! −_" ... 2 (b) Figure 3: Characteristics of an ideal Hilbert transformer: (a) magnitude response; (b) phase response. 23 Diniz, da Silva and Netto Hilbert transformers Using equation (3), the corresponding impulse response for the ideal Hilbert • transformer is given by π 0 0, for n = 0 1 jωn jωn h(n)= −je dω+ je dω = 2π #0 #−π 1 n % & [1−(−1) ] , for n = 0 πn " (18) By examining equation (17) we conclude, as in the case of the differentiator, that a • Hilbert transformer must be approximated, when using a linear-phase FIR filter, by either a Type-III or Type-IV structure. 24 Diniz, da Silva and Netto Summary Table 1: Ideal frequency characteristics and correspondingimpulseresponsesforlow- pass, highpass, bandpass, and bandstop filters, as well as fordifferentiatorsand Hilbert transformers. Filter type Magnitude response Impulse response |H(e jω )| h(n) ωc , for n = 0 1, for 0 ≤ |ω| ≤ ωc π Lowpass 0, for ω < |ω| ≤ π 1 c sin(ω n), for n "= 0 πn c ωc 1 − , for n = 0 0, for 0 ≤ |ω| < ωc π Highpass 1 1, for ωc ≤ |ω| ≤ π − sin(ω n), for n "= 0 πn c 27 Diniz, da Silva and Netto Summary Filter type Magnitude response Impulse response |H(e jω )| h(n) for | | 0, 0 ≤ ω < ωc1 (ωc2 − ωc1 ) , for n = 0 Bandpass for | | π 1, ωc1 ≤ ω ≤ ωc2 1 [sin(ωc2 n) − sin(ωc1 n)] , for n "= 0 0, for ωc2 < |ω| ≤ π πn for | | 1, 0 ≤ ω ≤ ωc1 (ωc2 − ωc1 ) 1 − , for n = 0 Bandstop for | | π 0, ωc1 < ω < ωc2 1 [sin(ωc1 n) − sin(ωc2 n)] , for n "= 0 1, for ωc2 ≤ |ω| ≤ π πn 28 Diniz, da Silva and Netto Summary Filter type Frequency response Impulse response H(e jω ) h(n) 0, for n = 0 Differentiator jω, for −π ≤ ω < π (−1)n , for n "= 0 n Hilbert −j, for 0 ≤ ω < π 0, for n = 0 1 n transformer j, for − π ≤ ω <0 [1 − (−1) ] , for n "= 0 πn 29 Diniz, da Silva and Netto FIR filter approximation by frequency sampling In general, the problem of FIR filter design is to find a finite-length impulse response • h(n),whoseFouriertransformH(e jω) approximates a given frequency response well enough. As seen in Section 3.2, one way of achieving such a goal is by noting that the DFT of • alength-N sequence h(n) corresponds to samples of its Fourier transform at the 2πk frequencies ω = N ,thatis N−1 − H(e jω)= h(n)e jωn (19) n"=0 and then N−1 2πk − 2πkn H(e j N )= h(n)e j N , for k = 0, 1, . ., (N − 1) (20) n"=0 30 Diniz, da Silva and Netto FIR filter approximation by frequency sampling It is then natural to consider designing a length-N FIR filter by finding an h(n) • whose DFT corresponds exactly to samples of the desired frequency response. In other words, h(n) can be determined by sampling the desired frequency • j 2π k response at the N points e N and finding its inverse DFT. This method is generally referred to as the frequency sampling approach. More precisely, if the desired frequency response is given by D(ω),onemustfirst • find ( ) ωsk A(k)e jθ k = D , for k = 0, 1, . ., (N − 1) (21) N ) * where A(k) and θ(k) are samples of the desired amplitude and phase responses, respectively. 31 Diniz, da Silva and Netto FIR filter approximation by frequency sampling Type I: Even order M and symmetrical impulse response. In this case, the phase • and amplitude responses must satisfy πkM θ(k)=− , for 0 k M (22) M + 1 ≤ ≤ M A(k)=A(M − k + 1), for 1 k (23) ≤ ≤ 2 and then, the impulse response is given by M 1 2 πk(1 + 2n) h(n)= A(0)+2 (−1)kA(k) cos (24) M + 1 M + 1 k"=1 for n = 0, 1, . ., M. 33 Diniz, da Silva and Netto Table 2: Impulse responses for linear-phase FIR filters with frequency sampling approach. Filter type Impulse response Condition h(n),for n = 0, 1, .
Load more

Recommended publications
  • Designing Filters Using the Digital Filter Design Toolkit Rahman Jamal, Mike Cerna, John Hanks
    NATIONAL Application Note 097 INSTRUMENTS® The Software is the Instrument ® Designing Filters Using the Digital Filter Design Toolkit Rahman Jamal, Mike Cerna, John Hanks Introduction The importance of digital filters is well established. Digital filters, and more generally digital signal processing algorithms, are classified as discrete-time systems. They are commonly implemented on a general purpose computer or on a dedicated digital signal processing (DSP) chip. Due to their well-known advantages, digital filters are often replacing classical analog filters. In this application note, we introduce a new digital filter design and analysis tool implemented in LabVIEW with which developers can graphically design classical IIR and FIR filters, interactively review filter responses, and save filter coefficients. In addition, real-world filter testing can be performed within the digital filter design application using a plug-in data acquisition board. Digital Filter Design Process Digital filters are used in a wide variety of signal processing applications, such as spectrum analysis, digital image processing, and pattern recognition. Digital filters eliminate a number of problems associated with their classical analog counterparts and thus are preferably used in place of analog filters. Digital filters belong to the class of discrete-time LTI (linear time invariant) systems, which are characterized by the properties of causality, recursibility, and stability. They can be characterized in the time domain by their unit-impulse response, and in the transform domain by their transfer function. Obviously, the unit-impulse response sequence of a causal LTI system could be of either finite or infinite duration and this property determines their classification into either finite impulse response (FIR) or infinite impulse response (IIR) system.
    [Show full text]
  • Finite Impulse Response (FIR) Digital Filters (II) Ideal Impulse Response Design Examples Yogananda Isukapalli
    Finite Impulse Response (FIR) Digital Filters (II) Ideal Impulse Response Design Examples Yogananda Isukapalli 1 • FIR Filter Design Problem Given H(z) or H(ejw), find filter coefficients {b0, b1, b2, ….. bN-1} which are equal to {h0, h1, h2, ….hN-1} in the case of FIR filters. 1 z-1 z-1 z-1 z-1 x[n] h0 h1 h2 h3 hN-2 hN-1 1 1 1 1 1 y[n] Consider a general (infinite impulse response) definition: ¥ H (z) = å h[n] z-n n=-¥ 2 From complex variable theory, the inverse transform is: 1 n -1 h[n] = ò H (z)z dz 2pj C Where C is a counterclockwise closed contour in the region of convergence of H(z) and encircling the origin of the z-plane • Evaluating H(z) on the unit circle ( z = ejw ) : ¥ H (e jw ) = åh[n]e- jnw n=-¥ 1 p h[n] = ò H (e jw )e jnwdw where dz = jejw dw 2p -p 3 • Design of an ideal low pass FIR digital filter H(ejw) K -2p -p -wc 0 wc p 2p w Find ideal low pass impulse response {h[n]} 1 p h [n] = H (e jw )e jnwdw LP ò 2p -p 1 wc = Ke jnwdw 2p ò -wc Hence K h [n] = sin(nw ) n = 0, ±1, ±2, …. ±¥ LP np c 4 Let K = 1, wc = p/4, n = 0, ±1, …, ±10 The impulse response coefficients are n = 0, h[n] = 0.25 n = ±4, h[n] = 0 = ±1, = 0.225 = ±5, = -0.043 = ±2, = 0.159 = ±6, = -0.053 = ±3, = 0.075 = ±7, = -0.032 n = ±8, h[n] = 0 = ±9, = 0.025 = ±10, = 0.032 5 Non Causal FIR Impulse Response We can make it causal if we shift hLP[n] by 10 units to the right: K h [n] = sin((n -10)w ) LP (n -10)p c n = 0, 1, 2, ….
    [Show full text]
  • Exploring Anti-Aliasing Filters in Signal Conditioners for Mixed-Signal, Multimodal Sensor Conditioning by Arun T
    Texas Instruments Incorporated Amplifiers: Op Amps Exploring anti-aliasing filters in signal conditioners for mixed-signal, multimodal sensor conditioning By Arun T. Vemuri Systems Architect, Enhanced Industrial Introduction Figure 1. Multimodal, mixed-signal sensor-signal conditioner Some sensor-signal conditioners are used to process the output Analog Digital of multiple sense elements. This Domain Domain processing is often provided by multimodal, mixed-signal condi- tioners that can handle the out- puts from several sense elements Sense Digital Amplifier 1 ADC 1 at the same time. This article Element 1 Filter 1 analyzes the operation of anti- Processed aliasing filters in such sensor- Intelligent Output Compensation signal conditioners. Sense Digital Basics of sensor-signal Amplifier 2 ADC 2 Element 2 Filter 2 conditioners Sense elements, or transducers, convert a physical quantity of interest into electrical signals. Examples include piezo resistive bridges used to measure pres- sure, piezoelectric transducers used to detect ultrasonic than one sense element is processed by the same signal waves, and electrochemical cells used to measure gas conditioner is called multimodal signal conditioning. concentrations. The electrical signals produced by sense Mixed-signal signal conditioning elements are small and exhibit nonidealities, such as tem- Another aspect of sensor-signal conditioning is the electri- perature drifts and nonlinear transfer functions. cal domain in which the signal conditioning occurs. TI’s Sensor analog front ends such as the Texas Instruments PGA309 is an example of a device where the signal condi- (TI) LMP91000 and sensor-signal conditioners such as TI’s tioning of resistive-bridge sense elements occurs in the PGA400/450 are used to amplify the small signals produced analog domain.
    [Show full text]
  • Transformations for FIR and IIR Filters' Design
    S S symmetry Article Transformations for FIR and IIR Filters’ Design V. N. Stavrou 1,*, I. G. Tsoulos 2 and Nikos E. Mastorakis 1,3 1 Hellenic Naval Academy, Department of Computer Science, Military Institutions of University Education, 18539 Piraeus, Greece 2 Department of Informatics and Telecommunications, University of Ioannina, 47150 Kostaki Artas, Greece; [email protected] 3 Department of Industrial Engineering, Technical University of Sofia, Bulevard Sveti Kliment Ohridski 8, 1000 Sofia, Bulgaria; mastor@tu-sofia.bg * Correspondence: [email protected] Abstract: In this paper, the transfer functions related to one-dimensional (1-D) and two-dimensional (2-D) filters have been theoretically and numerically investigated. The finite impulse response (FIR), as well as the infinite impulse response (IIR) are the main 2-D filters which have been investigated. More specifically, methods like the Windows method, the bilinear transformation method, the design of 2-D filters from appropriate 1-D functions and the design of 2-D filters using optimization techniques have been presented. Keywords: FIR filters; IIR filters; recursive filters; non-recursive filters; digital filters; constrained optimization; transfer functions Citation: Stavrou, V.N.; Tsoulos, I.G.; 1. Introduction Mastorakis, N.E. Transformations for There are two types of digital filters: the Finite Impulse Response (FIR) filters or Non- FIR and IIR Filters’ Design. Symmetry Recursive filters and the Infinite Impulse Response (IIR) filters or Recursive filters [1–5]. 2021, 13, 533. https://doi.org/ In the non-recursive filter structures the output depends only on the input, and in the 10.3390/sym13040533 recursive filter structures the output depends both on the input and on the previous outputs.
    [Show full text]
  • Digital Signal Processing Filter Design
    2065-27 Advanced Training Course on FPGA Design and VHDL for Hardware Simulation and Synthesis 26 October - 20 November, 2009 Digital Signal Processing Filter Design Massimiliano Nolich DEEI Facolta' di Ingegneria Universita' degli Studi di Trieste via Valerio, 10, 34127 Trieste Italy Filter design 1 Design considerations: a framework |H(f)| 1 C ıp 1 ıp ıs f 0 fp fs Passband Transition Stopband band The design of a digital filter involves five steps: Specification: The characteristics of the filter often have to be specified in the frequency domain. For example, for frequency selective filters (lowpass, highpass, bandpass, etc.) the specification usually involves tolerance limits as shown above. Coefficient calculation: Approximation methods have to be used to calculate the values hŒk for a FIR implementation, or ak, bk for an IIR implementation. Equivalently, this involves finding a filter which has H.z/ satisfying the requirements. Realisation: This involves converting H.z/ into a suitable filter structure. Block or flow diagrams are often used to depict filter structures, and show the computational procedure for implementing the digital filter. 1 Analysis of finite wordlength effects: In practice one should check that the quantisation used in the implementation does not degrade the performance of the filter to a point where it is unusable. Implementation: The filter is implemented in software or hardware. The criteria for selecting the implementation method involve issues such as real-time performance, complexity, processing requirements, and availability of equipment. 2 Finite impulse response (FIR) filter design A FIR filter is characterised by the equations N 1 yŒn D hŒkxŒn k kXD0 N 1 H.z/ D hŒkzk: kXD0 The following are useful properties of FIR filters: They are always stable — the system function contains no poles.
    [Show full text]
  • Digital Filter Design Digital Filter Specifications Digital Filter
    Digital Filter Design Digital Filter Specifications • Usually, either the magnitude and/or the • Objective - Determination of a realizable phase (delay) response is specified for the transfer function G(z) approximating a design of digital filter for most applications given frequency response specification is an important step in the development of a • In some situations, the unit sample response digital filter or the step response may be specified • If an IIR filter is desired, G(z) should be a • In most practical applications, the problem stable real rational function of interest is the development of a realizable approximation to a given magnitude • Digital filter design is the process of response specification deriving the transfer function G(z) Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra Digital Filter Specifications Digital Filter Specifications • We discuss in this course only the • As the impulse response corresponding to magnitude approximation problem each of these ideal filters is noncausal and • There are four basic types of ideal filters of infinite length, these filters are not with magnitude responses as shown below realizable j j HLP(e ) HHP(e ) • In practice, the magnitude response 1 1 specifications of a digital filter in the passband and in the stopband are given with – 0 c c – c 0 c j j HBS(e ) HBP (e ) some acceptable tolerances –1 1 • In addition, a transition band is specified between the passband and stopband – – c2 c1 c1 c2 – c2 – c1 c1 c2 Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra Digital Filter Specifications Digital Filter Specifications ω • For example, the magnitude response G(e j ) • As indicated in the figure, in the passband, ≤ ω ≤ ω of a digital lowpass filter may be given as defined by 0 p , we require that jω ≅ ±δ indicated below G(e ) 1 with an error p , i.e., −δ ≤ jω ≤ +δ ω ≤ ω 1 p G(e ) 1 p , p ω ≤ ω ≤ π •In the stopband, defined by s , we jω ≅ δ require that G ( e ) 0 with an error s , i.e., jω ≤ δ ω ≤ ω ≤ π G(e ) s , s Copyright © 2001, S.
    [Show full text]
  • Designing Linear-Phase Digital Differentiators a Novel
    DESIGNING LINEAR-PHASE DIGITAL DIFFERENTIATORS A NOVEL APPROACH Ewa Hermanowicz Multimedia Systems Department, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-952 Gdansk, Poland phone: + (48) 058 3472870, fax: + (48) 058 3472870, email: [email protected] ABSTRACT H (e jω ) = ( jω)k exp(− jωN / 2), ω < π (1) In this paper two methods of designing efficiently a digital k linear-phase differentiator of an arbitrary degree of where k=1,2,… and the frequency response differentiation are proposed. The first one utilizes a symbolic N expression for the coefficients of a generic fractional delay jω − jωn filter and is based on a fundamental relationship between the H k,N (e ) = ∑hk,N [n]e , ω < π (2) coefficients of a digital differentiator and the coefficients of n=0 the generic FD filter. The second profits from one of the of the approximating FIR of order N, i.e. crucial attributes of the structure invented by Farrow for FD jω jω jω filters. It lies in an alternate symmetry and anti-symmetry of Ek,N (e ) = H k (e ) − H k,N (e ) . In (1) N/2 stands for sub-filters which are linear-phase differentiators. The the “transport” delay inevitable in the target FIR. proposed design methods are illustrated by examples. Some Obviously, one can continue the process of deriving practical remarks concerning the usage of the Farrow closed form formulae for the DDk coefficients with higher structure are also included. degree of differentiation, i.e. for k>2. But the value of such formulae would be rather of theoretical nature.
    [Show full text]
  • Signal Processing with Scipy: Linear Filters
    PyData CookBook 1 Signal Processing with SciPy: Linear Filters Warren Weckesser∗ F Abstract—The SciPy library is one of the core packages of the PyData stack. focus on a specific subset of the capabilities of of this sub- It includes modules for statistics, optimization, interpolation, integration, linear package: the design and analysis of linear filters for discrete- algebra, Fourier transforms, signal and image processing, ODE solvers, special time signals. These filters are commonly used in digital signal functions, sparse matrices, and more. In this chapter, we demonstrate many processing (DSP) for audio signals and other time series data of the tools provided by the signal subpackage of the SciPy library for the design and analysis of linear filters for discrete-time signals, including filter with a fixed sample rate. representation, frequency response computation and optimal FIR filter design. The chapter is split into two main parts, covering the two broad categories of linear filters: infinite impulse response Index Terms—algorithms, signal processing, IIR filter, FIR filter (IIR) filters and finite impulse response (FIR) filters. Note. We will display some code samples as transcripts CONTENTS from the standard Python interactive shell. In each interactive Python session, we will have executed the following without Introduction....................1 showing it: IIR filters in scipy.signal ..........1 IIR filter representation.........2 >>> import numpy as np >>> import matplotlib.pyplot as plt Lowpass filter..............3 >>> np.set_printoptions(precision=3, linewidth=50) Initializing a lowpass filter.......5 Bandpass filter..............5 Also, when we show the creation of plots in the transcripts, we Filtering a long signal in batches....6 won’t show all the other plot commands (setting labels, grid Solving linear recurrence relations...6 lines, etc.) that were actually used to create the corresponding FIR filters in scipy.signal ..........7 figure in the paper.
    [Show full text]
  • Deconvolution Filters for Dynamic Rocket Thrust Measurements
    Deconvolution Filters for Dynamic Rocket Thrust Measurements Richard B.H. Ahlfeld Master of Science Thesis Aerospace Engineering Deconvolution Filters for Dynamic Rocket Thrust Measurements Master of Science Thesis For the degree of Master of Science in Aerodynamics at Delft University of Technology Richard B.H. Ahlfeld August 19, 2014 Faculty of Aerospace Engineering · Delft University of Technology The work in this thesis was carried out at Airbus Defence and Space in Ottobrunn, Germany. Copyright © Aerodynamics Group All rights reserved. DELFT UNIVERSITY OF TECHNOLOGY DEPARTMENT OF AERODYNAMICS The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering for acceptance the thesis entitled “Deconvolution Filters for Dynamic Rocket Thrust Measurements” by Richard B.H. Ahlfeld in fulfilment of the requirements for the degree of Master of Science. Dated: August 19, 2014 Supervisors: ii Richard B.H. Ahlfeld Master of Science Thesis Abstract Every spacecraft carries small rocket engines called thrusters for the purpose of orbit and position corrections in space. A precise operation of the thrusters saves fuel and a lower fuel consumption can extend the service life of the spacecraft. Precise thrust levels can be better obtained by pulsed firing than by continuous firing of the thrusters. To guarantee a precise operation, thrusters are tested extensively in a vacuum chamber beforehand on earth to measure their thrust. Measurement errors always impede the accurate determination of the rocket thrust. The measurement of pulsed rocket thrust is especially difficult, if using strain gage type thrust stands typical for the space industry. Their low first natural frequency results in a dominant transient response of the thrust stand structure, which interferes with the thrust signal.
    [Show full text]
  • Laboratory #5: RF Filter Design
    EEE 194 RF Laboratory Exercise 5 1 Laboratory #5: RF Filter Design I. OBJECTIVES A. Design a third order low-pass Chebyshev filter with a cutoff frequency of 330 MHz and 3 dB ripple with equal terminations of 50 W using: (a) discrete components (pick reasonable values for the capacitors) (b) What is the SWR of the filter in the passband (pick 100 MHz and 330 MHz)? B. Design a third order high-pass Chebyshev filter with a cutoff frequency of 330 MHz and 3 dB ripple with equal terminations of 50 W using: (a) discrete components (pick reasonable values for the capacitors) (b) What is the SWR of the filter in the passband (pick 330 MHz and 500 MHz)? (c) What does the SWR do outside the passband? II. INTRODUCTION Signal filtering is often central to the design of many communication subsystems. The isolation or elimination of information contained in frequency ranges is of critical importance. In simple amplitude modulation (AM) radio receivers, for example, the user selects one radio station using a bandpass filter techniques. Other radio stations occupying frequencies close to the selected radio station are eliminated. In electronic circuits, active filter concepts using OpAmps were introduced. One of the advantages of using active filters included the addition of some gain. However, due to their limited gain-bandwidth product, active filters using OpAmps see little use in communication system design where the operational frequencies are orders of magnitude higher than the audio frequency range. The two types of frequency selective circuit configurations most commonly used in communication systems are the passive LC filter (low, high, and bandpass responses) and the tuned amplifier (bandpass response).
    [Show full text]
  • Anti-Aliasing, Analog Filters for Data Acquisition Systems
    AN699 Anti-Aliasing, Analog Filters for Data Acquisition Systems Author: Bonnie C. Baker ANALOG VERSUS DIGITAL FILTERS Microchip Technology Inc. A system that includes an analog filter, a digital filter or both is shown in Figure 1. When an analog filter is INTRODUCTION implemented, it is done prior to the analog-to-digital conversion. In contrast, when a digital filter is imple- Analog filters can be found in almost every electronic mented, it is done after the conversion from ana- circuit. Audio systems use them for preamplification, log-to-digital has occurred. It is obvious why the two equalization, and tone control. In communication sys- filters are implemented at these particular points, how- tems, filters are used for tuning in specific frequencies ever, the ramifications of these restrictions are not quite and eliminating others. Digital signal processing sys- so obvious. tems use filters to prevent the aliasing of out-of-band noise and interference. This application note investigates the design of analog filters that reduce the influence of extraneous noise in Analog Analog A/D Digital data acquisition systems. These types of systems pri- Input Low Pass Conversion Filter marily utilize low-pass filters, digital filters or a combina- Signal Filter tion of both. With the analog low-pass filter, high frequency noise and interference can be removed from the signal path prior to the analog-to-digital (A/D) con- version. In this manner, the digital output code of the FIGURE 1: The data acquisition system signal chain conversion does not contain undesirable aliased har- can utilize analog or digital filtering techniques or a monic information.
    [Show full text]
  • Analog and RF Filters Design Manual: a Filter Design Guide by and for WMU Students
    Department of Electrical and Computer Engineering Analog and RF Filters Design Manual: A Filter Design Guide by and for WMU Students Dr. Bradley J. Bazuin Material Contributors: Dr. Damon Miller, Dr. Frank Severance, and Aravind Mathsyaraja Abstract: Students, practicing engineers, hobbyists, and researchers use a wide range of circuits as fundamental building blocks. This manual provides numerous analog circuits for study and implementation, many of which have been building blocks for circuitry built and tested at WMU. Disclaimer This is a technical report generated by the author as a record of personal research interest and activity. Western Michigan University makes no representation that the material contained in this report is correct, error free or complete in any or all respects. Thus, Western Michigan University, it’s faculty, it’s administration, or students make no recommendation for the use of said material and take no responsibility for such usage. Therefore, persons or organizations who choose to use this material do so at their own risk. Table of Contents Section Page 1 INTRODUCTION.............................................................................................................................................. 4 1.1 GENERAL TYPES OF FILTERS ............................................................................................................................ 4 1.2 REAL FILTERS RESPONSES ..............................................................................................................................
    [Show full text]