Something that repeats once per second has a period of 1 s. It also have a frequency of # 1/s#.One cycle per second is given a special name Hertz (Hz). Heat-damaged spots could be detected and the dielectric properties of polyimide appeared to remain unaltered at burn temperatures below 480 °C. 18.22 do not include Fresnel reflection losses, and when this factor is included the CW results are ~ 19 ± 2 cm–1 (0.5 THz) and ~ 30 ± 2 cm–1 (0.8 THz) for the undamaged samples(Petkie et al., 2009). 7-31, but the threshold parameter used here results in somewhat less noise removed. Comparison of a one-sided spectrum without using a window function and a one-sided spectrum using the Hamming window for speech data. New to Amplitude? 18.7. This reduces the amplitude of the lower frequency components containing the scene content and removes the zero frequency component. The signal level is low, so the striping noise is readily apparent, both in the image and in the amplitude spectrum, where it appears as the column through zero frequency. There are two places for manual intervention in this procedure, one for the width of the high-pass filter in step 1, which should be as small as possible while still removing most of the scene content, and the other for the threshold of step 2, which determines the extent of noise removal. The sampling rate is 1 kHz. As we can see, the baseline spectrum contains the meshing frequency component of 300 Hz and a sideband frequency component of 283.33 Hz (300–16.67). ирования антенн приёма широкополосных сигналов, преимущественно для антенн неэквидистантной решётки, Electronic device and communication method, Method and apparatus for testing phased array antennas, Apparatus and method for improving antenna sidelobe cancellation, Antennensystem zur breitbandigen satellitenkommunikation im ghz frequenzbereich mit hornstrahlern mit geometrischen konstriktionen, 宽带波束形成设备，宽带波束导向设备及相应的方法, Verfahren, vorrichtungen und telekommunikationsnetzwerk zum regeln der antennengewichte eines transceivers, Funkbasisstation mit Gruppenantenne und Sendekalibrierung, A new method for obtaining maximum gain from Yagi antennas, Vorrichtung zum empfang von sekundärradarsignalen mit quasi dynamischer oder dynamischer sektorisierung des zu überwachenden raumes und verfahren hierzu, Farfield calibration method used for phased array antennas containing tunable phase shifters, Verfahren zum adaptieren einer antennenkeule an laufende betriebsbedingungen, anordnung zur bildung einer adaptierten antennenkeule und adaptives antennensystem, Kommunikationseinrichtung mit übertragungs-diversity, Kommunikationssystem mit mehreren basisstationen mit adaptiven antennen und verfahren, Raumzeitliche signalverarbeitung für übertragungssysteme, Verfahren und vorrichtung zur übertragung mit mehreren antennen, Kalibrierung einer phasengesteuerten Gruppenantenne durch orthogonale Phasenfolge, System und Verfahren zum Mikrowellenabbilden unter Verwendung eines verschachtelten Musters in einem programmierbaren Reflektorarray, Strahlungswirkungsgradmessvorrichtung und Strahlungswirkungsgradmessverfahren, Hochisolierendes, doppelpolarisiertes Antennensystem mit Dipolstrahlungselementen, Strahlformungsarchitektur für die Abwärtsstrecke bei einer Anordnung mit stark überlappenden Keulen, Basisstationseinrichtung und verfahren zur steuerung eines antennenstrahls, a) Ändern der Phasen der Phasenschieber (, b) Bestimmen des Verhältnisses des maximalen-zu- Just enter the trigonometric equation by selecting the correct sine or the cosine function and click on calculate to get the results. The next task was to image the heat-damaged samples. As shown in Figure 4.26, four dominant modes (natural frequencies corresponding to locations of spectral peaks) can be easily identified from the displayed spectrum. Wir verkaufen gebrauchte Luxusuhren der Marken Rolex, Omega, Tudor, IWC, Breitling, Tag Heuer u.v.m. In some special applications, only the amplitude or power spectrum can be measured and it is necessary to recover the phase. Voids were also investigated, which simulate either manufacturing defects or damage caused by stress over time. This technique was devised in the 20th century at a time when Landell de Moura and Reginald Fessenden were conducting experiments using a radiotelephone in the 1900s. . The “design filter” step can be manual or semi-automated, as described in the text. However, when data length is short, the reduction in spectral leakage using a window function will be more prominent. Amplitude is an important parameter of waves and is the maximum displacement of points on a wave. Such models are valuable inasmuch as they draw attention to the precise features of the failure process that have wider significance and implications. Figure 7 shows the cepstra obtained from two zoom spectra, slightly displaced from each other in center frequency. . It is to be assumed that, during the measurements at this operating point, an acoustic resonance arises, which is not calculated in the simulations. The first sample was prepared to calibrate the system based on material thickness (coupon 1 in Fig. This can occur if the spacing between the latter is not sufficiently greater than the analysis bandwidth. With noun/verb tables for the different cases and tenses links to audio pronunciation and … 7-31. The images formed by the peak amplitude of the THz pulses are shown in Fig. Amplitude is also a very important property of a periodic motion. Correlation in time domain is equivalent to multiplication of the trace amplitude spectrum with the filter amplitude spectrum and subtraction of the trace phase spectrum from the filter phase spectrum in the frequency domain. FIGURE 4.26. In other words, determine the dominant mechanism(s); simplify it (them); and exploit the modelling successes of others in materials science and engineering. 18.6b correspond to the white marker dots (shown in Fig. The lower the B value is, the longer the wavelet is, and the lower the resolution is. Learn the translation for ‘Amplitude’ in LEO’s English ⇔ German dictionary. . In general, amplitude modulation definition is given as a type of modulation where the amplitude of the car… • Build and share your analysis. . Spenser cofounded Amplitude in 2012 to help companies build better products through product analytics. This means that the frequency bands of effective signals are extended, and the resolution of seismic data is improved (Wang et al., 2010). 18.6, with the heat-damaged areas within the circles (of the white marker dots of Fig. We can see that most of seismic signal components are below 3 Hz. Figure 2.20. For support, contact Amplitude on 0333 014 6363 . We developed an analytical model for MS wave amplitude on location information, kp index, wave normalized frequency, and normal angle A drastic fluctuation of MS wave amplitude distribution on the kp index was observed when kp > 5 A detailed global distribution of MS wave amplitude is presented . This approach to removing periodic noise from images dates from the earliest spacecraft missions (Rindfleisch et al., 1971) and has been applied to MSS (Pan and Chang, 1992), TM (Srinivasan et al., 1988), and Fuyo-1 imagery (Filho et al., 1996). The amplitude spectrum simply gives amplitude at each frequency. (B) Seismic profile after the spectrum whitening frequency extension. Robert A. Schowengerdt, in Remote Sensing (Third edition), 2007. This difference explains why the autocorrelation of any trace is a zero phase. . . . FIGURE 4.22. Invert and scale the result to zero for the noise components and one for all others, thus creating a noise mask. 3). . . Li Tan, Jean Jiang, in Digital Signal Processing (Second Edition), 2013. Because the harmonic pattern no longer passes through the effective ‘zero’ frequency, it is seen that there is no longer necessarily a positive peak in the cepstrum corresponding to the harmonic spacing, but there can even be positive and negative peaks on either side of a zero crossing. A well known example is X-ray crystal developing the double helix model for DNA in 1953 for example. THz TDS material parameter measurements for heat damage areas showing (a) indices of refraction and (b) absorption coefficients. Figure 18.6a shows the sample that was heated to 440 °F for 4 min over ~ 2 × 1.5 cm2 area. Amplitude, international leader in ultrafast lasers, is committed to the design and manufacturing of reliable and easy-to-use lasers, adhering to the best quality standards, including ISO 9001 and ISO 13485 (Medical) certification. 18.3. The high-pass filter has a 1/e width of 0.05 cycles/pixel, i.e., one-tenth of the highest frequency, and the threshold applied to the modified spectrum is simply midway between the minimum and maximum amplitude values. Enwenode Onajite, in Seismic Data Analysis Techniques in Hydrocarbon Exploration, 2014. Seismic profile before and after the spectrum whitening frequency extension. FIGURE 7-32. Note also that autocorrelation of a seismic trace in the time domain is equivalent to multiplying the amplitude spectrum by itself and subtracting the phase spectrum from itself. This is due to the 60-Hz power line interference when the ECG is acquired via the ADC acquisition process. Figures 4.28–4.31 show the baseline vibration signal and spectrum for a gearbox in good condition, along with the vibration signals and spectra for three different damage severity levels (there are five levels classified by SpectraQuest, Inc; the spectrums shown are for severity level 1 [lightly chipped]; severity level 4 [heavily chipped]; and severity level 5 [missing tooth]). In Fig. This problem can be very easily solved by making use of Hilbert transform theory (see HILBERT TRANSFORMS). . . . A practical question that may arise is, can the same filter remove noise from another part of the image? 7-30). The same effect can occur with baseband spectra, in cases where a sideband spacing is not an exact subharmonic of the carrier frequency, such as in signals from rolling element bearings and planetary gearboxes. In reflection mode, the magnitude of the first surface reflection and subsequent reflections would be approximately the same, which should enable a greater ability to locate the depth of a void. . As explained in the text, this difference is in the amplitudes of the frequency components, not their frequencies. . . . These results also compare well with CW transmission experiments on the identical samples (see Fig. Multiply the amplitude spectrum of the image by a “soft” high-pass frequency domain filter, such as an inverted Gaussian. 4. We now present another practical example for vibration signature analysis of a defective gear tooth, described in Section 1.3.5. (b) Phase spectra. Data taxonomy and instrumentation best practices using Amplitude SDKs, APIs, and inbound integrations. The value represents in some sense the average protrusion of the harmonic/sideband pattern above the base noise level, and is thus very signal-dependent as well as depending on such artifacts as the analysis bandwidth (relative to the harmonic/sideband spacing) and the type of window function used for the original analysis (e.g. . THz TDS images for three heated areas on glass fiber samples: (a) 440 °C for 4 min, (b) 430 °C for 6 min, and (c) 425 °C for 20 min. 18.4. Similar images can be shown using the area under the curve from the amplitude spectrum in the frequency domain. . Physical modelling provides the means to assess the relative severity of different fatigue loading regimes, constant amplitude vs. variable amplitude spectra, frequency effects and R- ratio effects as well as load/environment interactions. The Fourier spectrum is more complex, consistent with the detail in the image, but the noise characteristics are similar to those of the ocean area. This reduces the amplitude of the lower frequency components containing the scene content and removes the zero frequency component. 7-31); the frequency components are the same, which is why the same notch filter works, but their amplitudes are different. The white circular dots in Fig. In critical fatigue situations, where the objective is to design for longevity, durability, and structural integrity, then the balance is shifted in favour of physical modelling and away from the empirical approach. The ECG signal contains frequency components ranging from 0.05 to 100 Hz sampled at 500 Hz. An example for our image is shown in Fig. Frequenz und Periodendauer berechnen Hz ms Formel Formelsammlung Akustik Rechner Frequenzformel Schwingungsdauer Periode Dauer Perioden amplitude umrechnen t=1/f Wellenlänge Rechner Hertz Schwingung umrechnen Amplitude Kreisfrequenz - Eberhard Sengpiel sengpielaudio Note that the amplitude cepstra indicate the sideband spacings more clearly. 18.6c and less noticeable white dots in Fig. The signal level is low, so the striping noise is readily apparent, both in the image and in the, which is exists over a finite region of support and is zero outside this region and whose, Physical modelling of damage development in structural composite materials under stress. He took a continuous spark transmission and placed a carbon microphone in the antenna lead.The sound waves impacting on the microphone varied its resistance and in turn this varied the intensity of the transmission. The seismic data after the frequency extension is calibrated at the well points by using high-frequency synthesized seismograms. . The given below is the amplitude period phase shift calculator for trigonometric functions which helps you in the calculations of vertical shift, amplitude, period, and phase shift of sine and cosine functions with ease. . . Academia.edu is a platform for academics to share research papers. The speed of sound, for instance, is reduced locally by the elastic wall. Amplitude (a01, ..., a0n) in einem Speicher, a) mittels mindestens eines in der phasengesteuerten The voids show an area of reduced amplitude, most likely due to the multiple reflections from the air/composite interface. or customer.support@amplitude-clinical.com. Read about using the FFT on theTektronix DPO 2000 series oscilloscopes manual. 18.2) made on the samples to show the extent of the heat-damaged area. These results are consistent with other measurements made on glass fiber samples, where the index of refraction was 2.05–2.1 and the absorption coefficient was 12 cm–1 (0.5 THz) and 26–32 (0.8 THz) (Rutz et al., 2006b). . It has a visibly noticeable bubble or blister on its exterior, which roughly corresponds with the black area within the black oval. For tracked users, this preserves their full event streams and thus preserves “behaviors”. . Die Royal Mile ist eine sehr bekannte Straße in Edinburgh auf der sehr viele Touristen unterwegs sind. 18.5 where (a) represents the peak pulse amplitude and (b) shows the pulse position at each pixel (Mittleman, 2003). The measurements of a wave include wavelength, frequency, and amplitude. Learn more. FIGURE 4.25. We are event specialists with over 30 years of experience Amplitude Event Solutions has a proven track record providing AV and production services for corporate clients and public sector bodies across the UK. If we also block the pair of high-frequency columns on either side of the center noise spike, a more subtle, within-line coherent noise is also removed. DE3934155C2 DE19893934155 DE3934155A DE3934155C2 DE 3934155 C2 DE3934155 C2 DE 3934155C2 DE 19893934155 DE19893934155 DE 19893934155 DE 3934155 A DE3934155 A DE 3934155A DE 3934155 C2 DE3934155 C2 DE 3934155C2 Authority DE Germany Prior art keywords antenna phase amplitude arrangement antenna arrangement Prior art date 1988-10-13 Legal status … computing, An amplitude only reconstruction basically yields ‘rubbish’ compared to a phase only reconstruction which yields features that are recognisable in terms of the original signal. Our vibration amplitude testing machine varies the applied voltage to the vibration motor, and an accelerometer on the sled measures the resulting G. Accelerometers, due to their construction, have a … Automatic filter design for striping. Fourier amplitude filtering to remove striping from a nearly uniform ocean area in a TM image acquired on December 31, 1982. We can observe that the sidebands (fm±fi, fm±2fi …) become more dominant when the severity level increases. After measuring the indices of refraction for the glass, polyimide and composite, we investigated the heat-damaged samples to determine their material parameters, see Fig. Convolution of our seismic trace in the time domain is equivalent to multiplication of the trace amplitude spectrum with the filter amplitude spectrum and the addition of the trace phase spectrum with the filter phase spectrum in the frequency domain (Figure 2.21). There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In this lab you will begin to look at the frequency power spectrum of signals. The THz spot size was measured to be 1.5 mm and individual pixels were 1 × 1 mm2 in all of the scans except the calibration sample with 0.5 × 0.5 mm2 pixels. Even so, it is often meaningful to make comparisons between cepstra measured under the same operating conditions on the same machine (where the base noise level could be taken to be constant) and analyzed in the same way. Obtaining cepstra from zoom spectra, by the formal definition (inverse transform of log spectrum) and as the amplitude of the analytic signal obtained from the one-sided spectrum. Consider a sinusoidal modulating signal or message signal (am) of frequency (ωm) and amplitude (Am) given by: am = Am sin ωmt . Blocking the primary striping noise component results in a cleaner image, and blocking the three periodic noise components results in further improvement. The force of a vibration motor is governed by the equation: The index of refraction for the unaltered composite remained relatively constant in the THz frequency range at 2.05 ± 0.01 while the absorption coefficient was measured as 17.5 ± 0.8 cm–1 (0.5 THz), 27.5 ± 1.1 cm–1 (0.8 THz) and 38 ± 1.6 cm–1 (1 THz). . Vibration signal and spectrum for damage severity level 4. . M.J. Bohn, D.T. Similar images can be shown using the area under the curve from the, Calculation of discharge pressure pulsations of a screw compressor using the one-dimensional method of characteristics, 8th International Conference on Compressors and their Systems, . (1) and carrier wave (ac) of frequency (ωc) and amplitude (Ac) given by: ac = Ac sin ωct . The vibration data is collected by an accelerometer installed on the top of the gearbox. If the cepstrum calculation is carried out on the one-sided spectrum (positive frequencies only), then the resulting cepstrum will be analytic and complex (not to be confused with the ‘complex cepstrum’, which is real) and a peak will always be found at the correct quefrency in the amplitude of this complex function. The amplitude and frequency of mEPSC can be changed by the blockage of synaptic activity , and finally may result in the changes of synapses' structure , . Notice that in convolution the phase spectrums are added together, while in correlation the phase spectrums are subtracted one from another. 1 : the extent or range of a quality, property, process, or phenomenon: as. The noise DN standard deviation in this case is 0.69. . application of the least squares method, the maximum entropy criterion, Bayesian estimation etc. The approach is to examine the amplitude or power spectrum of the image to locate the noise frequency components, design a blocking (“notch”) filter7 to remove them, apply the filter to the noisy image spectrum in the frequency domain, and finally calculate an inverse Fourier transform to obtain the corrected image (Fig. We pride ourselves on our high levels of customer service, and our vast experience and expertise on providing peace of mind for our clients . In the field of ship design and design of other floating structures, a response amplitude operator is an engineering statistic, or set of such statistics, that are used to determine the likely behavior of a ship when operating at sea. The Fourier amplitude spectrum of the filtered image is then thresholded to yield the noise filter. The approximate depth of a delamination could be determined in the time domain by measuring the timing of a Fabry–Pérot reflection through a thin slice of the composite. Note that any editing or ‘liftering’ would have to be done on the complex function. (a) Amplitude spectra. Comparison of a spectrum without using a window function and a spectrum using the Hamming window for speech data. By continuing you agree to the use of cookies. R.B. Jonathan M. Blackledget, in Digital Signal Processing (Second Edition), 2006, Given that the amplitude spectrum and the phase spectrum, taken together, uniquely describe the time signature of a signal, it is pertinent to ask how these spectra, taken separately, contribute to the signal. 18.3. Added benefits include more options being made available to the designer, a reduced need for extensive and costly testing and more efficient and shorter design iteration cycles. FOR CLINICIANS. 4. . Randall, in Encyclopedia of Vibration, 2001. Thus, the Fourier phase of a signal is ‘more important’ than the Fourier amplitude and is less robust to error. Antennenanordnung angeordneten weiteren No part of this electronic publication/website may be reproduced in any form or by any means without prior written permission from Amplitude Media Group. Comparison of simulated and measured pressure pulsations at mp1. Here, X-rays with a constant wavelength of λ are diffracted by the three dimensional molecular structure (in a crystal defined by an object function O(x, y, z) which is of compact support. . That is, to decrease f1 by keeping the low-frequency components, or increase f2 by extending the high-frequency component, so as to increase the seismic resolution. The noise DN standard deviation is only 0.45 and 0.77. respectively; the mean DN is zero in both cases. 18.2). Figure 2.21. The noisy image is first high-pass filtered to remove the lower spatial frequency components. Xianzheng Zhao, ... Xiugang Pu, in Re-exploration Programs for Petroleum-Rich Sags in Rift Basins, 2018. 7-31) to another part of the same TM image. . Fig. The glass fiber composite absorbs a significant amount of the THz radiation, attenuating the signal, and limiting the use of Fabry–Pérot reflections for depth measurements. Antennenelements (, d) während des Betriebs der Antennenanordnung eine We use cookies to help provide and enhance our service and tailor content and ads. . Fig. The unit under test (UUT) is attached to a vibration sled – a metal block with a known mass. Because this image has higher frequency content than the ocean segment, some image frequency components are also being removed here. A comparable picture is shown in the results for op2. 11154 Huron Street, Suite 104 Northglenn, CO 80234 Phone 303.255.0843 [email protected]. . The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). . . Existing design methodologies at the higher structural size scales can be supported and justified by fundamental understanding at lower size scales. weiteren Antennenelemente (. . It is the range of pressure excursions. . . An important characteristic of Spectrum analyzers is the noise floor or si… The damage area heated to 430 °C for 6 min may have been affected by either a removal of the outer coating or a residue created during the heating process. . The amplitude spectrum of this block shows a more complex structure, as expected, but with similar noise components. For a real valued signal with A(ω) > 0, ∀ω, its zeros occur when ω+ θ(ω)=± nπ/2, n= 1,2,3… since, This can be observed by taking an amplitude only and a phase only reconstruction of a signal, i.e. 18.6c was inconclusive in showing evidence of the thermal damage. 18.5b is a result of the interpolation technique to smooth out the pixels and does not match the pattern of the glass weave within the composite. . Although the second and third harmonics again have comparable relations with one another, the amplitude of the basic harmonic is calculated as being much smaller than it occurs in the measurements. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Digital Signal Processing (Second Edition), Discrete Fourier Transform and Signal Spectrum, (one-sided spectrum), there is little difference between the, Seismic Data Analysis Techniques in Hydrocarbon Exploration, To describe seismic trace in the frequency domain requires both an, Seismic Reservoir Prediction Technologies for Re-exploration, Re-exploration Programs for Petroleum-Rich Sags in Rift Basins, Terahertz applications in the aerospace industry, Handbook of Terahertz Technology for Imaging, Sensing and Communications, ). . In frequency domain, seismic trace is described in terms of amplitudes and phases at certain frequencies. In preparation for measuring material parameters, we first measured a THz pulse and its amplitude spectra for the air reference and compared it with the pulse and spectrum through undamaged glass fiber shown in Fig. . To increase the resolution, therefore, the B value should be increased as much as possible. Neurons can slowly and cumulatively adjust their synaptic strength to compensate for the plasticity changes to maintain homeostasis of the neural network . Understand the differences between swept frequency, FFT, and real-time spectrum Analyzers, as well as the term resolution bandwidth. FIGURE 4.24. . Pressure is related to the degree of tissue displacement caused by vibration. Antennenelement (, a) eine Anordnung mehrerer Antennenelemente (, a) in einem ersten Meßschritt die Empfangsantenne (, b) während des nachfolgenden Betriebs lediglich die I've used the PyAudio default recording example, and added numpy and scipy. ; Glasgow ist zwar nicht die Hauptstadt Schottlands, aber die größte Stadt. . 7-32) was selected from the same scene. 18.2). The THz image of the damage area in Fig. We also compute the one-sided spectrum for a standard electrocardiogram (ECG) signal from the MIT–BIH (Massachusetts Institute of Technology–Beth Israel Hospital) Database. This could be down to modelling errors especially concerning the discharge piping. The first harmonic is most pronounced and the second harmonic is least pronounced. Petkie, in Handbook of Terahertz Technology for Imaging, Sensing and Communications, 2013. Comparison of a one-sided spectrum without using a window function and a one-sided spectrum using the Hamming window for seismic data. Sie ist fast eine Meile lang und verbindet die zwei königlichen Residenzen (Edinburgh Castle und Palace of Holyroodhouse).Deshalb wird sie Royal Mile genannt. The differing heights of the edges of the milled out areas causes a frequency dependence in amplitude intensity. minimalen Energieniveaus (r, c) Bestimmen einer Phase (P01, ..., P0n) und einer He previously worked as an algorithmic trader at DRW Trading Group and studied Bioengineering at MIT where he won Battlecode, MIT’s largest programming competition, twice. Next, we compute the one-sided spectrum for 32-bit seismic data sampled at 15 Hz (provided by the US Geological Survey, Albuquerque Seismological Laboratory) with 6,700 data samples. THz TDS (a) pulse and (b) amplitude spectra for air reference and glass fiber. . In particular, the foundation of physical modelling could be applied to solving a range of problems in composites. (2) Where, amis the modulating signal or message signal acis the carrier signal Amis the maximum amplitude of the message signal Acis the maximum amplitude of the carrier signal ωm is the frequency of the message … FIGURE 7-33. As demonstrated in Figure 4.22 (two-sided spectrum) and Figure 4.23 (one-sided spectrum), there is little difference between the amplitude spectrum using the Hamming window function and the spectrum without using the window function. The amplitudes from the simulations as well as the measurements decrease, since op2 is closer to the designed working conditions. Results showed that localized heat damage did not change the complex indices of refraction of the composite samples noticeably; however, changes in the THz signal were observed due to material blistering and/or residue deposited. Vibration signal and spectrum for damage severity level 1. . A period #P# is related to the frequency #f# # P = 1/f#. Thus, f2 rises, and correspondingly B rises too. 18.6. Indices of refraction and absorption coefficients in the THz frequency range were measured using THz TDS in transmission configuration for comparison of damaged and undamaged material states. US wave amplitude is defined as the difference between the peak pressure and average pressure values of the waveform (Fig. . Jonathan M. Blackledge, in Digital Image Processing, 2005. The filter derived previously removes this noise without appearing to harm the image. Increase in a family of harmonics/sidebands will only be detected if the lower amplitude limit is a constant noise level rather than a ‘bridging’ between adjacent components a fixed number of dB below the peaks. The capability of physical modelling is important in the design of experimental test programs that ensure critical loading regimes are examined.