Category Archives: Analysis and Signal Processing

Residential Noise Cancellation

Active cancellation probably won’t work. You need a clearly definable source, a point source preferable. It might be difficult to say where the source is in a house. Also, the cancellation only works on a small area where the listener stays put. That’s why it works in cars, however, you need a noisy car. Lotus cars had a system for cars but in their demo’s they would rent a cheap car. It was a system that plugged into the radio.

The active cancellation head phones work because they only have to cancel at your ear, a small area.

I like masking. It’s low cost and small portable systems are readily available. Otherwise one could purchase an active cancellation head phone but that wouldn’t’ be comfortable to sleep with.


Roger Anderson
Engineering Services and Instrumentation for Acoustics, Noise & Vibration
P.O. Box 100
Carver, MN 55315-0100

ATI Introduces Hyperspectral and Multispectral Imaging Techical White Papers by Dr. Richard Gomez

Dr. Gomez is the presenter of ATI’s Hyperspectral and Multispectral Imaging course scheduled to be presented on March 9-11, 2010 in Beltsville, MD.

This three-day class is designed for engineers, scientists and other remote sensing professionals who wish to become familiar with multispectral and hyperspectral remote sensing technology. Students in this course will learn the basic physics of spectroscopy, the types of spectral sensors currently used by government and industry, and the types of data processing used for various applications. Lectures will beenhanced by computer demonstrations. After taking this course, students should be able to communicate and work productively with other professionals in this field. Each student will receive a complete set of notes and the textbook, Remote Sensing: The Image Chain Approach.

View course sampler

Dr. Richard Gomez is a Research Professor at George Mason University (GMU) and Principal Research Scientist at the Center for Earth Observing and Space Research (CEOSR). At GMU he teaches and is actively involved in the scientific and technology fields of hyperspectral imaging and high resolution remote sensing. He has also served in industry and government (Texas Instruments and USACE). Dr. Gomez is internationally recognized as a leader and expert in the field of spectral remote sensing (multispectral, hyperspectral and ultraspectral) and has published extensively in scientific journals. He has organized and chaired national and international conferences, symposia and workshops. He earned his doctoral degree in physics from New Mexico State University. He also holds an M.S. and a B.S. in physics. Dr. Gomez currently serves as Director for the ASPRS Potomac Region and as Remote Sensing Chair for the IEEE-USA Committee on Transportation and Aerospace Technology Policy.

Signal Processing Books

Steve Kay provided information about Signal Processing books:

Modern Spectral Estimation: Theory and Application, Prentice Hall, 1988

Fundamentals of Statistical Signal Processing, Vol. I – Estimation Theory Prentice Hall, 1993

Fundamentals of Statistical Signal Processing, Vol II – Detection Theory, Prentice Hall, 1998 (matlab file downloadable)

Intuitive Probability and Random Processes Using MATLAB, Springer, 2006 ( downloadable incompleted DRAFT in PDF format) ( downloadable MATLAB CODE in TEX format) – downloaded files contain only probability portion of book, see Table of Content Listings below for random processes content (book in its entirety now available from Springer, 2006)

Table of Contents Listings

Fortran Programs of Modern Spectral Estimation Book

MISA Software

More on Sonar Search for AF 447

Information about sonar and side-scan sonar is presented in the short course
Sonar Signal Processing Jul 14-16, 2009 Beltsville, MD

The sonar search for the Air France Flight 447 flight and voice recorder continues with out any reported success. The underwater sonar has an acoustic frequency of 37.5kHz, transmitting initially with 1,060 dynes/cm2, and has a battery life of at least 30 days. Maximum detection range is 2–3km. The water depth is about 3500 m, so a towed sonar is required to get deep enough to have a chance to hear the pinger.

There is useful information at

French authorities have dispatched five ships: IFREMER research vesselPourquoi Pas; two tugboats, Fairmount Glacier and Fairmount Expedition; naval frigateVentôse; and nuclear submarine Emeraude.Ventôse has assisted with recovery of floating debris and bodies. Emeraude will conduct an initial search listening for the black-box pinger. Once this has been located, Pourquoi Pas shall carry out a side-scan sonar survey and there are plans to then deploy a mini-submarine to carry out a detailed photographic survey leading to recovery operations.

The accident location is 1,000km from the Brazilian coastline and the sea floor is extremely rugged (making side-scan sonar operations troublesome) and around 3,500 metres deep (making it difficult to detect the black-box pinger with a maximum range of 2–3km). Both operations will require a submersible or deep-tow capability for sensor deployments. Subsequent recovery of substantial aircraft parts will be an almost-impossible task and operations will probably be limited to flight recorder recovery and a detailed sonar and photographic survey.

Radar Theory and ATIcourses Technical Training

This is an interesting link about radar theory. ATIcourses provide many courses related to practical applications of radar to defense for airborne, ship and ground-based radar.

The Radar Theory Pages are taken from the R.A.F Standard Technical Training Notes (STTN) AP3302 Part 3 (2nd edition), the manual used in Royal Air Force Apprentice training from the mid 1960’s to the early 1970’s. The original document is quite out of date now, some of the symbols used are no longer in use for example and valves are mostly a distant memory. Eventually I hope to add appendices that reflect current practice but for the mean time I want to recreate the feel of the original manual.
I have endeavored to recreate the layout and page numbering of the original manual in order to retain the “feel” of the original. To support this “feel” I have placed buttons at the bottom of each page that allow the user to got to the next page, the previous page or return to the top of the current page. Therefore this section works like a book, just turn the page when you reach the bottom. To facilitate navigation I will include the contents and index pages complete with hypertext links eventually, in the mean time you will find links to the various sections on the left hand panel
The original document contains over 650 pages. This represents a lot of work with the PC and the scanner in order to get it all into HTML. I use Textbridge to scan the text and Paintshop Pro and MS Photoeditor to scan and manipulate the images. Please be patient, I’m sure I’ll get all 650 pages onto the network eventually!

These pages are not intended to be a treatise on radar techniques! It is more like a dictionary than an encyclopedia; acronyms will be spelt out, techniques and terms will be briefly explained. For more information get the books out and RTFM!

Ace d’ Base At the top of the profession, no one on the site can better this fellow!
AFC Automatic Frequency Control
Agile A radar system capable of rapidly jumping from one frequency to another. Used to defeat spot jamming.
Airway Controlled airspace in the form of a road in the sky. In the UK the airway is usually identified by a colour and a number ie Red 01, Green 15 etc. (A rich source of targets)
AMES Air Ministry Experimental Station, as in AMES Type 80 and so on.
AN/FPS-6 US built height finding radar. AKA “Nodding Horror”
AN/xxx-xx US military equipment designation – see next glossary page for full details
Ana-Prop Anomalous Propagation of radar signals that causes ground returns and targets to be seen out to greater than normal distances – or not at all!. Often caused by refraction of the signal in the atmosphere in regions of high pressure
Angels Height in thousands of feet, ie Angels 15 = 15,000 feet. (This term was also used in the early days of radar to describe returns caused by large flocks of birds. In those days they didn’t know what caused these returns, so if they weren’t aircraft they must be angels!)

Submarine Damages Towed Array Sonar

This is of interest to ATIcourses sonar group. It is clear that the towed sonar array would have detected the nearby submarine. There was not that much surface ship could do to maneuver to prevent the submarine from hitting the towed array. Conversely the submarine should have known that this class of surface ship was towing an array. I personally doubt that this was inadvertently.

A Chinese submarine hit an underwater towed array sonar being towed by the destroyer USS John McCain on Thursday.

The array was damaged, but the sub and the ship did not collide, the official said. A sonar array is a device towed behind a ship that listens and locates underwater sounds.

The incident occurred near Subic Bay off the coast of the Philippines.

The official, who declined to be named because the incident had not been made public, would not say whether the U.S. ship knew the submarine was that close to it. But of course the sonar knew the submarine was close, but could not maneuver to get out of the way.

However, the Navy does not believe this was a deliberate incident of Chinese harassment, as it would have been extremely dangerous had the array gotten caught in the submarine’s propellers.

The Navy has complained in the past that Chinese vessels, including fishing boats, have deliberately tried to disrupt U.S. naval activities in international waters near China. In one widely publicized incident in March, five Chinese vessels maneuvered close enough to the USNS Impeccable to warrant the use of a fire hose by the unarmed American vessel to avoid a collision. The Navy later released video of that incident.

Radar and Radar Signal Processing Systems Are Making Flying The Friendly Skies Safer From Bird Strikes

Radar and advanced radar signal processing technology can help make flying safer by avoiding bird strikes.

In the wake of the emergency crash landing of US Airways Flight 1549 in New York’s Hudson River on January 2009, the National Transportation Safety Board is conducting a hearing on implementing currently available avian radar technology to airports throughout the United States. The avian radar industry urges the Federal Aviation Administration (FAA) to make the friendly skies a safer place by immediately deploying commercially-available avian radar systems to our nation’s airports. Bird strikes pose a serious threat to aviation safety. According to the FAA “there were more than 7,400 bird strikes in the United States in 2007, including 110 that caused substantial damage to aircraft.”

According to Dr. Tim J. Nohara, President of Accipiter Radar “avian radar can help mitigate bird hazards where they are most likely to occur around the airport. Real-time monitoring and alerting of approaching flocks of birds helps wildlife control personnel better manage bird hazards.”

In 2006, the FAA began evaluating the avian radar program Accipiter Avian Radar to assess if the use of commercial avian radar at airports would be justified, and would not compromise safety and would be compatible with existing wildlife control operations. The FAA contends that due to the unusual circumstance of the birdstrike current avian radar systems could not have prevented the crash of flight 1549. Flight 1549 was an unusual in that it was a high altitude strike (2800 feet) and did not occur in the immediate vicinity of the airport.

Developers within the avian radar industry, however, assert that current avian radar technology could have prevented the crash. Gary W. Andrews, CEO of DeTect (a industry leading developer of avian radar systems) stated that although some avian radar systems do not have long-range detection capabilities systems, others such as MERLIN Aircraft Birdstrike Avoidance Radar can reliably detect and track bird flocks at a range of up to 8 miles.

Andrew’s contends that MERLIN Radar system has been successfully used throughout the globe for “birdstrike risk detection, tracking and alerting at commercial airports, military airfields, and space launch facilities, with real-time bird activity displays used by airfield managers, bird control staff and air traffic controllers”
Courses in radar and radar signal processing are now becoming available to the public. The Applied Technology Institute of Riva, MD., will offer a three-day course in July 13-15 in Laurel,MD. ATI’s Radar Signal Analysis and Processing using MATLAB course explores algorithms for signal detection, false alarms, tracking techniques and systems performance equations.

Radar Signal Analysis and Processing using MATLAB course is being held July 13-15, 2009 in Laurel, Maryland, in the Washington DC area.

Acoustic and Underwater Sound Meetings

ATIcourses teaches short courses in underwater sound, sonar and acoustics. See our schedule for our technical training seminars  at ATI Training Courses Here are some acoustic and underwater sound conferences that we include as a service to our readers.

June 22-26, 2009 – Third International Conference And Exhibition On Underwater Acoustic Measurements: Technology And Results, Nafplion, Greece,

August 20-22, 2009 – Active 2009, International Symposium on Active Control of Sound and Vibration, Ottawa, Canada,

August 23-26, 2009 – Inter-Noise 2009, 38th International Congress and Exposition on Noise Control Engineering, Ottawa, Canada,

October 26-28, 2009 – EuroNoise 2009, Action on Noise in Europe, Edinburgh, Scotland,

October 26-30, 2009 – 158th Meeting of the Acoustical Society of America, San Antonio, Texas,

April 19-23, 2010 – Joint Meeting Acoustical Society of America and Institute of Noise Control Engineering, Baltimore, Maryland,

Acoustic Analysis Software

ATI’s Advanced Topics In Underwater Acoustics course

The course provides an in-depth treatment of the latest results in a selection of core topics of underwater acoustics.Topics include software for analysis of acoustic signals and software to predict underwater propagation. Its aim is to make available to practitioners results in a tutorial form suitable for people who are already informed about the basics of underwater acoustics.

Avisoft is a company that makes a software package designed for bird and other animal researchers. They have a “lite” version available as a download.
Raven is a very capable acquisition and analysis software package from the Cornell group. Free Lite version. It now supports multi-channel recording
Sound Ruler is a free analysis and graphics package designed for animal sound analysis.
Adobe Audition Commericial Sound Analysis software. Expensive.
Sound Emission Analyzer (SEA), from the bioacoustics group at Pavia, Italy. Mainly developed for bioacoustic studies, this software can be used for a wide range of applications requiring real-time display of sounds and vibrations. It allows to view in real-time the spectrographic features of sounds acquired by any sound device compatible with Windows
BatSound software system: Real-time Imaging/Recording. Has evaluation version as download. Listed by Pettersson Elektronik AB: the Swedish Bat Detector company.
Syrinx A Windows program for spectral analysis, editing, and playback of acoustic signals.
Spectrogram 16 Spectrogram version 16 is a freeware dual channel audio spectrum analyzer for Windows which can provide either a scrolling time-frequency display or a spectrum analyzer scope display in real time for any sound source connected to your sound card.
Sonobat: software provides a comprehensive tool for analyzing and comparing high-resolution full-spectrum Sonograms of Bat echolocation calls recorded from full-spectrum and time-expansion bat detectors.
Ishmael Sound acquisition program with automatic call (signal) recognition, file annotation, acoustic localization
XBAT is a sophisticated architecture for sound analysis that allows you to write your own analysis tools in additon to the ones provided in the distribution.

Wavelets — “Beyond Comparison”

by D. Lee Fugal

Radar, Sonar, Geology and many other varied fields use Wavelets . They are usually presented in mathematical formulae, but can actually be understood in terms of simple comparisons with your data.

As a background, we first look at the Discrete Fourier Transform (DFT) or it’s faster and more famous cousin, the Fast Fourier Transform (FFT). These transforms can be thought of as a series of comparisons with your data, which we will call for now a “signal” for consistency. Signals that are simple waves of constant frequencies can be processed with ordinary DFT/FFT methods.

Real-world signals, however, often have frequencies that can change over time or have pulses, anomalies, or other “events” at certain specific times. This type of signal can tell us where something is located on the planet, the health of a human heart, the position and velocity of a “blip” on a Radar screen, stock market behavior, or the location of underground oil deposits. For these signals, we will often do better with wavelets. We now demonstrate both the Fourier and Wavelet Transforms of a simple pulse signal.

The Discrete Fourier Transform/Fast Fourier Transform (DFT/FFT)
We start with a point-by-point comparison of the pulse signal (D) with a high frequency wave or “sinusoid” of constant frequency (A) as shown in Figure 1 below. We obtain a single “goodness” value from this comparison (a correlation value) which indicates how much of that particular sinusoid is found in our own pulse signal.
Figure 1
Figure 2 We can observe that the pulse has 5 cycles in 1/4 of a second. This means that it has a frequency of 20 cycles in one second or “20 Hz.” The comparison sinusoid, A, has twice the frequency or 40 Hz. Even in the area where the signal is non-zero (the pulse) the comparison is not very good.

By lowering the frequency of A from 40 to 20 Hz (waveform B) we are effectively “stretching” the sinusoid (A) by 2 so it has only 20 cycles in 1 second. We compare point-by-point again over the 1-second interval with the pulse (D). This next correlation gives us another value indicating how much of this lower frequency sinusoid (now the same frequency as our pulse) is contained in our signal. This time the correlation of the pulse with the comparison sinusoid is very good. The peaks and valleys of B and the pulse portion of D align (or can be easily shifted to align) and thus we have a large correlation value.

Figure 1 shows us one more comparison of our original sinusoid (A) stretched by 4 and trimmed so it has only 10 cycles in the 1 second interval (C). This comparison with D is poor again. We could continue stretching and trimming until the sinusoid becomes a straight line having zero frequency or “DC” (named for the zero frequency of Direct Current) but all these comparisons will be increasingly poor.

Figure 3 An actual DFT (or functionally equivalent FFT) compares many “stretched” sinusoids (“analysis signals”) to the pulse rather than just the three shown here. The best correlation is found when the sinusoid frequency best matches that of the pulse. Figure 2 shows the first part of an actual FFT of our pulse signal D. The locations of our sample comparison sinusoids A, B, and C are indicated. Notice that the FFT tells us correctly that the pulse has primarily a frequency of 20 Hz, but does NOT tell us where the pulse is located in time!

The Continuous Wavelet Transform (CWT)
Wavelets are exciting because they too are comparisons, but instead of cor-relating with various stretched, infinite length unchanging sinusoids, they use smaller or shorter waveforms (“wave–lets”) that can start and stop where we wish.

By stretching and shifting the wavelet numerous times we get numerous correlations. If our signal has some interesting events embedded, we will get the best correlation when the stretched wavelet is similar in frequency to the event and is shifted to line up with it in time. Knowing the amounts of stretching and shifting we can determine both location and frequency.

Figure 3 demonstrates the process. Instead of sinusoids for our comparisons, we will use wavelets. Waveform A shows a Daubechies 20 (Db20) wavelet about 1/8 second long that starts at the beginning (t = 0) and effectively ends well before 1/4 second. The zero values are extended to the full 1 second. The point-by-point comparison with our pulse signal D will be very poor and we will obtain a very small correlation value.

Figure 4 In the previous FFT/DFT discussion we proceeded directly to stretching. In the Wavelet Transforms we shift the wavelet slightly to the right and per-form another comparison with this new waveform to get another correlation value. We continue to shift until the Db20 wavelet is in the position shown in B. We get a little better comparison than A, but still very poor because B and D are different frequencies.

After we have shifted the wavelet all the way to the end of the 1 second time interval we start over with a slightly stretched wavelet at the beginning and repeatedly shift to the right to obtain another full set of these correlation values. C shows the Db20 wavelet stretched to where the frequency is roughly the same as the pulse (D) and shifted to the right until the peaks and valleys line up fairly well. At this particular shifting and stretching we should obtain a very good comparison and large correlation value. Further shifting to the right, however, even at this same stretching will yield increasingly poor correlations.

In the CWT we thus have one correlation value for every shift of every stretched wavelet. To show the data for all these stretches and shifts, we use a 3-D display with the stretching (roughly inverse of frequency) as the vertical axis, the shifting in time as the horizontal axis, and brightness (or color) to indicate the strength of the correlation. Figure 4 shows a Continuous Wavelet Transform (CWT) display for this particular pulse signal (D). Note the strong correlation of the three larger peaks and valleys of the pulse with the Db20 wavelet, the strongest being where all the peaks and valleys best align.

The display shows that the best correlation occurs at the brightest point or at about 3/8 second. This agrees with what we already know about the pulse, D. The display also tells us how much the wavelet had to be stretched (or “scaled”) and this indicates the approximate frequency of the pulse. Thus we know not only the frequency of the pulse, but also the time of it’s occurrence!
Figure 5
We run into this simultaneous time/frequency concept in everyday life. For example, a bar of sheet music may tell the pianist to play a C-chord of three different frequencies at exactly the same time on the first beat of the measure.

For the simple example above we could have just looked at the pulse (D) to see its location and frequency. The next example is more representative of wavelets in the real world.

Figure 5 shows a signal with a very small, very short discontinuity at time 180. The Amplitude vs. Time plot of the signal is shown at the upper left but does not show the tiny “event”. The Magnitude vs. Frequency FFT plot tells what frequencies are present but does not indicate the time associated with those frequencies.

With the wavelet display, however, we can clearly see a vertical line at 180 at low scales when the wavelet has very little stretching, indicating a very high frequency. The CWT display also “finds” the large oscillating wave at the higher scales where the wavelet has been stretched and compares well with the lower frequencies. For this short discontinuity we used a short wavelet (a Db4) for best comparison.

This is an example of why wavelets have been referred to as a “mathematical microscope” for their ability to find interesting events of various lengths and frequencies hidden in data.

Besides acting as a “microscope” to find hidden events in our data, wavelets can also separate the data into various frequency components, as does the FFT. The FFT/DFT is used extensively to remove unwanted noise that is prevalent throughout the entire signal such as a 60 Hz hum. Unlike the FFT, however, the wavelet transform allows us to remove frequency components at specific times in the data. This allows us a powerful capability to throw out the “bad” and keep the “good” part of the data in that frequency range.

These types of transforms are called “Discrete Wavelet Transforms” (DWT). They also have easily computed inverse transforms (IDWT) that allow us to reconstruct the signal after we have identified and removed the noise or superfluous data for denoising or compression.

Undecimated or “Redundant” Discrete Wavelet Transforms (UDWT/RDWT)
In one type of DWT, the Redundant Discrete Wavelet Transform, or RDWT, we first compare (correlate) the Wavelet “filter” with itself. This produces a “Highpass Halfband Filter” or “superfilter.” When we compare or correlate our signal with this superfilter we extract the highest half of the frequencies. For a very simple denoising, we could just discard these high frequencies (for whatever time period we choose) and then reconstruct a denoised signal.

Multi-level RDWT’s allow us to stretch the wavelet, similar to what we did in the CWT, except that it is done by factors of 2 (twice as long, 4 times as long, etc.). This allows us stretched superfilters that can be halfband, quarter-band, eighth-band and so forth.
Figure 6
Conventional (Decimated) Discrete Conventional Transforms (DWT)
We stretched the wavelet in the CWT and the RDWT. In the conventional DWT, we shrink the signal instead and compare it to the unchanged wavelet. We do this by “downsampling by 2.” Every other point in the signal is discarded. We have to deal with “aliasing” (not having enough samples left to represent the high frequency components and thus producing a false signal). We must also be concerned with “shift invariance” (do we throw away the odd or the even values? — it matters!).

If we are careful, we can deal with these concerns. One amazing capability of the filters in the conventional DWT is alias cancellation where the basic wavelet and 3 similar “filters” combine to allow us to reconstruct the original signal perfectly. The stringent requirements on the wavelets to be able to do this is part of why they often look so strange (see Figure 8).

Figure 7 As with the RDWT, we can denoise our signal by discarding portions of the frequency spectrum — as long as we are careful not to throw away vital parts of the alias cancellation capability. Correct and careful downsampling also aids with compression of the signal. Modern JPEG compression uses wavelets. Figure 6 shows JPEG image compression. The image on the right was compressed by a ratio of 157:1 using a Biorthogonal 9/7 set of wavelets.

There are many types of Wavelets. Some come from mathematical expressions. Others are built from basic Wavelet Filters having as little as 2 points. The Db4, Db20, and Biorthogonal wavelets shown earlier are examples of this 2nd type. Figure 7 shows a 768 point approximation of a continuous Db4 wavelet with the 4 filter points (plus 2 zeros) superimposed.

Some wavelets have symmetry (valuable in human vision perception) such as the Biorthogonal Wavelet pairs. Shannon or “Sinc” Wavelets can find events with specific frequencies (these are similar to the Sinc Function filters found in traditional DSP). Haar Wavelets (the shortest) are good for edge detection and reconstructing binary pulses. Coiflets Wavelets are good for data with self-similarities (fractals) such as financial trends. Some of the wavelet families are shown in Figure 8.
Figure 8
You can even create your own wavelets, if needed. However there is “an embarrassment of riches” in the many wavelets that are already out there and ready to go. We have already seen that with their ability to stretch and shift that wavelets are extremely adaptable. You can usually get by very nicely with choosing a less-than-perfect wavelet. The only “wrong” choice is to avoid wavelets due to an abundant selection.

Bio + ad There is much more to discover than can be presented in this short overview. The time spent, however, in learning, understanding and correctly using wavelets for these “non-stationary” signals with anomalies at specific times or changing frequencies (the fascinating, real-world kind!) will be re-paid handsomely.

Article © 2009 Space & Signals Technologies LLC,
All Rights Reserved.

About the author
D. Lee Fugal is Founder and President of Space & Signals Technologies, LLC., a company specializing in the presentation of difficult concepts in an intuitive, understandable manner. He has over 30 years of industry experience in Digital Signal Processing (including Wavelets) and Satellite Communications. He has been a full-time consultant on numerous assignments since 1991. Additionally, Mr. Fugal offers short courses for Jim Jenkins at ATI (