The Scientist and Engineer's Guide to
Digital Signal Processing
By Steven W. Smith, Ph.D.

Three examples where DSP saved my butt!
by Steve Smith

Get Back - It's gonna blow!

THE PROBLEM
As shown below, the SECURE 1000 operates by passing an x-ray beam through various collimators, including a rotating chopper wheel containing several slits. As the chopper wheel rotates, a narrow beam of x-rays is formed that sweeps rapidly from right-to-left. The chopper wheel is a brass disk about 8 inches in diameter, 1/4 inch thick, and contains 4 silts (although 6 slits are shown in the illustration). The chopper wheel turns at about 2,000 rpm, and is very quiet, much less than normal conversation.

Here's the problem: a customer paid us to make the chopper spin three times faster, i.e., 6000 rpm. Three times the speed means nine times the stored energy. Worse yet, at 6000 rpm it sounded louder than a jet airplane taking off; people standing nearby backed away in fear! I did too! We had two choices: hope the customer was deaf, or find a way to reduce the noise.

HOW DSP SAVED THE DAY
The first step in reducing the noise was to understand how it was being generated. Three possibilities were identified: (1) the disk could be unbalanced, (2) the radial slits could be catching the air, or (3), the surface of the disk could be causing air turbulence. This is where DSP came in. Several seconds of the noise was digitized and stored (using a microphone, analog-to-digital converter, and personal computer). The frequency spectrum of this signal was calculated via the FFT, and is displayed below.

In this experiment, the chopper wheel was turning at 90 hertz (rotations per second). Noise resulting from an imbalance therefore shows up at 90 Hz, plus its harmonics, 180 Hz, 270 Hz, and so on. On the other hand, noise originating from the four slits shows up at four times this frequency, 360 Hz, plus its harmonics, 720 Hz, 1080 Hz, 1440 Hz, etc. Lastly, noise from random air turbulence is spread equally across all frequencies. The result? As shown in the frequency spectrum, nearly all the noise was originating from the slits. When we plugged them with plastic inserts, the noise went away. Problem solved- thank's to DSP.

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It was suppose to be a 12 bit converter?

THE PROBLEM
The shipping date of our prototype bone densitometer was only three weeks away when we found the problem. The high-voltage being applied to the x-ray tube was jumping all over (say, +/- 10% over a few seconds). Clearly unacceptable- the system needed a stability of better than 0.1%; anything less would make the final bone measurement meaningless. The high-voltage was controlled by a digital feedback loop. An analog-to-digital converter allowed the on-board computer to monitor the high-voltage. In turn, the computer could correct errors through a digital-to-analog converter controlling the drive circuits of the high-voltage power supply.

The stability problem turned out to be in the analog-to-digital converter: it was only an 8 bit device, incapable of achieving 0.1% precision. But there was an even more severe problem, the analog-to-digital conversion was trashed with noise. As shown on the left below, the digital output randomly toggled over about a dozen digital numbers. The system should have been designed with 12 bits; it was designed with 8 bits; but it operated with only about 5 bits of usable data. As any good electrical engineer would, our first step was to plaster the ADC with capacitors. No luck- the noise was coming from high current pulses in the ground plane of the electrical panel- very difficult to solve. Two months minimum to redesign the problem areas. What a mess.

DSP TO THE RESCUE
First, the fancy explanation: we used a multirate technique. The original system sampled at 100 samples per second. We increased the sampling rate to 100,000 samples per second, and then used a digital low-pass filter to eliminate the noise. This was followed by a decimation to lower the sampling rate back to 100 samples per second. Voila! The digital data was now equivalent to direct sampling using 10 bits, as shown in the above figure on the right.

Too complicated? Here's a simpler explanation. We acquired 1000 samples each 10 milliseconds. Averaging these 1000 readings provided a single value each 10 millisecond, i.e., a sampling rate of 100 samples per second. Since 1000 values were averaged, the noise in the signal was reduced by the square-root of 1000, or about 32. While this is a very simple technique, it illustrates the tremendous power of DSP to replace hardware with software. In this case, a dozen lines of code saved months of hardware redesign.

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Well, my simulations weren't exactly right
(sorry about your $50,000)

THE PROBLEM
When I was developing the prototype of the SECURE 1000 , I knew there may be a problem related to shading in the images. Preliminary measurements had shown that the perimeter of the image would be darker than the center. This is caused by several effects: how the image area is scanned, the way x-rays backscatter from the body, the detector characteristics, etc. I needed to better understand this problem before writing the display software or designing the detector array.

So, I spent several days running computer simulations of the imaging geometry. I had done many such simulations before and they had always provided insight into the physics involved. The results looked good; the intensity at the center of the image would only be slightly greater than at the perimeter; a ratio of about 1.5 to 1. No problem, so I went ahead and wrote the software and built the detector array.

A few months later, the prototype was complete and taking its first images. Oh no! - the intensity in the center of the image was more like eight times the intensity at the perimeter. The simulations had been junk! The image on the left shows the problem: the center is too bright, while the border is too dark. Better think of something quick- the investors are making ugly sounds.

DSP SOLVES THE PROBLEM
Digital filtering was able to convert the raw image (on the left) into a processed image (on the right). This is a great example of how DSP can improve the understandability of data. The processed image contains the same information as the raw image, but in a form tailored to the characteristics of the human visual system. The improvement is obvious; look at the buckles on the shoes, the ring on the finger, and the simulated explosive on the chest.

The world of science and engineering is filled with signals: images from remote space probes, voltages generated by the heart and brain, radar and sonar echoes, seismic vibrations, and countless other applications. Digital Signal Processing is the science of using computers to understand these types of data. This includes a wide variety of goals: filtering, speech recognition, image enhancement, data compression, neural networks, and much more. DSP is one of the most powerful technologies that will shape science and engineering in the twenty-first century. Suppose we attach an analog-to-digital converter to a computer, and then use it to acquire a chunk of real world data. DSP answers the question: What next?