The Fourier transform is one of the most fundamental concepts in the information sciences. It’s a method for representing an irregular signal such as the voltage fluctuations in the wire that connects an MP3 player to a loudspeaker as a combination of pure frequencies. It’s universal in signal processing, and it can be used to compress image and audio files, solve differential equations and price stock options, among other things.

The reason the Fourier transform is so prevalent is the FFT, devised in the mid-1960s, which made it practical to calculate Fourier transforms on the fly. Like the FFT, the new algorithm works on digital signals. A digital signal is just a series of numbers - discrete samples of an analog signal, such as the sound of a musical instrument.

The FFT takes a digital signal containing a certain number of samples and expresses it as the weighted sum of an equivalent number of frequencies. “Weighted” means that some of those frequencies count more toward the total than others. Indeed, many of the frequencies may have such low weights that they can be safely disregarded. That’s why the Fourier transform is useful for compression. An eight-by-eight block of pixels can be thought of as a 64-sample signal, and thus as the sum of 64 different frequencies. But as the MIT researchers point out in their paper, empirical studies show that on average, 57 of those frequencies can be discarded with minimal loss of image quality.

Signals whose Fourier transforms include a relatively small number of heavily weighted frequencies are called “sparse.” The new algorithm determines the weights of a signal’s most heavily weighted frequencies; the sparser the signal, the greater the speedup the algorithm provides. Indeed, if the signal is sparse enough, the algorithm can simply sample it randomly rather than reading it in its entirety.

“In nature, most of the normal signals are sparse,” says Dina Katabi, associate professor of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) and one of the developers of the new algorithm. Consider, for instance, a recording of a piece of chamber music: The composite signal consists of only a few instruments each playing only one note at a time. A recording, on the other hand, of all possible instruments each playing all possible notes at once wouldn’t be sparse - but neither would it be a signal that anyone cares about.

The new algorithm relies on two key ideas. The first is to divide a signal into narrower slices of bandwidth, sized so that a slice will generally contain only one frequency with a heavy weight. In signal processing, the basic tool for isolating particular frequencies is a filter. But filters tend to have blurry boundaries: One range of frequencies will pass through the filter more or less intact; frequencies just outside that range will be somewhat attenuated; frequencies outside that range will be attenuated still more; and so on, until frequencies are reached that are filtered out almost completely.
If it so happens that the one frequency with a heavy weight is at the edge of the filter, however, it could end up so attenuated that it can’t be identified. So the researchers’ first contribution was to find a computationally efficient way to combine filters so that they overlap, ensuring that no frequencies inside the target range will be unduly attenuated, but that the boundaries between slices of spectrum are still fairly sharp.

Once they’ve isolated a slice of spectrum, however, the researchers still have to identify the most heavily weighted frequency in that slice. They do this by repeatedly cutting the slice of spectrum into smaller pieces and keeping only those in which most of the signal power is concentrated.

The team plans to present the new algorithm at the Association for Computing Machinery’s Symposium on Discrete Algorithms (SODA).

A new algorithm that improves on the fast Fourier transform (FFT) was developed by a team of MIT researchers. The algorithm can help to dramatically compress music and video files. The picture shows sine waves of several frequencies. Photo: Public Domain

“The success of the e-commerce channel will be enhanced by a multichannel approach, where retailers leverage the store to make the e-commerce channel even more appealing to consumers,” Mim Burt, research director at Gartner, said. “In many product categories, consumers prefer to shop online and take possession in the store. Multichannel retailers that offer the ability to order online and take possession in the store will be offering increased flexibility to customers, which should enhance revenue for them.”

The multichannel forecast shows that the U.K. leads the U.S. significantly in the current percentage of e-commerce, which was approximately 9.3 percent of retailers’ revenue in 2011. This contrasts with the U.S. percentage of slightly less than 5.3 percent of retailers’ revenue for 2011. U.S. retailers must focus on boosting e-commerce channel sales and become more multichannel aligned in their strategies. They can do this, for example, by leveraging their store assets to complement and enhance sales in both channels. Western European markets, particularly in the U.K., have benefited from generally high Internet penetration and usage, a higher online per capita expenditure, and a better multichannel fulfillment infrastructure.

“Executing on cross-channel consistency will prove challenging, as retailers continue to grapple with siloed business process and a plethora of disparate applications,” Burt said. “Most challenging are the product-centric organizational structures that are no longer suitable for today’s customer-centric approach, which should take full account of customers shopping across current and emerging touch points.”

Channels have grown as largely separate entities, and business metrics in retail remain overwhelmingly product and channel-focused. Retailers need to change internal organizational alignments to execute a consistent cross-channel shopping experience. Requirements of shoppers across channels and the customer shopping process should be their guiding principles, rather than focusing on the ROI of multichannel initiatives.

“Focusing on ROI on multichannel is a misnomer,” said John Davison, managing vice president at Gartner. “Retailers should focus on identifying the impact of investments in one channel on the other channels. For example, our multichannel retailers’ forecast shows revenue from the mobile channel through 2015 is less than 2 percent, but retailers should not underestimate the impact this channel will have in pushing sales to other channels. Equally, an expected drop in store revenue does not mean reduced investment in their stores. In fact, the store will require more investment targeted at cross-channel shopper fulfillment as its importance as the hub of the retailer’s multichannel offer increases.”

The U.K. leads the U.S. significantly in the current percentage of e-commerce, which accounted for approximately 9.3 percent of retailers’ revenue in 2011, compared to slightly less than 5.3 percent in the U.S. Photo: www.imagine-your-world.com

By attaching a microphone to a touchscreen, the CMU scientists showed they can tell the difference between the tap of a fingertip, the pad of the finger, a fingernail and a knuckle. This technology, called TapSense, enables richer touchscreen interactions. While typing on a virtual keyboard, for instance, users might capitalize letters simply by tapping with a fingernail instead of a finger tip, or might switch to numerals by using the pad of a finger, rather toggling to a different set of keys.

Another possible use would be a painting app that uses a variety of tapping modes and finger motions to control a pallet of colors, or switch between drawing and erasing without having to press buttons.

"TapSense basically doubles the input bandwidth for a touchscreen," said Chris Harrison, a Ph.D. student in Carnegie Mellon's Human-Computer Interaction Institute (HCII). "This is particularly important for smaller touchscreens, where screen real estate is limited. If we can remove mode buttons from the screen, we can make room for more content or can make the remaining buttons larger."

The technology also can use sound to discriminate between passive tools made from such materials as wood, acrylic and polystyrene foam. This would enable people using styluses made from different materials to collaboratively sketch or take notes on the same surface, with each person's contributions appearing in a different color or otherwise noted.

"TapSense can tell the difference between different parts of the finger by classifying the sounds they make when they strike the touchscreen," fellow Ph.D. student Julia Schwarz said. An inexpensive microphone could be readily attached to a touchscreen for this purpose. The microphones already in devices for phone conversations would not work well for the application, however, because they are designed to capture voices, not the sort of noise that TapSense needs to operate.

The researchers found that their proof-of-concept system was able to distinguish between the four types of finger inputs with 95 percent accuracy, and could distinguish between a pen and a finger with 99 percent accuracy.

A new technology called TapSense uses microphones to distinguish between the tap of a fingertip, the pad of the finger, a fingernail and a knuckle to interact with devices through a touchscreen. Photo: www.imagine-your-world.com

“The PC market in Western Europe suffered from weak demand in both the professional and consumer sectors, a market which also faced inventory issues caused by overstocking in 2010,” said Meike Escherich, principal analyst at Gartner. “The much anticipated uptake in the professional segment, in the wake of migration to Windows 7, was subdued by the negative economic outlook. PC shipments in the professional segment declined 9 percent in the second quarter of 2011. The biggest decline continued to come from the consumer segment which decreased 27 percent year-on-year.”

PC shipments in the UK totaled 2.5 million units in the second quarter of 2011, a decline of 15 percent compared with the same period in 2010. The professional market remained weak with a decline of 13.5 percent. The migration to Windows 7 and replacement of aging PCs continued to be muted by the negative economic outlook.

“PCs are not attracting consumers' disposable income, particularly in light of alternative devices. While remaining an important device to consumers, there are few compelling technological reasons to drive PC replacements,” said Isabelle Durand, principal analyst at Gartner.

PC shipments in France totaled 2.3 million units in the second quarter of 2011, a decline of 17.8 percent compared with the same period a year ago. It performed below expectations and remained weak due to slow consumer demand and lower PC shipments.

“For the fourth consecutive quarter, the PC market in France showed decline,” said Durand. “It also exhibited the weakest PC growth of the three major countries in Western Europe in the second quarter of 2011.”

The consumer market declined 33 percent partly due to the rise in popularity of media tablets and smartphones, which impacted PC purchases. The professional market increased 9 percent in the second quarter of 2011 but volumes were not significant enough to compensate for the drop in consumer demand. The mobile PC market accounted for 67 percent of total PC shipments, with volumes declining 18 percent. Desktop PCs declined 18 percent year-on-year. Of the total mobile segment, mini-notebook sales declined 49 percent in the second quarter of 2011. Apple made its entry in the top five PC vendors ranking in the second quarter, and it was the only top five vendors to exhibit shipment growth.

“The French PC market is expected to improve in the second half of 2011, with more attractive back-to-school promotions compared to a year ago and product refreshes,” said Durand. “However, the availability of new media tablet models will lead to a price battle in the mobile market. Some level of government austerity measures due to the recent economic issues could also impact consumer confidence and spending in France.”

PC shipments in Germany totaled 2.4 million units in the second quarter of 2011, a decrease of 13.3 percent compared with the same period in 2010. This marks the second consecutive quarter of double-digit shipment decline. The PC market continued to be hit by poor mobile PC sales that decreased 14 percent. Desktop PC shipments declined 12 percent in the quarter. The double-digit fall in mobile PC sales was mainly caused by a steep decline in mini-notebook shipments, which decreased 43 percent.

HP continued to lead in the German PC market as it accounted for 13.3 percent of PC shipments in the second quarter of 2011. Demand in the professional PC market has improved as organizations released budgets to migrate aging PCs to Windows 7. HP in particular seemed to benefit from this upturn in the professional market.

“Given the hype around media tablets such as the iPad, retailers were very conservative in placing orders for PCs,” said Escherich. “Instead, many of them wanted to secure space for media tablets.”

PC shipments in the second quarter of 2011 declined in Western Europe. The only real bright spot was Apple. The company made its entry in the top five PC vendors ranking. Photo: www.imagine-your-world.com

“We have written the application from the ground up in HTML5, so that customers can also access their content offline directly from their browser,” said Dorothy Nicholls, Director, Amazon Kindle. “The flexibility of HTML5 allows us to build one application that automatically adapts to the platform you're using - from Chrome to iOS. To make it easy and seamless to discover new books, we've added an integrated, touch optimized store directly into Cloud Reader, allowing customers one click access to a vast selection of books.”

The Kindle Cloud Reader can be seen as Amazon’s answer to Apple’s App Store policies. To comply with the latest rules, Amazon removed the buy-button from the Kindle app late last month. Through the new application, users can now access over 950,000 eBooks through the browser based app that applies updates automatically to.

According to a 2010 study from Goldman Sachs, Amazon did have a 58 percent market share of eBook sales in the U.S. at this time, followed by Barnes & Noble (27 percent) and Apple (9 percent.) The Kindle Cloud Reader will be available on additional web browsers, including Microsoft’s Internet Explorer, Firefox, and the BlackBerry PlayBook browser in the coming months.
The Kindle Cloud Reader is available for download here.

A new app for Amazon’s Kindle allows users to access over 950,000 eBooks through the Safari and Chrome web browser. Photo: www.imagine-your-world.com