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Gilbert Strang, author of the classic textbook Linear Algebra and Its Applications, once referred to the fast Fourier transform, or FFT, as “the most important numerical algorithm in our lifetime.” No wonder. The FFT is used to process data throughout today’s highly networked, digital world. It allows computers to efficiently calculate the different frequency components in time-varying signals—and also to reconstruct such signals from a set of frequency components. You couldn’t log on to a Wi-Fi network or make a call on your cellphone without it. So when some of Strang’s MIT colleagues announced in January at the ACM-SIAM Symposium on Discrete Algorithms that they had developed ways of substantially speeding up the calculation of the FFT, lots of people took notice.

“FFTs are run billions of times a day,” says Richard Baraniuk, a professor of electrical and computer engineering at Rice University, in Houston, and an expert in the emerging field of compressive sensing, which has much in common with the approaches now being applied to speed up the calculation of FFTs.

Efforts to improve the calculation of Fourier transforms have a long and generally overlooked history. While most engineers associate the FFT with the procedure James Cooley of IBM and John Tukey of Princeton described in 1965, specialists recognize that it has much deeper roots. Although he never published it, the renowned German mathematician Carl Friedrich Gauss had worked out the basic approach, probably as early as 1805—predating, remarkably enough, even Fourier’s own work on the topic.

Given that great mathematical minds have been thinking about how to speed up this particular calculation for more than two centuries, how is it that progress is still being made? The fundamental reason is that the newer methods are tailored to run fast for only some signals—ones that are termed “sparse” because they contain a relatively small number of frequency components of significant size. The traditional FFT takes the same amount of computational time for any signal.

“Certainly there are applications where you need to run the full FFT because the data are not sparse at all,” says Piotr Indyk of MIT’s Computer Science and Artificial Intelligence Laboratory, who developed the new algorithms in collaboration with his colleague Dina Katabi and two students, Haitham Hassanieh and Eric Price. Fortunately, many real-world signals satisfy this sparsity requirement.

“Most signals are sparse,” says Katabi, who points out that when you send, say, a video file over wireless channels, transmitting only a few percent of the frequency content is typically sufficient—and in line with the sparsity levels that her group’s new algorithms handle well. Baraniuk adds that the frequency content of many natural signals, be they astronomical images or bird chirps, tends to be concentrated among the lower frequencies. “Sparsity is everywhere,” he says.

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Where fft is used?


“Red Hat makes our processes more efficient by reducing manual intervention and errors, and enabling us to make decisions based on real-time information from our systems,” says Saurav Sinha, CIO, IndiGo.

Uniting hundreds of applications for business success and passenger safety

IndiGo is India’s largest passenger airline. It relies on many commercial off-the-shelf (COTS), aviation-specific applications to support passenger ticket booking, crew scheduling, catering, load calculation, and other business functions and services. Additionally, the airline handles Aircraft Communications Addressing and Reporting System (ACARS) messages from its aircraft. These services are not only key to IndiGo’s success, but many of them are also critical to ensuring passenger safety.

However, these applications required significant manual intervention to operate and maintain, leading to inefficiency and risk of human error. The airline also lacked a way to integrate its three primary application systems—scheduling, engineering, and reservations—and hundreds of smaller applications connected to these systems. Data entered into one application would have to be manually reentered in another application.

To better connect data from more than 400 applications and make it easier to use for its more than 25,000 employees, IndiGo sought to use a new integration solution to unite its application data in a single interface.

“Data was being entered for our passengers, engines, or our crews, but it was not available for other end users, like airports, to access,” said Charu Verma, Vice President of IndiGo. “The challenge we faced was to offer real-time access to this data and to be able to use it to make faster, better decisions. But if we wanted to provide a single interface for accessing application data, it meant that we needed a way to collect and integrate all of that data.”

Adopting a highly available, open-source integration platform

After working with an Australian technology partner to evaluate options and pricing, IndiGo chose Red Hat Fuse as its new integration solution. The airline selected Fuse based on its agility, flexibility, and real-time data transfer capabilities.

Red Hat Fuse is a distributed integration platform that connects applications across legacy systems, application programming interfaces (APIs), and other IT environments using service-oriented architecture (SOA) and standardized packaging frameworks. Using Fuse, integration experts, application developers, and business users can independently develop connected solutions in the environment of their choosing. The unified platform lets users collaborate, business units self-serve, and organizations ensure governance.

IndiGo’s teams worked with Red Hat Consulting to validate the deployment architecture and establish code quality best practices.

“After integrating our 3 primary systems, we then started connecting those with the smaller systems,” said Verma. “This project was finished in just 2 years, which was a big achievement, because we had thought that would take at least 3 years.”

Improving customer and employee experience with easier data access, saved time and reduced errors with a single, highly available data interface

With data accessible to every IndiGo employee from a common user interface, the airline can save work time by removing the need for duplicate data entry across systems. This approach also decreases the risk of manual errors. When changes are made to a core system, Red Hat Fuse ensures all connected applications automatically begin receiving data from the new system

“For example, crew members would have to spend almost 30 minutes filling out various reports after completing a flight. Now, the GroupPortal application unifies data from 20 applications, letting them complete that same work within 5 minutes.”

“IndiGo has used Fuse to migrate data between 250 applications with zero downtime. “We have 4 Red Hat Fuse servers, and the availability is 99.5%,” exulted Abhinash Srivastava, Director of Information Technology at IndiGo.

Saved ₹500 million with more accurate fuel weight calculations.

Aircraft fuel needs are calculated based on cargo and passenger numbers, but these numbers can change immediately before an aircraft’s departure.

“There would always be changes in cargo weight or number of passengers, which meant the fuel amount required for the flight also needed to change,” stated Verma. “Before Red Hat Fuse, we couldn’t make those changes, because we could not get the data needed from various sources in the last 30 minutes before departure.”

IndiGo can now use Red Hat Fuse to see real-time load information and calculate precise fuel needs. With more accurate predictions, the airline has reduced the cost associated with carrying unneeded fuel, saving ₹500 million per year.

Improved passenger experience

With better integration of service systems through Red Hat Fuse, crews and airports can communicate faster and make more informed decisions. Faster messaging reduces the potential for flight delays or cancellations, leading to a better passenger experience. Additionally, third-party integration with banks and other organizations simplifies the ticketing process. Even catering services benefit from real-time data integration by helping ensure passengers receive the correct meal during their flight.

“Payment processing required a lot of manual effort involving spreadsheets shared between the travel agent, the bank, and us,” said Verma. “Now, within 5 minutes of a customer making a payment, agents can complete their bookings.”

Continuing the digital transformation

IndiGo has now established an agile, reliable integration platform that ensures passengers, crew, employees, and third-party partners get the information they need in real time across hundreds of applications.

“Red Hat makes our processes more efficient, so manual intervention and error are reduced, and we can make decisions based on real-time information from our systems,” said Saurav Sinha.

The airline plans to continue seeking to improve its operations. “The next step in our transformation is to explore other innovations, such as microservices, API management, and container-based systems,” added Charu Verma.

About IndiGo

IndiGo is India’s largest passenger airline, with a market share of 47.2% as of September 2019. It primarily operates in India’s domestic air travel market as a low-cost carrier with a focus on 3 pillars: low fares, being on time, and delivering a courteous and hassle-free experience. IndiGo has become synonymous with being on time. Since its inception in August 2006, it has grown from a carrier with one plane to a fleet of 257 aircraft.

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