A new algorithm performs Fourier transforms using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing.

Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionised science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves ...

Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous ...

The linear canonical transform (LCT) is a versatile integral transform that generalises classical transforms such as the Fourier, fractional Fourier, and Fresnel transforms. By utilising four ...

An interesting aspect of time-varying waveforms is that by using a trick called a Fourier Transform (FT), they can be represented as the sum of their underlying frequencies. This mathematical insight ...

When James Cooley and John Tukey introduced the Fast Fourier transform in 1965, it revolutionized signal processing and set us on course to an array of technological breakthroughs. But today’s ...

Homework Set 4 Problem 4 . Inverse z-transforms. Hint – look at the region of convergence to see whether you are expecting a signal that dies away as t tends to + infinity, or as t tends to – infinity ...

This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise ...