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It all started almost a century ago, in 1920s. A new undersea transatlantic telegraph cable had been laid. The idea of transmitting speech over the new telegraph cable caught the fancy of Homer Dudley, a young engineer who had just joined Bell Telephone Laboratories. This led to the invention of Vocoder - its close relative Voder was showcased as the first machine to create human speech at the 1939 New York World's Fair. However, the voice quality of vocoders was not good enough for use in commercial telephony. During the time speech scientists were busy with vocoders, several major developments took place outside speech research. Norbert Wiener developed a mathematical theory for calculating the best filters and predictors for detecting signals hidden in noise. Linear Prediction or Linear Predictive Coding became a major tool for speech processing. Claude Shannon established that the highest bit rate in a communication channel in presence of noise is achieved when the transmitted signal resembles random white Gaussian noise. Shannon’s theory led to the invention of Code-Excited Linear Prediction (CELP). Nearly all digital cellular standards as well as standards for digital voice communication over the Internet use CELP coders. The success in speech coding came with understanding of what we hear and what we do not. Speech encoding at low bit rates introduce errors and these errors must be hidden under the speech signal to become inaudible. More and more, speech technologies are being used in different acoustic environments raising questions about the robustness of the technology. Human listeners handle situations well when the signal at our ears is not just one signal, but also a superposition of many acoustic signals. We need new research to develop signal-processing methods that can separate the mixed acoustic signal into individual components and provide performance similar or superior to that of human listeners.