Manfred Robert Schroeder
I love Mathematics and Languages (Italian and Dutch being my favorites).
My main hobbies are Photography and Computer Graphics, especially after I won First Prize at the Las Vegas International Computer Art Exhibition in 1969 (see examples below).
I also like Skiing and Bicycling (the photo shows me biking on Nantucket).
I have written three books:
Number Theory in Science and Communication (Springer, 5th edition) and
Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, both hugely successful.
Recently my latest book Computer Speech: Recognition, Compression, Synthesis was published by Springer (2nd edition). It includes a brief history of speech research and introductions to modern signal analysis and monaural and binaural hearing. The book summarizes my long involvement with speech research at
Recent talks and articles
My first scientific publication ("On the representation of the specific heat of solids by Einstein and Debye terms" ) was followed, in 1952, by my Ph.D. thesis in Göttingen, which was concerned with the distribution of normal modes in cavities . I discovered that even a highly symmetric (cubic) cavity, when perturbed by small irregularities, would show a peculiar distribution of its resonance frequencies that is now recognized as a tell-tale sign of chaotic dynamics. This work, although widely ignored at the time, did land me a job, in 1954, in the Research Department of AT&T Bell Laboratories at Murray Hill, New Jersey. At Bell, having had my fill of cavities, I started working in speech and hearing. From 1958 to 1969 I was in charge of acoustics and speech research. One of the highlights of those years was my long collaboration with Bishnu Atal and the invention, in 1967, of linear predictive coding (LPC) of speech signals . In 1972, working with Joseph Hall, I proposed perceptual coding of audio signals, taking into account the masking properties of the human ear . This in turn led to code-excited linear prediction (CELP) -- now ubiquitous in synthetic speech . During my Bell years I was awarded a total of 45 US patents for inventions in speech and other fields.
Three days after arriving in New York (on the "Andrea Doria", then still afloat) I met my future wife, Anny Menschik. Our three children, Marion, Julian and Alexander, were born in New York City and Summit, New Jersey, and are now living in Bremen (Germany), La Jolla and San Francisco.
In 1969, the five of us moved to Göttingen in Germany where I had become a professor of physics and director of the Drittes Physikalische Institut. At Göttingen I lectured on coherent optics, applications of number theory, deterministic chaos, nonlinear dynamics and fractals. All my lecture courses included demonstration experiments. The students loved it (and my assistant Heinrich Henze and I loved it perhaps even more).
During my scientific career I received a number of "metals": the Gold medals of the Acoustical Society of America and the Audio Engineering Society, and the Lord Rayleigh and Helmholtz medals. But more than any formal recognition, I enjoyed working with my students, not least those from the Studienstiftung des Deutschen Volkes, the top students of the university representing a wide spectrum of interests.
Over the years I have also been elected to several learned societies: the American Academy of Arts and Sciences (founded in 1780), the National Academy (which gives me annual excuses to travel to Washington), the New York Academy of Sciences, which recently promoted me from Member to Fellow, and the Göttingen Akademie der Wissenschaften. The Göttingen academy is unique in that it conducts frequent plenary sessions, in which natural scientists, mathematicians, philosophers, historians, philologists, jurists and theologians report on their work -- a unique opportunity to look across the fence from the narrow confines of one's own field.
Another activity, much enjoyed, was my long collaboration with the French composer Pierre Boulez, particularly the planning of the Institut de Recherche et de Coordination Acoustique/Musique at the Centre Pompidou in Paris.
Before becoming involved with the Pompidou, I was a member of the "rescue squad" for the acoustics of Philharmonic Hall at Lincoln Center for the Performing Arts in New York City . Apart from improving the sound, other beneficial results were new methods for measuring reverberation time  and for diffusing sound waves by surfaces based on number-theoretic principles . After my move to Göttingen, D. Gottlob, K.F. Siebrasse and I, with the support of the German Science Foundation (DFG), conducted a major study of concert hall acoustics . Orchestral music recorded in 22 halls, mostly in Europe, was reproduced in the Göttingen anechoic chamber using a special method that allowed the sound to be evaluated in a free acoustic field (without wearing earphones). The main result: good acoustics requires strong and early arriving lateral sound waves at a listener's head . Unfortunately, this is precisely what is missing in most modern concert halls, which -- in contrast to many older halls -- are relatively wide and have low ceilings, producing an undesirable “monophonic” sound. This observation confirmed results by A.H. Marshall, M. Barron and others and lead directly to the above mentioned reflection phase gratings based on quadratic residues and other number-theoretic principles .
One of my abiding interests has been the monaural phase sensitivity of human hearing. Already at Bell, in the 1950s, I had built a "phase organ" that generated periodic signals with 31 Fourier components with phase angles adjustable to either 0 or 180 degrees. The resulting tone complexes showed a wide variety of musical timbers many of them reminiscent of vowels. This finding contradicts Ohm's Law of Acoustics, which says that the ear is essentially phase deaf. These experiments gave me the idea of fabricating synthetic speech signals with a fixed flat power spectrum but a time-varying phase spectrum. This idea lay dormant for a long time until Hans Werner Strube and I revived it and demonstrated that, indeed, intelligible speech could be generated from phase changes alone, leaving the power spectrum fixed .
The graphic Eikonal below shows another example of this philosophy: from nearby one sees just a tangle of black curves, but from afar it looks like ... (squinting or viewing in dim light helps in seeing what's "behind" Eikonal). This image, programmed by Wolfgang Möller, is a solution of the eikonal equation of geometric optics . The curves are the wavefronts of a light wave emanating from near the center of the picture and traveling through a medium of variable refractive index.
Several of my computer graphics are based on number-theoretic relationships and prime numbers. The star-like image Prime Spectrum below, programmed, appropriately enough, by my star programmer Sue Hanauer, shows the magnitude of the Fourier transform of the distribution of pairs of numbers that have no common divisors . To produce this picture, Sue had to have the Murray Hill computer center shut down for one afternoon to tie several processors together because, in 1965, even the largest of Bell's machines did not have enough core memory for a 1024 x 1024 Fast Fourier transform (a cinch for a lowly laptop today).
More recently I have created a series of computer graphics in which the colors of the rainbow represent the phase of complex functions in the complex (Gaussian) plane. The example Poles and Zero below shows the phase of a rational function with one zero and two poles. It is interesting to note that poles and zeroes, like opposite electric charges, "attract" each other while poles repel other poles.
 Z.f.Physik 321, 312 (1952) with W. Brenig.
 Acustica 4, 45 (1954).
 Proc. IEEE Conf. on Comm. and Process., pp.360-361 (1967). See also Bell Syst. Tech. J. 49 (8), pp.1973-1986 (1970) with B.S.Atal .
 Proc. Int. Conf. on Acoustics, Speech, and Signal Proc. pp. 573-576 (1978) with B.S.Atal.
 Proc. Int. Conf. on Acoustics, Speech and Signal Proc. 3 pp. 1668-1671 (1982) with B.S.Atal.
 J. Acoust. Soc. Amer. 40 (2), 434 (1966) with B.S.Atal, G.M.Sessler, J.E.West.
 J. Acoust. Soc. Amer. 37, 409 (1965).
 J. Acoust. Soc. Amer. 57 (1), 149 (1975).
 J. Acoust. Soc. Amer. 56, 1195 (1974) with D.Gottlob, F.K.Siebrasse.
 J. Acoust. Soc. Amer. 65 (4), 958 (1979).
 in R. N. Thurston (ed.): Physical Acoustics Vol. 18, pp. 1-20 (Academic Press 1988).
 J. Acoust. Soc. Amer. 79, 1580 (1986) with H.W.Strube.
 Comm. Assoc. Computing Machinery 12(2), 95 (1969).
 The Mathematical Intelligencer 5 (1), 36 (1983).
 The Mathematical Intelligencer 4 (3), 158 (1982).