# Maximum length diffusors

One-dimensional maximum length diffusor constructed from one sequence with the length *N* = 7

Two-dimensional maximum length diffusor constructed from two sequences with the length *N* = 7

The construction of maximum length diffusors is based, as their name suggests, on the maximum length sequences known from number theory. These are sequences of the numbers +1 and -1 repeating periodically after a certain length *N*. All maximum length sequences have a common characteristic that makes them very interesting for metrology and the construction of diffusors: their Fourrier Transform has a white spectrum. Consequently, when a maximum length sequence is transformed into a measuring signal it sounds like white noise. If the sequence is used as a design pattern for a wall surface with alternating wells of two different depths, incident sound is evenly scattered into all spatial directions. This seems to make little sense at first, but the scattering characteristics of a diffusor can be described by a formula which is quite similar to the Fourier Transform. Consequently the two phenomena are closely related. Schroeder was first to implement this idea in the form of the maximum length diffusor.

Thus maximum length diffusors consist of individual wells of two different depths. Ideally two deep wells should be separated by thin, vertical well dividers. The dividers improve the scattering effect with obliquely incident sound. The best scattering effect occurs at the frequency whose quarter wavelength corresponds to the well depth. The width of the wells should be less than or equal to half the wavelength.

Unfortunately the effectiveness of maximum length diffusors is limited to a rather narrow frequency band so that they are rarely used. The bandwidth is about one octave.

Wall structures of stripe-shaped construction only scatter sound in the direction perpendicular to the stripes. An elegant way to achieve scattering in two directions is to construct two-dimensional diffusors. This requires multiplication of two independent maximum length sequences so that a pattern consisting of individual square fields results.