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Showing posts from January, 2023

Linear Feedback Shift Registers for Dummies

For the past several years, I've been interested in "correlation orthogonal" sequences, such as maximal length sequences (MLS, or M-sequences), Gold and Kasami sequences, Zadoff-Chu sequences, and so forth, for applications like measuring the impulse response of audio systems and room acoustics---what is broadly thought of as system identification .   M-sequences are generated by linear feedback shift registers (LFSR). Gold and Kasami sequences are generated by XOR'ing multiple M-sequences in various phases. Gold sequences are used in spread-spectrum radio applications such as GPS, where they are known as Gold Codes.  Because the transfer function (the frequency and phase response of a system, such as a loudspeaker) is the Fourier Transform of the impulse response, MLS became the dominant method for audio transfer function measurements starting in the late-80 [1].  In the early 00s, sine sweep methods were were rediscovered and popularized by Angelo Farina [2] and hav...