Digital Signal Processing (DSP) has revolutionized the storage and
transmission of audio and video signals in consumer electronics and
also in scientific settings. The main advantage of DSP is its
robustness: although all of the operations have to be implemented (by
necessity) in not quite ideal hardware, the a priori knowledge that
all correct outcomes must lie in a very restricted set of well
separated numbers makes it possible to recover them by round off
appropriately. However, many signals (audio signals e.g.) are not
digital but are rather analog in nature. For this reason the first
step in any digital processing of such signals is a conversion of the
analog signal to the digital world. The question is then what is the
most efficient method to do such a conversion. A first mathematical
look would conclude the problem to be trivial: sample at Nyquist rate
and encode these samples in binary.However, this is generally not done
in practice. Rather engineers use a quite unexpected encoding
consisting of high oversampling of the signal followed by very coarse
(e.g. one bit) quantization. Such methods of encoding lead to an array
of interesting mathematical questions. This talk will discuss one bit
quantization methods with an eye to explaining why engineers prefer
this method. The talk requires no background in signal processing and
little mathematical sophistication.