Time and Frequency Representation of Signals and Systems (1989)

The concept of time and frequency representation of signal dates back to the first notation for music: a sequence of notes to be played in time, s(t), each note being associated with a fundamental frequency and its higher harmonics. From a mathematical viewpoint we can associate the time function s(t) to its Fourier transform S(f). However, S(f) is independent of time and gives no indication as to the note to be played at each particular time instant. It would therefore be useful to introduce a representation of signals simultaneously in time and frequency. This is the aim of this book.