The first project of this book culminates with the synthetic bell choir programs in Chapter 5. Each bell of the bell choir is simulated using the simplest possible oscillating system, a damped simple harmonic oscillator. In spite of the simplicity of this system compared to a real bell, the effect is convincing. The programs developed in Chapter 5 and contained in the music directory on the companion disk read a musical score from a disk file and produce a file containing a digital waveform suitable for playing through a standard D/A converter.
Chapter 1 examines the most basic concepts of digital signal processing: What is a discrete-time frequency? How are discrete-time frequencies related to continuous-time frequencies? Chapter 2 develops the continuous-time solutions to the differential equation for a damped simple harmonic oscillator. An understanding of the continuous-time system is necessary for the discrete-time solutions developed in Chapter 3. Chapter 4 uses the discrete-time solutions developed in Chapter 3 to simulate a bell and an organ pipe. Although the sound of the bell is quite convincing, the organ pipe sounds more like a cheap tin whistle. Chapter 5 shows how these simple harmonic oscillators can be used to write a music synthesizer program. This includes an introduction to the modern style of programming used in this book.