Signal Processing in C

PART 1

Bells and Bell Choirs

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.