**Synthesis Theory**

Mid-term Exam (Fujinaga, October 1997)

(5 points per question)

1. What is the lowest frequency component when a 25 kHz sine wave is sampled at 40kHz? Explain. What is this phenomenon called?

2. Derive and explain the linear interpolation equation in detail using diagrams.

3. What is the S/N ratio of 16-bit linear conversion system, what are the advantages and disadvantages over a 8-bit system.

4. What are the primary differences between MIDI data processing and digital audio data processing?

5. A table lookup oscillator uses a table with 1024 values that defines one cycle of oscillator's wave form. If the sampling rate is 40kHz, what sampling increment will produce the frequency of 625Hz? Explain.

6. What is the most fundamental theorem of additive synthesis theory? Why is this theorem so important? What are the limitations in its application for music compositions?

7. If the sampling rate is 20kHz, how many samples are needed to produce a sine wave of 200Hz for 2 sec? How many samples are in one cycle? What is the period of the sine wave?