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# Exercises

1. If 0 dB corresponds to an amplitude of 1, how many dB corresponds to amplitudes of 1.5, 2, 3, and 5? (Answer: about 3, 6, 10, and 14.)

2. Two uncorrelated signals of RMS amplitude 3 and 4 are added; what's the RMS amplitude of the sum?

3. How many uncorrelated signals, all of equal amplitude, would you have to add to get a signal that is 9 dB hotter?

4. What is the angular frequency of middle C at 44100 samples per second?

5. If is an audio signal, show that:

and

where is the window size. Under what conditions does equality hold for each one?

6. If is the SINUSOID of Section 1.1, and making the assumptions of section 1.2, show that its RMS amplitude is approximately . Hint: use an integral to approximate the sum. Since the window contains many periods, you can assume that the integral covers a whole number of periods.

Next: Wavetables and samplers Up: Acoustics of digital audio Previous: conversion between frequency and   Contents   Index
msp 2003-12-08