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 an audio signal $x[n], n = 0, ..., M-1$ has peak amplitude 1, what is the minimum possible RMS amplitude? What is the maximum possible?

6. If $x[n]$ is the Sinusoid of Section 1.1, and making the assumptions of section 1.2, show that its RMS amplitude is approximately $a / {\sqrt 2}$. 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.