Hi im reading miller's book, and i want to know the answers of the exercise to compare with my results. if someone was kind enough to respond I would be grateful.

Exercises

1. A sinusoid (Page 1) has initial phase φ = 0 and angular frequency ω =

π/10. What is its period in samples? What is the phase at sample number

n = 10?

2. Two sinusoids have periods of 20 and 30 samples, respectively. What is

the period of the sum of the two?

3. If 0 dB corresponds to an amplitude of 1, how many dB corresponds to

amplitudes of 1.5, 2, 3, and 5?

4. Two uncorrelated signals of RMS amplitude 3 and 4 are added; what’s

the RMS amplitude of the sum?

5. How many uncorrelated signals, all of equal amplitude, would you have to

add to get a signal that is 9 dB greater in amplitude?

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

7. Two sinusoids play at middle C (MIDI 60) and the neighboring C sharp

(MIDI 61). What is the difference, in Hertz, between their frequencies?

8. How many cents is the interval between the seventh and the eighth har-

monic of a periodic signal?

9. If an audio signal x[n], n = 0, ..., N − 1 has peak amplitude 1, what is the

minimum possible RMS amplitude? What is the maximum possible?