Exercises

1. A phasor~ object has a frequency of 441 Hertz (at a sample rate of 44100.) What is the amplitude of the DC component? The fundamental? The partial at 22050 Hertz (above which the partials fold over)?

2. A square wave oscillates between 1 and -1. What is its RMS amplitude?

3. In Section 10.3 a square wave was presented as an odd waveform whose Fourier series consisted of sine (and not cosine) functions. If the square wave is advanced 1/8 cycle in phase, so that it appears as an even function, what does its Fourier series become?

4. A rectangle wave is 1 for 1/4 cycle, zero for 3/4 cycles. What are the strengths of its harmonics at 0, 1, 2, 3, and 4 times the fundamental?

5. How much is $1 + 1/9 + 1/25 + 1/49 + 1/81 + \cdots$?