Synthesis Theory Mid-term Exam (Fujinaga, March 1998) (5 points per question) 1. Convolve the following two sequence of numbers: 1 3 1 2 -2 4 2 -1 2 0 1 Why does one use FFT to perform convolutions? 2. At 48Khz sampling rate, what is the width of the frequency bin for 2048-point Fourier Transform? How many bins does the result have? What is the frequency range does these bins cover? 3. What two kinds of filters are used in the CsoundÍs reverb unit? How are they connected? Show with a diagram. Why does it simulate reverberation? 4. Why are bits reversed in FFT? What is the primary advantage of using FFT over FT, give an example. 5. What is the advantage of using constant-Q spectrum analysis over FFT? What is the disadvantage? 6. Find the frequency (magnitude) response of the filter: y(n) = x(n) + x(n-2). Derive using z-transform. What kind of a filter is it? 7. What factors make machine recognition of human-performed rhythm difficult?