In the generation of music by computer, the process of modulation is extremely important. When playing an instrument, the player typically does it in three stages: (1) rise time, (2) sus-tained time and (3) decay time. Suppose we model these three stages as an envelope continuous-time signal given by

where r(t) is the ramp signal.

(a) For a simple tone x(t) = cos (2Ï€t/T₀), the modulated signal is y(t) = x(t)e(t). Find the period T₀ so that 100 cycles of the sinu-soid occur for the duration of the envelope signal.

(b) Simulate in the modulated signal using the value of T₀ and a simulation sampling time of T_s = 0.1. Plot y(t) and e(t) (discretized with the sampling period T_s) and listen to the modulated signal using sound.

Transcribed Image Text:

[r(t) – r(t – 3)]-Ir(t – 20) – r(t – 30)] e(t) = 3 10