Question

Hw9 SP19.pdf Download Press F11 toexit full screen Q6 (10pts.) You can synthesize music (singals) several ways. One is the additive method where your sum pure sinusoids to build up a signal (Fourier expansion). Another method is the subtractive method where you create harmonics with square or saw-toothed wave and filter out the parts you do not want. Plot at least 7 non-zero terms of amplitude/phase line spectra of a saw-toothed wave form so that a sound engineer can evaluate which signals are available for manipulation. V(signal) 0.9 0.8 0.7V 0.6V 0.5V 0.4 0.3 0.2V 0.1 0.0 Select an area to comment on 0.0ms.2s 0.4ms 0.6ms0.8ms 1.0ms 1.2ms 1.4ms.6ms1.8ms

Answer 1

Given that The Fourier - series expansion of saw - toothed wave form. Since, the signal V_signal(t) is a odd- signal it consists of only DC - term and cosine terms. i.e., a_0 notequalto 0 a_n = 0 b_n notequalto 0 a_0 = 1/T integral_0^T V_signal (t) dt = 1/1ms integral_0^1ms t/1ms dt = 1/(1 ms)^2[t^2/2]_0^1ms \r\n a_0 1/(1ms)^2 [(1ms)^2/2] = 1/2 a_0 = 0.5 volts implies a_n = 2/T integral_0^T V_signal (t). cos n w_0 t dt {V_signal (t) = t/1ms: 0 < t < T} {T = 1ms w_0 = 2 pi/T = 2 pi/1ms = 2000 pi} implies a_n = 2/1ms integral_0^1ms t/1ms cos n(2000 pi) t. dt a_n = 2/(1ms)^2 [integral_0^1ms t cos(2000 pi n t) dt] consider, I_1 = integral_0^1ms t cos(2000 pi n t) dt = integral_0^1ms (1 - t) cos(2000 pi n t) dt \r\n I_1 = integral_0^1ms 1ms cos(2000 pi n t) dt - I 2I_1 = 1ms/2000 times n pi [sin (2000 pi n