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Signal theory and Medical biocomputation
TASK II – SIGNALS AND NOISE
Lab Instructor: Ing. Diego Almeida Ph.D Developed by: Ing. Graciela Salum Ph.D - Ing. Karla Miño **Group:
1.- Determine is the signal are analog, digital, continuous and discrete in time? 2.- With Matlab, draw a sinusoidal signal with amplitude 2 and periods equal to 10 seconds, 8 sec, 5 sec, 2 sec, 1 sec, 0.1 sec and 0.01 sec. Obtain a conclusion. 3.- Draw the following functions. Indicate which of the following signals in continuous time are periodic. Determine the fundamental period.** a) 𝑥(𝑡) = 2 𝑠𝑖𝑛 (10𝜋t + π 6
b) 𝑥(𝑡) = 𝑠𝑖𝑛 (31t) c) 𝑥(𝑡) = 0.2 𝑠𝑖𝑛 (4 𝜋t)
Signal theory and Medical biocomputation d) 𝑥(𝑡) = 4 cos (20𝜋𝑡 + π 3
4.- Use Matlab in order to represent each function of point 3. 5.- Determine whether or not each the following signals is periodic through using fundamental period: a) 𝑥(𝑡) = cos(𝑤𝑜𝑡) b) 𝑥(𝑡) = 𝑒𝑗𝑤𝑜𝑡, use hint: 𝑒𝑗𝑤𝑜𝑡^ = cos(𝑤𝑜𝑡) + 𝑗 sin(𝑤𝑜𝑡) c) 𝑥(𝑡) = cos (𝑡 + π 4
6.- Two sinusoidal signals (s1[n] and s2[n]) have phase angle zero. The frequencies are f1= 0.5 Hz and f2=0.1 Hz and the amplitudes are A1=2, A2=1. If s[n]=s1[n]+s2[n], a) draw s1, s2 and s. b) Determine T1, T2 and T. Note: represent the functions every 0. seconds. 7.- Indicate which of the following signals in discrete time are periodic. Determine the fundamental period. a) 𝑥[n] = 2 cos [ πn 2
]
b) 𝑥[n] = 4 𝑠𝑖𝑛 [ πn 4
]
c) 𝑥[n] = cos [ π 2 𝑛] cos [ π 4
𝑛]
d) 𝑥[n] = 2 cos [ π 4 𝑛] + cos [ π 4
𝑛]
8.- Use Matlab in order to represent the functions in exercises 7. 9.- Determine whether the signal is periodic or aperiodic signal?
- 𝑥(𝑡) = 𝑠𝑖𝑛 ( 2 π 3
- 𝑥(𝑡) = cos ( π 3 𝑡) + sin ( π 4
Signal theory and Medical biocomputation 11.- Given the signal x(t) shown in Figure, obtain: a) x(t + 1); b) x(- t + 1); and c) x(3/2 t); 12.- A continuous-time signal x(t) is shown in Figure. Sketch and label carefully each of the following signals: a) x(t- 1); b) x(2- t); c) x(2t + 1); and d) x(4 - t/2). 13.- A discrete-time signal is shown in Figure. Sketch and label carefully each of the following signals: a) x[n- 4]; b) x[3 - n]; c) x[3n]; and d) x[3n + 1]. Energy and power signal 14.- Determine whether or not each the following signals is power, energy or neither: a) 𝑥(𝑡) = 𝑒−𝑎𝑡^ 𝑢(𝑡)
Signal theory and Medical biocomputation b) 𝑥(𝑡) = 𝐴 cos(𝑤𝑜 𝑡) for 𝑇𝑜 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 and 𝑇𝑜 =2𝜋𝑤𝑜 c) 𝑥(𝑡)= 𝑡 𝑢(𝑡)
- Find whether the signal power or energy signal a) 𝑥(𝑡)=
t for 0 ≤t ≤ 12 − t for 1 ≤ t ≤ 2 0 otherwise b) 𝑥(𝑡)= 5cos(𝜋𝑡) +sin(5𝜋𝑡)
