Consider the signal

s(t)=u_(t-t_(0))-u(t-t_(1))

, where

u(t)

is the step function,

t_(0)=1s

, and

t_(1)=5s

.\ a. (3p) Using pencil and paper, draw three vertically stacked and time-aligned graphs, as follows:

{

(

:-t_(0))

} on the top,

u(t-t_(1))

in the middle, and

s(t)

at the bottom. Time aligned means that a vertical bar will intersect all graphs at the same time instance. Do the plot for a time window

t_(win )=[-8s,8s]

\ b. (1p) Compute

s_(t)=2s

\ c. (1p) Compute

s(t

)

=

(

5.001s)

\ d. (3p) Redo point (a) using Python, a time window

t_(win )=[-8s,8s]

with 801 points (including the interval limits) for

x

-axis array.\ Hint: use

n

p. heaviside(InArray,

x2

) function where

ln

Array is the input array and

x2=1

(see examples on internet)\ e. The signal

s[nT_(s)]

is after sampling

s(t)

with a sampling frequency

f_(s)=100Hz

(i.e., the sampling interval

T_(s)=(1)/(f_(s))

).\ f. (2p) Using python plt.stem() function plot

s[nT_(s)]

for the same time interval as above. Show on the

x

-axis the sample index

n

.

Consider the signal s(t)=u(tt0)u(tt1), where u(t) is the step function, t0=1s, and t1=5s. a. (3p) Using pencil and paper, draw three vertically stacked and time-aligned graphs, as follows: u(t t0) on the top, u(tt1) in the middle, and s(t) at the bottom. Time aligned means that a vertical bar will intersect all graphs at the same time instance. Do the plot for a time window twin=[8s,8s] b. (1p) Compute s(t=2s) c. (1p) Compute s(t=5.001s) d. (3p) Redo point (a) using Python, a time window twix=[8s,8s] with 801 points (including the interval limits) for x-axis array. Hint: use np heaviside(InArray, 2 ) function where InArrax is the input array and 2=1 (see examples on internet) e. The signal s[nTs] is after sampling s(t) with a sampling frequency fs=100Hz (i.e., the sampling interval Ts=1/fs). f. (2p) Using python plt.stem() function plot s[nTs] for the same time interval as above. Show on the x-axis the sample index n