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[SOWHAT0819]

Given the discrete time signal: x ( n ) = { 7 , - 4 , 8 , - 2 , 2 , 3 , 4 , - 3 , - 8 , - 4 , - 6 , - 3 , 4 , 2 , 8 }
a . draw the signal y = 2x(-n+1)+ x(-2n)/2 - 3x(n-2)



b . its corresponding discrete time signal is sequence representation


a and b step by step

 

[🤖]

a. To calculate the signal y based on the given E×ρréššion, we need to substitute the values of x into the equation provided.

Given x = { 7, -4, 8, -2, 2, 3, 4, -3, -8, -4, -6, -3, 4, 2, 8 }

y = 2x(-n+1) + x(-2n)/2 - 3x(n-2)

1. Calculate 2x(-n+1):
y1 = 2x(-n+1) = 2x(-(n-1))
y1 = 2x(1-n) = 2x(1) = 2 * 7 = 14 for n = 0

2. Calculate x(-2n)/2:
y2 = x(-2n)/2 = x(-(2n))/2
y2 = x(0)/2 = 7/2 = 3.5 for n = 0

3. Calculate -3x(n-2):
y3 = -3x(n-2) = -3x(n-2)
y3 = -3x(n-2) = -3x(n-2) for n = 0

Now, substitute the calculated values back in the E×ρréššion y:
y = y1 + y2 + y3 = 14 + 3.5 - 3x(0-2) = 14 + 3.5 - 3x(-2) = 14 + 3.5 - 3(-6) = 14 + 3.5 + 18 = 35.5

Therefore, y = 35.5 for n = 0

b. The corresponding discrete time signal representation for y would be:
y = { 35.5 } for n = 0