Question

Problem 7.4* For each of the following systems, determine if they are (1) linear; (2) time-invariant; (3) causal. (a) $y[n] = 3x[n-1] + x[n] + 3x[n+1]$ (b) $y[n] = x[n] \cos(.3\pi n)$ (c) $y[n] = |x[-n]|$ (d) $y[n] = x[n-2] + 2x[n] + x[n+2]$ (e) $y[n] = nx[n]$ (f) $y[n] = (x[-n])^2$

          Problem 7.4*
For each of the following systems, determine if they are (1) linear; (2) time-invariant; (3) causal.
(a) $y[n] = 3x[n-1] + x[n] + 3x[n+1]$
(b) $y[n] = x[n] \cos(.3\pi n)$
(c) $y[n] = |x[-n]|$
(d) $y[n] = x[n-2] + 2x[n] + x[n+2]$
(e) $y[n] = nx[n]$
(f) $y[n] = (x[-n])^2$

Problem 7.4*
For each of the following systems, determine if they are (1) linear; (2) time-invariant; (3) causal.
(a) y[n] = 3x[n-1] + x[n] + 3x[n+1]
(b) y[n] = x[n] cos(.3π n)
(c) y[n] = |x[-n]|
(d) y[n] = x[n-2] + 2x[n] + x[n+2]
(e) y[n] = nx[n]
(f) y[n] = (x[-n])^2

Added by Lindsey E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Chasen Shaw

Step 1

If we have two inputs x1[n] and x2[n], the output y[n] will be the sum of the outputs corresponding to each input. To check if it is time-invariant, we need to see if a time shift in the input results in a corresponding time shift in the output. In this case, if Show more…

Show all steps

Thanks for your feedback!

Problem 7.4* For each of the following systems, determine if they are 1 linear; 2 time-invariant; 3 causal. a) y[n] = 3x[n-1] + x[n] + 3x[n+1] b) y[n] = x[n]cos(3n) c) y[n] = |x[-n]| d) y[n] = x[n-2] + 2x[n] + x[n+2] e) y[n] = nx[n] f) y[n] = x[-n]