1. For each of the following discrete-time systems, determine whether or not the sys- tem is (1) linear, (2) causal, (3) time-invariant, (4) stable, and/or (5) FIR. Please write "yes" or "no" in each block. Assume |g[n]| < Bg <∞ for all n. Show all your work. Part System Linear? Causal? Time-invariant? Stable? FIR? (a) y[n] = 1 (b) y[n] = cos(x[n])g[n+1] (c) y[n] = x[-1] + x[n] M (d) y[n] = bx[n — k] k=0 2. Write down the impulse response for each signal in Problem 1. Simplify your an- swer as much as possible. = 3. Given x[n] {1,2,3}, carefully draw the following signals. Label the time and amplitude axes so the graph is unambiguous. (a) xa[n] = x[n-2]. (b) x[n] = x[-n – - 2] (c) xc [n] = x[-2n + 1] 8 (d) xa[n] = k=-co x[n - 3k]
1. For each of the following discrete-time systems, determine whether or not the sys- tem is (1) linear, (2) causal, (3) time-invariant, (4) stable, and/or (5) FIR. Please write "yes" or "no" in each block. Assume |g[n]| < Bg <∞ for all n. Show all your work. Part System Linear? Causal? Time-invariant? Stable? FIR? (a) y[n] = 1 (b) y[n] = cos(x[n])g[n+1] (c) y[n] = x[-1] + x[n] M (d) y[n] = bx[n — k] k=0 2. Write down the impulse response for each signal in Problem 1. Simplify your an- swer as much as possible. = 3. Given x[n] {1,2,3}, carefully draw the following signals. Label the time and amplitude axes so the graph is unambiguous. (a) xa[n] = x[n-2]. (b) x[n] = x[-n – - 2] (c) xc [n] = x[-2n + 1] 8 (d) xa[n] = k=-co x[n - 3k]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. For each of the following discrete-time systems, determine whether or not the
sys-
tem is (1) linear, (2) causal, (3) time-invariant, (4) stable, and/or (5) FIR. Please write
"yes" or "no" in each block. Assume |g[n]| < Bg < o for all n. Show all your work.
Part System
Linear? Causal? Time-invariant? Stable?
FIR?
(a) y[n] = 1
(b) y[n] = cos(x[n])g[n+1]
(c)
y[n] = x[-1] + x[n]
M
(d) y[n] = brx[n – k]
k=0
2. Write down the impulse response for each signal in Problem 1. Simplify your an-
swer as much as possible.
3. Given x[n] = {1,2,3}, carefully draw the following signals. Label the time and
amplitude axes so the graph is unambiguous.
(a) xa[n] = x[n – 2].
(b) xp[n] = x[-n – 2]
(c) xe[n] = x[–2n + 1]
00
(d) xa[n] = E x[n – 3k]
k=-0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8abb620-dd30-457c-b5f1-4da9380dd779%2F1f3c74bc-c205-45b4-8b19-f900264689e8%2Fz48fv55_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. For each of the following discrete-time systems, determine whether or not the
sys-
tem is (1) linear, (2) causal, (3) time-invariant, (4) stable, and/or (5) FIR. Please write
"yes" or "no" in each block. Assume |g[n]| < Bg < o for all n. Show all your work.
Part System
Linear? Causal? Time-invariant? Stable?
FIR?
(a) y[n] = 1
(b) y[n] = cos(x[n])g[n+1]
(c)
y[n] = x[-1] + x[n]
M
(d) y[n] = brx[n – k]
k=0
2. Write down the impulse response for each signal in Problem 1. Simplify your an-
swer as much as possible.
3. Given x[n] = {1,2,3}, carefully draw the following signals. Label the time and
amplitude axes so the graph is unambiguous.
(a) xa[n] = x[n – 2].
(b) xp[n] = x[-n – 2]
(c) xe[n] = x[–2n + 1]
00
(d) xa[n] = E x[n – 3k]
k=-0
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