Signals and Systems Basics - 28/Chapter1/Solution of problem 1.28d of oppenheim/System Properties

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Solution of problem number 1.28d of chapter 1 of signals and systems text book written by
Alan V. Oppenheim
Alan S. Willsky
S. Hamid Nawab

#problem1.28d
#withmemory
#noncausal
#linear
#nonlinear

1.28 Determine which of the properties listed in Problem 1.27 hold and which do not
hold for each of the following discrete-time systems. Justify your answers. In each
example, y[n] denotes the system output and x[n] is the system input.
(a) y[n] = x[- n]
(b) y[n] = x[n - 2] - 2x[n - 8]
(c) y[n] = nx[n]
(d) y[n] = Ev{x[n - 1]}

(e) y[n] = 0, n = 0
(f) y[n] = 0, n = 0
x[n + 1], n ::::: -1 x[n], n ::::: -1
(g) y[n] = x[4n + 1]

Solution of problem 1.41 of Alan V Oppenheim by Rajiv Patel(AIR 5, GATE 2012)

Consider a systemS with input x[n] and output y[n] related by
y[n] = x[n]{g[n] + g[n- 1]}.
(a) If g[n] = 1 for all n, show that Sis time invariant.
(b) If g[n] = n, show that Sis not time invariant.
(c) If g[n] = 1 + ( -l)n, show that Sis time invariant.

solution of problem number 1.26a, 1.26b, 1.26c, 1.26d and 1.26e of Alan V oppenheim
Alan S. Willsky
S. Hamid Nawab
by
Rajiv Patel
All India Rank - 5 in GATE 2012

Solution of problems 1.27a,1.27b,1.27c,1.27d,1.27e,1.27f,1.27g of
Alan V. oppenheim