Q1: Consider the eight-point decimation-in-time (DIT) flow graph shown below Stage I Stage 2 Stage 3 (0) X(0) w 14) X(1) -1 (2) X(2) wi 16) X(3) w: X(4) w (5) X(5) w: wi (3) X(6) w: w? 17) X(7) (a) What is the gain of the "signal path" that goes from x(7) to X(2)? (b) How many paths lead from the input to a given output sample? Is this true for every output sample? (c) Compute X(3) using the operations dictated by this flow graph.

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QI: Consider the eight-point decimation-in-time (DIT) flow graph shown below
Stage I
Stage 2
Stage 3
(0)
X(0)
4)
X(1)
-1
(2)
X(2)
wi
16)
• X(3)
-1
X(4)
w!
(5)
X(5)
(3)
X(6)
wi
w?
17)
X(7)
(a) What is the gain of the "signal path" that goes from x(7) to X(2)?
(b) How many paths lead from the input to a given output sample? Is this true for
every output sample?
(c) Compute X(3) using the operations dictated by this flow graph.
Transcribed Image Text:QI: Consider the eight-point decimation-in-time (DIT) flow graph shown below Stage I Stage 2 Stage 3 (0) X(0) 4) X(1) -1 (2) X(2) wi 16) • X(3) -1 X(4) w! (5) X(5) (3) X(6) wi w? 17) X(7) (a) What is the gain of the "signal path" that goes from x(7) to X(2)? (b) How many paths lead from the input to a given output sample? Is this true for every output sample? (c) Compute X(3) using the operations dictated by this flow graph.
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