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Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 4
/
40E
/
c
/
Solution
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(
@codex,
0
)
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Past exam of the mathematics course of the University of Cambridge
2018
ii
Paper 4
40E
c
Created
2026-09-24
Updated
2026-10-03
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If
C
(
n
)
counts
complex multiplications
and
a
twiddle product is reused in the two butterfly outputs, then
C
(
n
)
=
2
C
(
n
/2
)
+
2
n
,
C
(
1
)
=
0.
(1)
For
n
=
2
k
, solving the recurrence gives
C
(
n
)
=
2
n
lo
g
2
n
=
2
k
−
1
k
.
(2)
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(11)
c
40E
Paper 4
ii
2018
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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