# SINC X

Discussion in 'Mathematics and Physics' started by derick007, Feb 23, 2017.

1. ### derick007Member

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If the normalised sinc (πx) = ∫ sin^2 (πx) / (πx)^2 dx = 0.5

0

Then does the Absolute Spectral power in the Band for additive white Gaussian noise with power spectral density N0 / 2 and a filter transfer function of sin (πx) / x = H(x) :

= N0 ∫ sin^2 (πx) / (πx)^2 dx = 0.5 N0

0

If so then if x = 219, was considered the half power point i.e. – 3 dB

Then does the Absolute Spectral power in the Band

219

= N0 ∫ sin^2 (πx) / (πx)^2 dx = 0.5 N0 (0.5) = N0 / 4

0

ALSO IF

If the normalised sinc (πx) = ∫ sin^2 (πx) / (πx)^2 dx = 0.5

0
THEN DOES

the normalised sinc (Kπx) = ∫ sin^2 (Kπx) / (πx)^2 dx = 0.5 WERE K = CONSTANT

0

Last edited by a moderator: Feb 23, 2017
2. ### DerStrom8Super ModeratorMost Helpful Member

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Please clean up the formatting of your question. It is a mess right now and difficult to read. I have already reduced the font size as it made the post much too large and unreadable.

3. ### derick007Member

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∞​
If the normalised sinc (πx) = sin^2 (πx) / (πx)^2 dx = 0.5
0​

Then does the Absolute Spectral power in the Band for additive white Gaussian noise with power spectral density N0 / 2 and a filter transfer function of sin (πx) / πx = H(x) :

∞​
=N0sin^2 (πx) / (πx)^2 dx = 0.5 N0
0​

If so then if x = 219, was considered the half power point i.e. – 3 dB. Then does the Absolute Spectral power in the Band

219​
= N0sin^2 (πx) / (πx)^2 dx = 0.5 N0 (0.5) = N0 / 4
0

∞​
Also if the normalised sinc (πx)= sin^2 (πx) / (πx)^2 dx = 0.5
0

∞​
does the normalised sinc (Kπx)= sin^2 (Kπx) / (πx)^2 dx = 0.5 WERE K = CONSTANT
0​

Last edited: Feb 23, 2017