SINC X

∞

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

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.

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

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) :


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

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