{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

soln8 - R Balan Homework#8 Solutions MATH 464 I The window...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R. Balan Homework #8 Solutions MATH 464 I . The window is g ( x ) = Π( x ) . a) f ( x ) = e 2 πix . The windowed Fourier transform is V g f ( w,t ) = Z ∞-∞ e- 2 πiwx f ( x ) g ( x- t ) dx = Z e- 2 πix ( w- 1) Π( x- t ) dx = = e- 2 πit ( w- 1) Z e- 2 πiy ( w- 1) Π( y ) dy = e- 2 πit ( w- 1) sinc ( w- 1) b) f ( x ) = e 2 πiax . The windowed Fourier transform is V g f ( w,t ) = Z ∞-∞ e- 2 πiwx f ( x ) g ( x- t ) dx = Z e- 2 πix ( w- a ) Π( x- t ) dx = = e- 2 πit ( w- a ) Z e- 2 πiy ( w- a ) Π( y ) dy = e- 2 πit ( w- a ) sinc ( w- a ) c) f ( x ) = e 2 πiax + e 2 πibx . The windowed Fourier transform is V g f ( w,t ) = Z ∞-∞ e- 2 πiwx f ( x ) g ( x- t ) dx = Z e- 2 πix ( w- a ) Π( x- t ) dx + Z e- 2 πix ( w- b ) Π( x- t ) dx = = e- 2 πit ( w- a ) Z e- 2 πiy ( w- a ) Π( y ) dy + e- 2 πit ( w- b ) Z e- 2 πiy ( w- b ) Π( y ) dy == e- 2 πit ( w- a ) sinc ( w- a )+ e- 2 πit ( w- b ) sinc ( w V g f ( w,t ) = Z ∞-∞ e- 2 πiwx f ( x ) g ( x- t ) dx = Z...
View Full Document

{[ snackBarMessage ]}