Summary1 - n ) = A cos( n + ) = A cos( n + 2 kn + ) The...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Summary 1 Hamid Jafarkhani Digital Signal Processing Summary 1 – p. 1/ 4
Background image of page 1

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

View Full DocumentRight Arrow Icon
Continuous-Time Sinusoidal Signals X a ( t ) = A cos(Ω t + θ ) = A cos(2 πFt + θ ) If we fix the frequency, F , then X a ( t ) is periodic. If two sinusoids have different values of F , then they are different functions. As F increases, the sinusoid oscillates faster. Summary 1 – p. 2/ 4
Background image of page 2
Discrete-Time Sinusoidal Signals X ( n ) = A cos( ωn + θ ) = A cos(2 πfn + θ ) A discrete-time sinusoid is periodic only if its frequency f is a rational number. X ( n ) = cos( n ) is not periodic! Discrete-time sinusoids with different frequencies can be identical. X k (
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n ) = A cos( n + ) = A cos( n + 2 kn + ) The highest rate of oscillation in a discrete-time sinusoid is attained when = (or =- ) or equivalently f = 1 2 (or f =-1 2 ). Summary 1 p. 3/ 4 Some Useful Definitions Energy: E = s n =- | x ( n ) | 2 Cross correlation between real signals x ( n ) and y ( n ) : r xy ( l ) = s n =- x ( n ) y ( n-l ) Auto correlation (real signal): r xx ( l ) = s n =- x ( n ) x ( n-l ) Summary 1 p. 4/ 4...
View Full Document

Page1 / 4

Summary1 - n ) = A cos( n + ) = A cos( n + 2 kn + ) The...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online