DstTimeSinusoids_handouts

DstTimeSinusoids_handouts - Discrete-Time Sinusoids Dr....

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Unformatted text preview: Discrete-Time Sinusoids Dr. Deepa Kundur Texas A&M University Dr. Deepa Kundur (Texas A&M University) Discrete-Time Sinusoids 1 / 23 Discrete-Time Sinusoids Periodicity Recall if a signal x ( t ) is periodic , then there exists a T > such that x ( t ) = x ( t + T ) If no T > can be found, then x ( t ) is non-periodic . Dr. Deepa Kundur (Texas A&M University) Discrete-Time Sinusoids 2 / 23 Discrete-Time Sinusoids Continuous-time Sinusoids To find the period T > of a general continuous-time sinusoid x ( t ) = A cos( t + ) : x ( t ) = x ( t + T ) A cos( t + ) = A cos( ( t + T ) + ) A cos( t + + 2 k ) = A cos( t + + T ) 2 k = T T = 2 k where k Z . Note : when k is the same sign as , T > . Therefore, there exists a T > 0 such that x ( t ) = x ( t + T ) and therefore x ( t ) is periodic . Dr. Deepa Kundur (Texas A&M University) Discrete-Time Sinusoids 3 / 23 Discrete-Time Sinusoids Discrete-time Sinusoids To find the integer period N > (i.e., ( N Z + ) of a general discrete-time sinusoid x [ n ] = A cos( n + ) : x [ n ] = x [ n + N ] A cos( n + ) = A cos( ( n + N ) + ) A cos( n + + 2 k ) = A cos( n + + N ) 2 k = N N = 2 k where k Z ....
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DstTimeSinusoids_handouts - Discrete-Time Sinusoids Dr....

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