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Unformatted text preview: ω = 2 π 5 . How many distinct CT HRCEs do we have? What is the common period of all HRCEs? Write down the expression of the discrete-time harmonically related complex (HRCE) for a given fundamental frequency ω = 2 π 5 . How many distinct DT HRCEs do we have? What is the common period of all HRCEs? Run the following matlab program. t=linspace(-2,6); omega=2*pi/5; k=4; fourth=cos(k*omega*t); k=-1; negative_first=cos(k*omega*t); plot(t,fourth,t,negative_first) grid on; You will see two curves: One is the CT HRCE with k = 4 and the other is the CT HRCE with k =-1. As seen in the ﬁgure, for k = 4 and for k =-1, the two CT HRCEs: cos ( 4 2 π 5 t ) and cos ( (-1) 2 π 5 t ) are obviously diﬀerent. Use the ﬁgure and explain why for the discrete-time (DT) HRCE, we have cos ± 4 2 π 5 n ¶ = cos ± (-1) 2 π 5 n ¶ . (3)...
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This note was uploaded on 10/07/2010 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue.
- Fall '06