By Thomas W. Schultz

At the present time, every little thing from cellphones to microwaves to CD avid gamers all include microcontrollers, or miniature desktops, which must be programmed to accomplish particular projects. Designing such platforms calls for an knowing of either microprocessor electronics and programming languages. This publication is written for the economic electronics engineer who must use or swap to the Intel 8051 kin of microcontrollers and enforce it utilizing a c program languageperiod. .

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**Example text**

Sketch and label each of the ( a ) x ( t ) u ( l - t ) ; ( b ) x ( t ) [ u ( t )- u(t - I)]; (c) x ( t ) H t - - 1 0 1 2 t Fig. 1-27 (a) By definition ( 1 . 1 9 ) and x(r)u(l - t ) is sketched in Fig. 1-28(a). 19) u -( t - 1 = and x ( t ) [ u ( r )- u(t - I ) ] is sketched in Fig. 1-28(b). O

1-27. Sketch and label each of the ( a ) x ( t ) u ( l - t ) ; ( b ) x ( t ) [ u ( t )- u(t - I)]; (c) x ( t ) H t - - 1 0 1 2 t Fig. 1-27 (a) By definition ( 1 . 1 9 ) and x(r)u(l - t ) is sketched in Fig. 1-28(a). 19) u -( t - 1 = and x ( t ) [ u ( r )- u(t - I ) ] is sketched in Fig. 1-28(b). O

1 SIGNALS AND SYSTEMS (4 Fig. 6. Find the even and odd components of x ( r ) Let x,(r) and x,(I) = eJ'. be the even and odd components of ei', respectively. eJ' = x , ( I ) + x , ( I ) From Eqs. ( 1 . 6) and using Euler's formula, we obtain x,( I ) = $ ( e J r+ e - J ' ) = cos I x,,(I) = f(ei'-e-j') =jsint Show that the product of two even signals or of two odd signals is an even signal and that the product of an even and an odd signaI is an odd signal. Let x ( t ) =xl(t)x2(t). If X J I ) and x 2 ( l ) are x ( - l ) =x,(-I)X,(-t) and x(t) is even.