In Electrical Engineering, the periodic especially sinusoidal signals arise frequently. Aperiodic function p(t) with the fundamental period T, satisfies p(t)=p(t+kT) for all t andall integer k. We define a sinusoidal signal asz(t)=Z,+ZpeakCOS(ot+¢),where Z, is the offset, Zpeak is the peak value, w=27 /T=2tf is the angular frequency (inrad/s), o is the phase (in radians), T is the period and f is the frequency (in Hz=s').Note that, these are Ao, C1, 0 and T in the figure below. (Note: The phase ø is definedin radians. However, we often write it in degrees!)2.51.51AoT0.5-1123t[s]a. Express a sine wave (i.e. y(t)=YpeakSin(wt)) in the form given above.реаb. Let us given the signal r(t)=-5+10cos(314t-45°). Find the offset, peak,frequency, period and phase of this signal.c. The rms (root-mean-square) value Pms (also, nominal value or effective value)of a periodic function p(t) is defined as Pdt . Note that, the%3Dintegration should be on a full-period and the limits can be changed as to andto+T to get the same result. Find the rms value of a sinusoidal function for bothzero offset (Zo=0) and non-zero offset (Zo=0).d. The function exp(t)= Aexp(-t/t)=Ae“ is the (decaying) exponential function,where t=1/a is called the time constant. This function is an important functionin mathematics and engineering. Some critical values: Assuming A=1,exp(0)=1, exp(T)=1/e>0.37 and exp(5t)>0. We can relate the (complex)exponential function and sinusoidal function as follows: e"=cos(0)+jsin(0),where j=-1. Then the sinusoidal function can be expressed as the real part ofel0 +e¯j0e". We can also use the equation: cos(0) = -2Derive a similarequation for sin(0) and write the function given in part b. in terms of complexexponentials.(1)J

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In Electrical Engineering, the periodic especially sinusoidal signals arise frequently. A periodic function p(t) with the fundamental period T, satisfies p(t)=p(t+kT) for all t and all integer k. We define a sinusoidal signal as z(1)=Z,+ZpeakCOS(ot+ø), where Z, is the offset, Zpeak is the peak value, w=27 /T=2rf is the angular frequency (in rad/s), ø is the phase (in radians), T is the period and f is the frequency (in Hz=s"). Note that, these are Ao, C1, 0 and T in the figure below. (Note: The phase ø is defined in radians. However, we often write it in degrees!)

In Electrical Engineering, the periodic especially sinusoidal signals arise frequently. A periodic function p(t) with the fundamental period T, satisfies p(t)=p(t+kT) for all t and all integer k. We define a sinusoidal signal as z(1)=Z,+ZpeakCOS(ot+ø), where Z, is the offset, Zpeak is the peak value, w=27 /T=2rf is the angular frequency (in rad/s), ø is the phase (in radians), T is the period and f is the frequency (in Hz=s"). Note that, these are Ao, C1, 0 and T in the figure below. (Note: The phase ø is defined in radians. However, we often write it in degrees!)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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