Signals and Systems - Electrical Engineering

224 C H A P T E R 3: The Laplace Transform which satisfies the initial conditions and attempts to follow the input signal. This ...

3.5 Analysis of LTI Systems 225 If we letx(t)=δ(t), the output isy(t)=h(t)or h(t)=δ(t)+βh(t−τ) and ifH(s)=L[h(t)], then the Lapl ...

226 C H A P T E R 3: The Laplace Transform 3.6 What Have We Accomplished? Where Do We Go from Here?.................... In this ...

Problems 227 and zero elsewhere. The raised cosine is used in communications to transmit signals with minimal interference. Find ...

228 C H A P T E R 3: The Laplace Transform (c) The inverse Laplace transform of X(s)= 3 s− 4 s(s+ 1 )(s+ 2 ) should give a respo ...

Problems 229 3.11. Convolution integral Consider the following problems related to the convolution integral: (a) The impulse res ...

230 C H A P T E R 3: The Laplace Transform (a) Use the integral formula to findP(s), the Laplace transform of p(t). Determine th ...

Problems 231 (b) Ify(^1 )( 0 )= 1 andy( 0 )= 1 are the initial conditions for the above differential equation, findY(s). If the ...

232 C H A P T E R 3: The Laplace Transform 3.22. Poles, stability, and steady-state response The steady-state solution of stable ...

Problems 233 (a) Find and plot the poles and zeros ofH(s). Is this BIBO stable? (b)Find the frequency 0 of the inputx(t)=2 cos( ...

234 C H A P T E R 3: The Laplace Transform FindY 2 (s)=L[y 2 (t)]using the convolution property of the Laplace transform and fin ...

Problems 235 (a) Carefully plot the half-wave rectified signaly(t)fromx(t). (b) Lety 1 (t)be the period ofy(t)between 0 ≤t≤ 1. S ...

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CHAPTER 4 Frequency Analysis: The Fourier Series.................................................. A Mathematician is a device f ...

238 C H A P T E R 4: Frequency Analysis: The Fourier Series exponentials or sinusoids are used in the Fourier representation of ...

4.2 Eigenfunctions Revisited 239 where we letH(j 0 )equal the integral in the second equation. The input signal appears in the ...

240 C H A P T E R 4: Frequency Analysis: The Fourier Series The above representation ofx(t)corresponds to the Fourier representa ...

4.2 Eigenfunctions Revisited 241 frequency, with time generates a cosine of the indicated frequency, amplitude, and phase. The t ...

242 C H A P T E R 4: Frequency Analysis: The Fourier Series FIGURE 4.1 RC circuit and corresponding phasor circuit. vs(t) 1 Ω 1F ...

4.2 Eigenfunctions Revisited 243 the delay. Find the frequency response of the ideal communication system, and use it to determi ...