Signals and Systems - Electrical Engineering

344 CHAPTER 5: Frequency Analysis: The Fourier Transform If the input of the spectrum analyzer isx(t), the output of either the ...

5.8 Additional Properties 345 It is important to realize that shifting in time does not change the frequency content of the sign ...

346 CHAPTER 5: Frequency Analysis: The Fourier Transform after applying the sifting property ofδ(). The above shows that this F ...

5.8 Additional Properties 347 sinceu(t−τ)as a function ofτequals u(t−τ)= { 1 τ <t 0 τ >t We thus have that F   ∫t −∞ x(τ ...

348 CHAPTER 5: Frequency Analysis: The Fourier Transform n If X( 0 )(i.e., the dc value of X()) is zero, then the operator 1 /( ...

5.8 Additional Properties 349 and a second derivative gives d^2 x(t) dt^2 =δ(t)− 2 δ(t− 1 )+δ(t− 2 ) Using the time-shift and th ...

350 CHAPTER 5: Frequency Analysis: The Fourier Transform The Fourier transform of 2u(t− 1 )is− 2 je−j/+ 2 πδ()so that Y()= − ...

Problems 351 Table 5.1Basic Properties of the Fourier Transform Time Domain Frequency Domain Signals and constants x(t),y(t),z(t ...

352 CHAPTER 5: Frequency Analysis: The Fourier Transform (a) Find the Fourier series coefficientX 0 for each of the values ofT 0 ...

Problems 353 is finite, indicating the signal is absolutely integrable and also finite energy. (b)Use the Laplace transform to f ...

354 CHAPTER 5: Frequency Analysis: The Fourier Transform which is imaginary function of, thus its computational importance. Sho ...

Problems 355 (a) Plotx(t)andy(t). (b)FindX()and carefully plot its magnitude spectrum. IsX()real? Explain. (Use MATLAB to do t ...

356 CHAPTER 5: Frequency Analysis: The Fourier Transform 5.16. Periodic signal-equivalent representations Applying the time and ...

Problems 357 5.20. Filter for half-wave rectifier Suppose you want to design a dc source using a half-wave rectified signalx(t)a ...

358 CHAPTER 5: Frequency Analysis: The Fourier Transform (b)Suppose you wish to obtain a band-pass filterG(j)fromH(j). If the ...

CHAPTER 6 Application to Control and Communications........................................... Who are you going to believe? Me ...

360 C H A P T E R 6: Application to Control and Communications frequency, bandwidth, spectrum, and modulation developed by means ...

6.2 System Connections and Block Diagrams 361 Cascading of LTI Systems Given two LTI systems with transfer functionsH 1 (s)=L[h ...

362 C H A P T E R 6: Application to Control and Communications FIGURE 6.3 Cascading of (a) an LTV and (b) an LTI system. The out ...

6.3 Application to Classic Control 363 FIGURE 6.4 Negative-feedback connection of systems with transfer functionH 1 (s) andH 2 ( ...