Signals and Systems - Electrical Engineering

284 C H A P T E R 4: Frequency Analysis: The Fourier Series 4.10.3 Multiplication of Periodic Signals Ifx(t)andy(t)are periodic ...

4.10 Other Properties of the Fourier Series 285 and thus 0.5︸︷︷X︸k Zk =0.25 ∑ m XmXk−m ⇒ Xk= 1 2 ∑ m XmXk−m (4.48) so thatα=0.5. ...

286 C H A P T E R 4: Frequency Analysis: The Fourier Series value is zero). The derivative of a periodic signal is obtained by c ...

4.10 Other Properties of the Fourier Series 287 nExample 4.17 Letg(t)be the derivative of a triangular train of pulsesf(t), of p ...

288 C H A P T E R 4: Frequency Analysis: The Fourier Series FIGURE 4.18 Two periods of the approximate triangular signal xN(t)us ...

4.11 What Have We Accomplished? Where Do We Go from Here? 289 for k = 2:N, xa = xa + 2 * abs(X(k)) * cos(w0 * (k - 1). * t + ang ...

290 C H A P T E R 4: Frequency Analysis: The Fourier Series systems will be introduced and exemplified by its application in fil ...

Problems 291 (b) Suppose that the system is represented by a first-order differential equation, y′(t)+ 5 y(t)=x(t) wherey(t)is t ...

292 C H A P T E R 4: Frequency Analysis: The Fourier Series 4.9. Fourier series coefficients via Laplace—MATLAB The computation ...

Problems 293 (a) Find the Fourier series coefficients forx(t)andy(t). (b) Use MATLAB to plot the magnitude line spectra of the t ...

294 C H A P T E R 4: Frequency Analysis: The Fourier Series 4.15. Figuring out Fourier’s idea Fourier proposed to represent a pe ...

Problems 295 4.19. Using properties to find the Fourier series Use the Fourier series of a square train of pulses (done in this ...

296 C H A P T E R 4: Frequency Analysis: The Fourier Series (a) Given that an integral ofp(t)is the area under the curve, find a ...

Problems 297 (c) The line spectrum of the pure tonep(t)=cos( 2 πfAt) only displays one harmonic, the one corresponding to thefA= ...

298 C H A P T E R 4: Frequency Analysis: The Fourier Series Use MATLAB to compute and plot the approximationˆx(t)and the errrorε ...

CHAPTER 5 Frequency Analysis: The Fourier Transform........................................... Imagination is the beginning of c ...

300 CHAPTER 5: Frequency Analysis: The Fourier Transform the frequency content of a signal by processing it with an LTI system w ...

5.2 From the Fourier Series to the Fourier Transform 301 AsT 0 →∞,Xnwill tend to zero. To avoid this we defineX(n)=T 0 Xnwhere{ ...

302 CHAPTER 5: Frequency Analysis: The Fourier Transform 5.3 Existence of the Fourier Transform For the Fourier transform to exi ...

5.4 Fourier Transforms from the Laplace Transform 303 The following rules of thumb will help you get a better understanding of t ...