By Simon Haykin
Deals the main whole, updated assurance to be had at the ideas of electronic communications. specializes in easy matters, bearing on idea to perform anywhere attainable. a number of examples, labored out intimately, were incorporated to assist the reader advance an intuitive snatch of the speculation. issues coated comprise the sampling procedure, electronic modulation concepts, error-control coding, powerful quantization for pulse-code modulation, coding speech at low bit radio, details theoretic options, coding and machine verbal exchange. as the ebook covers a wide variety of subject matters in electronic communications, it may fulfill numerous backgrounds and pursuits.
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10 ≤ m ≤ 10 3. 34) which is one way of realizing a delta function in the frequency domain. 34) as one way of defining the delta function δ ( f ). 10 Evolution of the sum of m complex exponentials toward a delta function in the frequency domain as m becomes increasingly larger. 6 Fourier Transforms of Periodic Signals We began the study of Fourier analysis by reviewing the Fourier series expansion of periodic signals, which, in turn, paved the way for the formulation of the Fourier transform. Now that we have equipped ourselves with the Dirac delta function, we would like to revisit the Fourier series and show that it can indeed be treated as a special case of the Fourier transform.
34) which is one way of realizing a delta function in the frequency domain. 34) as one way of defining the delta function δ ( f ). 10 Evolution of the sum of m complex exponentials toward a delta function in the frequency domain as m becomes increasingly larger. 6 Fourier Transforms of Periodic Signals We began the study of Fourier analysis by reviewing the Fourier series expansion of periodic signals, which, in turn, paved the way for the formulation of the Fourier transform. Now that we have equipped ourselves with the Dirac delta function, we would like to revisit the Fourier series and show that it can indeed be treated as a special case of the Fourier transform.
B) Spectrum of the Dirac comb. 40) = f0 ∞ n = –∞ G ( f n ) δ ( f – f n ), –∞ < f < ∞ where f n = nf 0 . 14). 14) with f 0 = Δf . 41) is one form of Poisson’s sum formula. 17), provided, of course, we permit the use of the Dirac delta function. In so doing, we have closed the “circle” by going from the Fourier series to the Fourier transform, and then back to the Fourier series. Consequences of Ideal Sampling Consider a Fourier transformable pulselike signal g(t) with its Fourier transform denoted by G(f).