Hey I have a question Would you happen to know what book these pages are from? M
ID: 2267484 • Letter: H
Question
Hey I have a question Would you happen to know what book these pages are from? My professor didn’t give me the books name and I can’t figure it out I’m in Signals and Systems II32 Orthogonal Functions and Fourier Series /2 In both of the preceding examples, the real and imaginary parts of the com- plex coefficients could have been sketched instead of the amplitude and phase spectra without any loss of information. However, as noted previously, the amplitude and phase are more meaningful for our purposes, since they can be interpreted as the amplitude and phase of a sinusoid. SUMMARY In this chapter we have expended substantial time and effort in motivating, defining, and developing the idea of a Fourier series representation of a signal or waveform. In Section 2.2 we provided the initial motivation and introduced sets of functions that possess the property of orthogonality. The two most important forms of Fourier series for our purposes, the trigonometric and the complex exponential forms, were presented in Sections 2.3 and 2.4, respectively, and their use illustrated. In Sections 2.5 and 2.6 we concentrated on simplifying the Fourier series calculations and supplying some previously ignored mathe- matical details. The important concept of a spectrum of a periodic signal was introduced in Section 2.7 and examples were given to clarify calculations. As we shall sece, Section 2.7 serves as a critical stepping-stone to the definition of the Fourier transform in Chapter 3. PROBLEMS 21 For the two vectors Bo-3a. 4a, and B. +2a, determine the component of Bo in the B, direction and the component of B, in the Bo direction 22 Determine whether each of the following sets of vectors is orthogonal. Are they orthonormal? (b) Bo =-i,t i, and Bl =-i,-i, We desire to approximate the vector by a linear combination of the vectors y, and y 2.3 where y =-4, and y,--i,-i, Find the coefficients d1 and d2 such that the approximation minimizes the least squares loss function given by A A Complete Example 22.1 by considering cases (2) and (3). 24
Explanation / Answer
Please refer the following books for the mentioned pages :-
1)
Signals and Systems
Alan V. Oppenheim, Alan S. Willsky - Signal theory (Telecommunication)
2)
Signals and Systems
Alan V. Oppenheim, Alan S. Willsky, Ian T. Young