ELG 3120 Signals and Systems Chapter 3 1/3 Yao Chapter 3 Fourier Series Representation of Period Signals 3.0 Introduction • Signals can be represented using complex exponentials – continuous-time and discrete-time Fourier series and transform. • If the input to an LTI system is expressed as a linear combination of periodic complex exponentials or sinusoids, the output can also be expressed in this form. 3.1 A Historical Perspective By 1807, Fourier had completed a work that series of harmonically related sinusoids were useful in representing temperature distribution of a body. He claimed that any periodic signal could be represented by such series – Fourier Series . He also obtained a representation for aperidic signals as weighted integrals of sinusoids – Fourier Transform . Jean Baptiste Joseph Fourier 3.2 The Response of LTI Systems to Complex Exponentials It is advantageous in the study of LTI systems to represent signals as linear combinations of basic signals that possess the following two properties: • The set of basic signals can be used to construct a broad and useful class of signals.