ABSTRACT
In this chapter, the authors examine the representation of periodic functions in sampled form, a requirement when using a computer and digital signal processing. They establish the conditions necessary for an acceptable approximation that leads to the discrete Fourier transform series. The authors consider the complex form of sinusoidal signals, which are useful as building blocks or basis functions from which they can construct other signals. The authors consider both continuous- and discrete-time functions. Thus, if a periodic nonsinusoidal signal is applied to a system and if the higher frequencies in the expansion are attenuated more than the lower frequencies, the output signal will be smoother than the original. The transducer that detects heartbeats is a linear time-invariant system whose input is the periodic heart signal and the output is a signal observed on an oscilloscope that is supposed to resemble the original signal.
