ABSTRACT
Signal processing is a very broad field. Examples include filtering of electrical signals to remove 60 Hz interference, equalization of audio signals, processing of electrocardiograms to determine features of the heartbeat, enhancement of noisy speech signals to improve intelligibility, and enhancement of images to emphasize edges. Various mathematical operations may be performed on a signal or a combination of signals. Obvious ones include differentiating or integrating a signal, and combining two or more signals using addition, subtraction, multiplication, or division. Other operations are also important in the context of signal analysis. The original signal is transformed by some appropriate mathematical operation to result in a frequency-domain quantity. This frequency-domain quantity allows for the interpretation of the signal in terms of the basic constituent components of various frequencies. Fourier series are useful only for analyzing periodic signals. In addition to periodic signals, certain aperiodic signals may be studied using the Fourier transform.
