Signals and Systems PDF

INTRODUCTION

This text studies signals and systems.We encounter both of them daily almost everywhere. When using a telephone, your voice, an acoustic signal, is transformed by the microphone, a system, into an electrical signal. That electrical signal is transmitted, maybe through a pair of copper wires or a satellite circulating around the earth, to the other party and then transformed back, using a loudspeaker, another system, into your voice. On its way, the signal may have been processed many times by many different systems. In addition to their role in communications, signals are used in medical diagnoses and in detecting an object, such as an airplane or a submarine. For example, the electrocardiogram (EKG) shown in Figure 1.1(a) and the brain waves (EEG) shown in Figure 1.1(b) can be used to determine the heart condition and the state of mind of the patient. Figures 1.2(a) and 1.2(b) show another type of signal: the total number of shares traded and the closing price of a stock at the end of each trading day in the New York Stock Exchange. Other examples of signals are the U.S. gross domestic product (GDP), consumer price index, and unemployment rate. We also use signals to control our environment and to transfer energy. To control the temperature of a home, we may set the thermostat at 20◦C in the daytime and, to save energy, 15◦C in the evening. Such a control signal is shown in Figure 1.3(a). Electricity is delivered to our home in the sinusoidal waveform shown in Figure 1.3(b), which in the United States has peak magnitude of 110×√2 volts and frequency of 60 hertz (Hz, cycles per second).

All aforementioned signals depend on one independent variable—namely, time—and are called one-dimensional signals. Pictures are signals with two independent variables; they depend on the horizontal and vertical positions and are called two-dimensional signals. Temperature, wind speed, and air pressure are four-dimensional signals because they depend on the geographical location (longitude and latitude), altitude, and time. If we study the temperature at a fixed location, then the temperature becomes a one-dimensional signal, a function of time. This text studies only one-dimensional signals, and the independent variable is time. No complex-valued signals can arise in the real world; thus we study only real-valued signals.