# Signals and Systems

## Synopsis

The third edition ofSignals and Systemsprepares students for real-world engineering applications. It is concise, focused, and practical. The text introduces basic concepts in signals and systems and their associated mathematical and computational tools. It also stresses the most important concepts in signal analysis (frequency spectra) and system analysis (stability and frequency responses) and uses them throughout, including the study of seismometers and accelerometers.
Signals and Systems, 3/e, introduces every term carefully and develops every topic logically. It distinguishes amplitudes and magnitudes, as well as lumped and distributed systems. It presents engineering concepts as early as possible and discusses transform theory only as needed. Also, the text employs transfer functions and state-space equations only in the contexts where they are most efficient. Transfer functions are used exclusively in qualitative analysis and design, and state-space equations are used exclusively in computer computation and op-amp circuit implementation. Thus, the students' time is focused on learning only what can be immediately used.
Including an author commentary on the best way to approach the text,Signals and Systems, 3/e, is ideal for sophomore- and junior-level undergraduate courses in systems and signals. It assumes a background in general physics (including simple circuit analysis), simple matrix operations, and basic calculus.

## Excerpt

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.

1.2 CONTINUOUS-TIME (CT), DISCRETE-TIME (DT), AND DIGITAL SIGNALS

A signal is called a continuous-time (CT) signal if it is defined at every time instant in a time interval of interest and its amplitude can assume any value in a continuous . . .

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