# Chap1 - Signal Processing of Discrete-time Signals Andrew C...

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Unformatted text preview: Signal Processing of Discrete-time Signals Andrew C. Singer and David C. Munson Jr. January 26, 2009 2 Chapter 1 Overview of Discrete-time Signal Processing 1.1 DSP overview: This is a textbook covering the topic of discrete-time signal processing. The tremendous advances in inte- grated circuit technologies have enabled a remarkable revolution in the way in which we measure and process information. The types if information, or the signals as we call them, that we have interest in process- ing can range widely from measurements of our environment, such as temperature, rainfall, geophysical or siesmic data, to signals governing man-made machines of interest, such as the velocity of a moving vehicle, or the fuel-injector modulating signals within our cars, to pureuly man-made sources of information, such as radio or television signals, or the MP3 encodings of recorded music. The abstract concept of a signal, is that of a measurement of a quantity of interest that is indexed by an associated reference axis. Most often, we will refer to this reference axis as the time axis for the signal and refer to these as signals that vary as a function of time. For example, within an analog circuit, we may measure the voltage across a given resistor within the circuit fabric and label this signal v r ( t ) to denote that this is the voltage v of a particular resistor r taken at a particular point in time t. As time varies, the voltage may be plotted against the independent variable t to produce a voltage vs. time plot, where we typically assume that negative time is to the left, and positive time to the right. For most of signals of interest, there is a common notion of a reference time, t = 0 , such that signals may be plotted with this reference time in the center, so long as the reference time is known to those interpreting the graph. Another example of a signal may be the sequence of closing prices of the Dow Jones Industrial Averages (DJIA) as reported daily from the New York Stock Exchange. Unlike the resistor voltage example, the sequence of prices will be indexed by an integer reference axis indicating the speci c day in a sequence of days at which the index took on a particular value. We may write p [ n ] , to denote the closing price of the DJIA on the n th day of trading, referenced to some common day n = 0 . Note that while the resistor voltage v r ( t ) could be referenced to any time t taking on any real value, the price p [ n ] can only be referenced to n taken as an integer. We refer to signals whose index t can take on any real value as continuous-time signals, since the time signal is assumed to be available over a continuum of values t . We refer to signals whose index n can only take on values from the integers, i.e. only discrete values, as discrete-time signals. While this text is largely about discrete-time signal processing, that is the processing and analysis of discrete- time signals, we will also be interested in understanding how similar properties of continuous-time signals...
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Chap1 - Signal Processing of Discrete-time Signals Andrew C...

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