4 Practical MATLAB® Applications for Engineers
1.2 Objectives
After completing this chapter the reader should be able to
Mathematically defi ne the most important analog and discrete signals used in
practical systems
Understand the sampling process
Understand the concept of orthogonal signal
Defi ne the most widely used orthogonal signal families
Understand the concepts of symmetric and asymmetric signals
Understand the concept of time and amplitude scaling
Understand the concepts of time shifting, reversal, compression, and expansion
Understand the reconstruction process involved in transforming a discrete signal
into an analog signal
Compute the average value, power, and energy associated with a given signal
Understand the concepts of down-, up-, and resampling
Defi ne the concept of modulation, a process used extensively in communications
Defi ne the multiplexing process, a process used extensively in communications
Relate mathematically the input and output of a system (analog or digital)
Defi ne the concept and purpose of a window
Defi ne when and where a window function should be used
Defi ne the most important window functions used in system analysis
Use the window concept to limit or truncate a signal
Model and generate different continuous as well as discrete time signals, using the
power of MATLAB1.3 Background
R.1.1 The sampling or Nyquist–Shannon theorem states that if a continuous signal f(t)
is band-limited* to fm Hertz, then by sampling the signal f(t) with a constant period
T ≤ [1/(2.fm)], or at least with a sampling rate of twice the highest frequency of f(t), the
original signal f(t) can be recovered from the equally spaced samples f(0), f(T), f(2T),
f(3T), ..., f(nT), and a perfect reconstruction is then possible (with no distortion).
The spacing T (or Ts) between two consecutive samples is called the sampling period
or the sampling interval, and the sampling frequency Fs is defi ned then as Fs = 1/T.
R.1.2 By passing the sampling sequence f(nT) through a low-pass fi lter* with cutoff fre-
quency fm, the original continuous time function f(t) can be reconstructed (see
Chapter 6 for a discussion about fi lters).
*^ The concepts of band-limit and fi ltering are discussed in Chapters 4 and 6. At this point, it is suffi cient for the
reader to k now that by sampling an analog function using the Nyquist rate, a discrete function is created from
the analog function, and in theory the analog signal can be reconstructed, error free, from its samples.