Time Domain Representation of Continuous and Discrete Signals 45
where
f is the input sampled vector (f(n)).
M the down-sampling integer rate factor, or the resampling rate is 1/M times the
original rate. The resulting length is given by length(fM) = [length (f)]/M.
N the order of the (Chebyshev type-1) fi lter used to accomplish the resampling.
fi r a 30 -poi nt low-pa s s fi lter forward direction only with cutoff frequency wc = π/M,
before resampling is done.
The decimation process of the fi rst two options uses an IIF Chebyshev low-pass
type-1 fi lter with forward and backward directions (see Chapter 6 for information
regarding fi lters).
R.1.134 The MATLAB function resample returns the sequence f LM, consisting of f resa-
mpled with a rate that is the ratio of two integers given by L/M.
The syntax of the function resample with some options is indicated as follows:fLM = resample(f, L, M)fLM = resample(f, L, M, R)fLM = resample(f, L, M, h)[fLM, h] = resample(f, L, M)where R is the input rate with a default value of 10. This function uses an FIR, and
a Kaiser window with β = 5 (windows are presented later in this section).
R.1.135 The process referred to as multiplexing consists of merging two (or more) discrete
sequences f 1 (n) and f 2 (n) into a single sequence by alternating the samples of f 1 (n)
with f 2 (n). Then the resulting multiplexed, or in short mux sequence is given bymux(f 1 , f 2 ) = [f 1 (1) f 2 (1) f 1 (2) f 2 (2) f 1 (3) f 2 (3) ... f 1 (n − 1) f 2 (n − 1) f 1 (n) f 2 (n)]The lengths of the sequences of f 1 and f 2 are assumed to be n (equal). Then the
length of mux (f 1 , f 2 ) sequence is 2n. If the sequences are f 1 (n) and f 2 (m), where n > m,
then by increasing the length of f 2 to n, by making the last n − m samples zeros,
the two sequences (lengths) became equal and the mux command can then be safely
used.
R.1.136 Signals may also be classifi ed according to the probability of predicting its behav-
ior with certainty or with some sort of ambiguity into
a. Deterministic or nonrandom
b. Probabilistic, stochastic, or random
R.1.137 Deterministic signals can be expressed in terms of a well-defi ned process, table,
rules, or by a mathematical relation (equation). These type of signals are fully
predictable.
R.1.138 Random signals are not predictable; they are noise-like functions where particular
values or samples are not important, but rather the statistical information over
a large range of samples is, such as the expected value, the mean, and standard
deviation. Most signals encountered in practical applications and in this text are
real and deterministic. Observe that random signals cannot be reproduced, but
may carry valuable information. The more unpredictable or random a signal is the
more information it carries.