FOURIER SERIES - Signals, Systems, and Transforms - page 181

y ( t )

Y max

Y min

Figure 4.21 Total response for the system
of Example 4.7. t (s)

0 2 4

Three points are now given concerning Example 4.8:

1. The Fourier-series approach gives the amplitudes and phases of the sinu-
soidal components (the frequency spectrum) of the output signal. However,
the variation of the output signal with time is not evident, as illustrated in
the examples.
2. Even with this simple system, numerical integration (a system simulation)
is the simplest method for finding the system output as a function of time.
For complex systems, simulations are almost always used to determine a
system's time response.
3. For a physical signal, a spectrum analyzer can be used to determine the sig-
nal spectrum. A spectrum analyzer is an electronic instrument designed to
determine signal spectra.

This section develops a steady-state analysis procedure for LTI systems with
periodic inputs. The procedure does not give a plot of the time response; instead,
the frequency spectra of the output is calculated.
This procedure introduces us to the frequency response of LTI systems,
which is one of the most important concepts of LTI system analysis and design. The
frequency-response concept is extended to aperiodic signals in Chapters 5 and 6.

4.6 FOURIER SERIES TRANSFORMATIONS

Table 4.3 gives the Fourier coefficients for seven common signals. We now give two
procedures that extend the usefulness of this table. In developing these procedures,
we will use the notation of (4.38),

q

C kx e jkv 0 t . x(t) =

a

k=- q