Page 68 - Fundamentals of Communications Systems

2.20 Chapter Two

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Time, t, sec Frequency, f, Hz
(a) The impulse response. (b) The spectrum, |H( f)|.
Figure 2.6 A lowpass filter impulse response and the spectrum. (a) The impulse response, h(t), of a filter obtained
by truncating (93 ms) and time-shifting (46.5 ms) (b) an ideal lowpass (W = 2.5 kHz) filter impulse response.

EXAMPLE 2.30
In this example the signal from Example 2.1 is to be filtered by the filter from the
previous example. For this example we assume that T p = 907µs. Figure 2.8 shows the
measured energy spectrum of the input and output, and Figure 2.9 shows the input and
output time waveforms for this example. The impact of filtering in the frequency domain
is clearly evident. The elimination of the high-frequency components of the pulse signal
eliminates the sharp transitions and produces some ringing effects.

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Frequency, f, Hz Frequency, f, Hz
(a) Input (b) Output
Figure 2.7 (a) The energy spectrum of the voice signal before and (b) after filtering by a lowpass filter of bandwidth
2.5 kHz.