of Microprocessors

SOURCE-SIGNAL ANALYSIS
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Fig. 16-2. Wideband and narrowband spectrograms. (A) Narrowband (45 Hz).
(B) Wideband (300 Hz). Source: Applications of Digital Signal Processing,
Alan V. Oppenheim, Editor, Prentice-Hall, 1978.
be determined. Unfortunately, spectral analysis is limited in the frequency
and time resolution that it can show. This is not due to any particular
shortcoming in the computation or the plotting method but instead is due to
a fundamental law of physics. Since the unit of frequency is "events per
second" and the unit of time is seconds, it should be intuitively obvious that
precise measurement of the amplitude of a frequency component in the presence
of other components will take a finite amount of time. In fact, if
frequency resolution of X hertz is desired, a segment of sound lasting a
minimum of l/X sec must be analyzed. Even the human ear is subject to this
limitation. As tone bursts are made shorter, there is greater difficulty in
identifying exactly what the pitches are.
The two spectrograms in Fig. 16-2 illustrate the time-frequency
tradeoff. The first spectrogram is called a narrowband analysis because the
analysis bandwidth is about 45 Hz. This allows individual harmonics of the
sound (a human voice) to show clearly. The waving up and down of the
horizontal lines, which are the harmonics, is the result of changing voice