Digital Signal Processing Reference
In-Depth Information
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Fig. 10
Illustration of bandpass signal structure in time- and frequency domains.
Left half
shows
a principal bandpass signal spectrum and the corresponding time-domain waveform.
Right half
,
in turn, shows the corresponding lowpass equivalent signal spectrum and the corresponding time-
domain complex signal as a time-varying phasor in complex plane
Fig. 11
Illustration of
complex filtering (complex
convolution) in terms of
complex signals (
upper
)and
parallel real signals (
lower
)
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Thus in general, 4 real multiplications (plus two additions) and 4 real convolutions
(plus two additions) are needed, respectively, in the physical implementations. This
is illustrated in Fig.
11
for general complex convolution. Obvious simplifications
occur if either of the components (input signal or filter impulse response) is real
valued.
