Complex filters can be used in low IF architecture especially in DSP in order to phase out (reject) the image signal. How are complex filters implemented in the analog domain?
closed as too broad by Marcus Müller, A_A, lennon310, Matt L., jojek♦ Oct 10 '18 at 15:18
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Vector Modulators and Single Sideband Mixer (frequency translator) are the common and relatively simple analog component for rejecting the image signal.
The top block diagram in this post is the architecture of a vector modulator and single sideband mixer and explains in further detail how it provides image rejection using complex signalling.
Normally we see these components with a real input where an internal 90° splitter immediately converts the input to a complex signal and then it is further processed. However there is no reason these can't also be used in identical fashion with the quadrature splitter bypassed in the case of a low IF IQ signal already exists.
This would be the favored approach for eliminating the image signal.
However to implement a generic complex filter in the analog domain, you would need to do the following with four real filters as shown in the diagram below. This is related to performing full complex multiplication with real signals as given by:
$$(s_I+js_Q)(c_I-jc_Q)$$ $$= (s_Ic_I+s_Qc_Q) + j(s_Ic_Q-s_Qc_I)$$
Corresponding to the multiplication of a signal (s) with a coefficient such as in an FIR filter (c) showing that we have an I and Q input, multiplied by and I an Q coefficient, resulting in a I (real part given by $s_Ic_I+s_Qc_Q$) and Q (Imaginary part given by s_Ic_Q-s_Qc_I).
Equivalently complex analog filtering (the filtering of a complex input with a complex impulse response) is formed with four real filters as shown in the graphic below. Each filter has a real impulse response given by $h_i(t)$ or $h_q(t)$ corresponding the real and imaginary portion of the complex impulse response desired.
Also to add, I did come across this: https://ieeexplore.ieee.org/abstract/document/4151912
Note that SAW filters are an analog equivalent of an FIR filter ("all=zero" filter, with poles at infinity, formed by the summation of weighted delays)