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A new class of continuous-time (CT) two-dimensional (2D) filters based on available 2D IIR wave digital filters (WDFs) is proposed. This class of CT filters is free of the aliasing and switching power dissipation of discrete-time versions and also free of the quantization noise caused by digital underflow. Importantly, the transfer functions do not undergo warping in the temporal-frequency domain due to the bilinear transformation. The method essentially approximates each ideal CT delay element of the 2D IIR WDFs with an analog all-pass block. VLSI circuit implementations of the proposed method are described where inverter-based CMOS circuit that implements the required all-pass transfer function is simulated using 90 nm CMOS BSIM4 models in Cadence.