This paper proposes a method for the synthesis of ladder wave digital filters (WDFs) directly from the digital domain. This method avoids the need for the synthesis of analog reference filters conventionally required in WDF design. This direct method allows for the determination of the WDF coefficients from the digital domain transfer function. This is similar to conventional infinite impulse response (IIR) filter coefficient determination but the WDF will give a more efficient realization. Due to the WDFs power complementary properties, a first-order ladder WDF can simultaneously realize both lowpass and highpass responses using the same structure, while a second-order WDF can realize both the bandpass and bandstop responses simultaneously. By appropriately choosing the WDF adaptor configuration and structure, tunable parameters can be determined from the digital domain transfer function that controls the 3dB cut-off frequency of the lowpass and highpass filters, and the centre frequency and 3-dB bandwidth of the bandpass and bandstop filters. This results in the WDFs requiring a minimum number of multipliers for realization.
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