A Design Method for a Variable Cascaded FIR Hilbert Transformers with Transmission Zero-Like Behavior

Physical quantities, such as temperature and weight, are commonly measured as DC signals. In practical applications, however, these signals are often corrupted by superimposed sinusoidal noise originating from disturbances like power lines and mechanical vibrations. The effective removal of this noise is crucial for achieving high-precision measurements. An effective approach for canceling such noise involves generating an Inverse-phase signal, a task for which cascaded Hilbert transformers are often employed. However, conventional approaches suffer from approximation errors that cannot be forced to zero at arbitrary angular frequencies, leading to inaccuracies in the resulting Inverse-phase signal. To address this issue, this paper proposes a novel design method that directly incorporates a variable parameter into the amplitude response of the second-stage Hilbert transformer. This enables the angular frequency of the transmission zero-like behavior to be arbitrarily and continuously controlled within multiple predefined ranges, without the need to redesign the filter coefficients. The proposed design problem can be efficiently formulated as a linear programming problem. Detailed design examples are provided to demonstrate the effectiveness and flexibility of the proposed method, verifying that the transmission zero-like behavior can be precisely positioned at any desired angular frequency.