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Abstract
SummaryFinite word length linear‐phase finite impulse response filters can be implemented using low‐cost devices. Among them, the single‐band peak‐constrained least squares filters are the most common one employed in many engineering applications. To design these filters, it is required to define the specifications on the maximum passband ripple magnitude, the maximum stopband ripple magnitude, and the number of bits for representing the filter coefficients. Most of the existing works on the filter design are on the determination of the filter coefficients based on a given set of these specification parameters. However, very few works are on the determination of these specification parameters. Hence, this paper establishes the analytical relationships among these specification parameters. In particular, the relationship between the total ripple energy and the maximum ripple magnitude of the filter, the relationship between the number of bits for representing the filter coefficients and the total ripple energy of the filter, and the relationship between the number of bits for representing the filter coefficients and the maximum ripple magnitude of the filter are established. Computer numerical simulations are presented for verifying the obtained results.
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