Pole-zero placement algorithm for the design of digital filters with fractional-order rolloff

Optimal analog‐to‐digital transformation of fractional‐order Butterworth filter using binomial series expansion with Al‐Alaoui operator

“…The design of infinite impulse response (IIR) digital filters can be achieved using two main approaches, such as designing directly in the digital domain (e.g., pole–zero placement algorithms) 1 or transforming an analog filter into its digital counterpart by using an appropriate s ‐to‐ z mapping function 2 . The direct digital design approach is generally preferred since it is challenging to concurrently preserve both the stability and the frequency response of analog filters when they are digitized 1 . However, the direct digital design method does not utilize the rich collection of existing analog filter models to obtain their digital equivalents.…”

“…2 The direct digital design approach is generally preferred since it is challenging to concurrently preserve both the stability and the frequency response of analog filters when they are digitized. 1 However, the direct digital design method does not utilize the rich collection of existing analog filter models to obtain their digital equivalents. The transformation technique can be particularly useful in the design of digital fractional-order filters where a wealth of analog fractional-order filter models on the Butterworth, [3][4][5][6][7][8][9][10][11][12][13] Chebyshev, 14 inverse-Chebyshev, 15 elliptic, 16 and generalized filters [17][18][19][20][21][22][23] already exist in the literature.…”

Fractional order FIR differentiator design using particle swarm optimization algorithm

“…PSO is used to optimize the interlacing of zero‐pole pairs. Hollmann and Stevenson proposed a pole‐zero placement algorithm to design a digital filter directly in the discrete domain with fractional order roll‐off. Result concludes its superiority in subjective and objective measures compared with existing design methods.…”

Optimal design of the noise transfer function of ΔΣ modulators: IIR strategies, FIR strategies, FIR strategies with preassigned poles

“…Attempting a constrained NTF optimization can be complex. The problem of optimally determining the coefficients of a discrete time filter is still a hot topic in many application fields (e.g., see [23][24][25] for a few representative cases). The complication induced by the different treatment necessitated by the numerator and denominator of rational polynomial functions often requires approximations, heuristic techniques, or specific assumptionsonthe filter structure [23].…”

“…The problem of optimally determining the coefficients of a discrete time filter is still a hot topic in many application fields (e.g., see [23][24][25] for a few representative cases). The complication induced by the different treatment necessitated by the numerator and denominator of rational polynomial functions often requires approximations, heuristic techniques, or specific assumptionsonthe filter structure [23]. Restriction to finite impulse response (FIR) arrangements can often help achieve exact solutions [13,14,24,25].Conversely, the presence of constraints defined in the frequency domain for every possible frequency, implies semi-infinite programming [26] and may make the optimization harder to tackle.…”