Constrained least square design of FIR filters without specified transition bands

Abstract

We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response.We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design h e a r and minimum phase FIR filters and gives the best L2 filter and a continuum of Chebyshev filters as special cases.

Design of Lattice Form Optical Delay Line Structure for Microwave Band Pass Filter Applications

“…The center frequency of the mth passband is shifted by 2π(m − 1)/(M ∆τ ), where ∆τ is the unit delay time (the FSR corresponds to 1/∆τ ). The constrained least square algorithm [10] is used to synthesize a M = 5 lattice form band pass optical delay line filter and the various parameters are calculated. Table 1 shows the calculated circuit parameters of coupling coefficient angles of directional couplers and the phase shift values of the phase shifters (θ nA , θ nB , ϕ nA and ϕ nB ) with number of stages k = 35.…”

Least mean squared error-design of complex FIR filters with quantized coefficients

“…This method is a special case of a more general design method, which is thereafter introduced. This second, more general approach is similar to the IIR filter design method used in [10] and was successfully applied in [6], [7], [5] to the design of finite wordlength filters according to a constrained least squared error criterion [1], [23]. In this approach the coefficients are quantized successively: In each iteration step one coefficient is chosen (according to a certain selection criterion) and quantized.…”

“…The minimization of the MSE with respect to h yields Sĥ = b, (23) where the solutionĥ represents the coefficient vector of the filter with the minimal MSE…”

“…Thus, introducing fixed coefficients into the MSE reduces the order of the system of linear equation (52) by the number of fixed coefficients h i Q [κQ] compared with the original LMSE design (23). Hence, the knowledge of coefficients leads to computational savings.…”

Building efficient spectrum-agile devices for dummies

“…Unfortunately, neither the typical windowedapproach nor the Parks-McClellan algorithm can produce a filter that satisfactorily meets these three constraints. Thus, we adopt a constrained least squares algorithm [21] for filter design. We design our filters, using this algorithm, to have 64 taps, a passband ripple of 0.1dB and an overlapping spectrum bandwidth that is approximately 10% of the total filter bandwidth.…”