Design of optimum high-order finite-wordlength digital FIR filters with linear phase

Spectral Analysis of Rectangular, Hanning, Hamming and Kaiser Window for Digital Fir Filter

“…As multiplication of sequences ( )and ( ) in time domain is equivalent to convolution of ( )and ( ) (in the frequency domain, it has the effect of smoothing ( ). The several effects of windowing the Fourier coefficients of the filter on the result of the frequency response of the filter are: a) major effect is that discontinuities in ( )becometransition bands between values on either side of the discontinuity, b) The width of the transition bands depends on the width of the main lobe of the frequency response of the window function, ( ) ( ), c) Since the filter frequency response is obtained via convolution relation, it is clear that the resulting filters are never optimal in any sense, d) As (the length of the window function) increases, themain lobe width of ( ) is reduced which reduces the widthof the transition band, but this also introduces more ripple in the frequency response, and e) The window function eliminates the ringing effects at band edge and does result in lower side lobes at the expense of an increase in the width of the transition band of the filter [5], [6]. The FIR filter design process via window functions can be split into several steps.…”

Design of discrete coefficient frequency-response-masking FIR digital filters

“…Let x i C n be the set containing all the elements of C n excluding x i . We quantize each coefficient of the optimal continuous coefficient vector X c one by one [6]- [7] according to the following procedure.…”

“…However, this requires a lengthy computation if the dimension of the problem is high. One way to solve the problem is to quantify the optimal continuous coefficient values one by one [6]- [7]. This way is adopted in [6] to solve discrete coefficient FIR filter design, and for the design of optimum high-order finite word length FIR filters in [7].…”

“…One way to solve the problem is to quantify the optimal continuous coefficient values one by one [6]- [7]. This way is adopted in [6] to solve discrete coefficient FIR filter design, and for the design of optimum high-order finite word length FIR filters in [7]. In this paper, this idea is firstly described to devise the FRM filter coefficient with finite word length which searches along one path.…”

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.…”