Extrapolated impulse response filter and its application in the synthesis of digital filters using the frequency-response masking technique

FRM-Based FIR Filters with Minimum Coefficient Sensitivities

“…Thus, E{(∆H x (e jω )) 2 } = N x ε 2 (11) Applying the result of (11), (4) becomes E{(∆H(e jω )) 2 (15) and (16), we have ||∆H(e jω )|| 2 = S 2 ε 2 (17) From (17), and since ε 2 = E{(∆h x (i)) 2 } by definition, it is clear that S 2 is a coefficient sensitivity measure. In order to minimize S 2 , the peak ripple magnitude of H(e jω ), denoted as δ, may be set as a constraint and S 2 becomes the objective for minimization as in (18).…”

“…HE frequency response masking (FRM) technique [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] has received much attention for the synthesis of very sharp digital filters with very sparse coefficients. It has found applications in diverse fields including the synthesis of various types of filters such as half-band filters [21]- [23], 2D filters [24], IIR filters [25]- [28], filter banks [29]- [34], decimators and interpolators [35], [36], and Hilbert transformers [37], [38], FPGA implementations [39][40][41], transmultiplexer design [42], ECG signal processing [43], hearing aids [44], digital audio [45]- [49] application and analysis, speech recognition [50], array beamforming [51], software radio [52], and noise thermometer [53].…”

Optimized Design of Extrapolated Impulse Response FIR Filters with Raised-Cosine Windows

“…Based on this characteristic, a design of FIR filters with low complexity was proposed. By making use of similarities among side lobes, the extrapolated technique predicts current side lobe from preceding ones so as to prolong the orders and improve the performance of filters [1][2][3][4]. Furthermore, for a first order system, the time response is h(n) ale" u(n) , and the scale value is a constant h(n1 + k) h(n1) = e ,k This means the latter part is proportional to the former one.…”

Frequency-Response Masking Filters Based on Serial Masking Schemes

“…the filter structure, the design method, and the implementation. The introduction of various FRM structures has significantly enhanced the computational efficiency of the FRM technique [19,21,22,25,45,[48][49][50][51][52][53]. Non-linear optimization techniques further reduce the arithmetic operations in the FRM filters, where the coefficients of all subfilters in an FRM structure are optimized simultaneously [6, 15-18, 31, 34, 35].…”