Quadrature mirror filter bank design based on hybrid bee colony technique

Figures & data

Figure 1. The process of two channel quadrature mirror filter bank.

Figure 2. Flow chart of HBCT technique.

Table 1. The coefficients of prototype filter after optimization (N = 48).

Filter coefficients	Values
h0(0)= h0(47)	−0.0000045430497975
h0(1)= h0(46)	−0.0000098392710997
h0(2)= h0(45)	0.0000246909167798
h0(3)= h0(44)	0.0000250916855514
h0(4)= h0(43)	−0.0000446787746104
h0(5)= h0(42)	−0.0000733096834442
h0(6)= h0(41)	0.0000017446111596
h0(7)= h0(40)	0.0002870033133665
h0(8)= h0(39)	0.0002025974240886
h0(9)= h0(38)	−0.0010237579549928
h0(10)= h0(37)	−0.0006003699654017
h0(11)= h0(36)	0.0029718056724678
h0(12)= h0(35)	0.0009474391127381
h0(13)= h0(34)	−0.0071788654613222
h0(14)= h0(33)	−0.0004340674710466
h0(15)= h0(32)	0.0150192729274227
h0(16)= h0(31)	−0.0026805949842865
h0(17)= h0(30)	−0.0283657750808152
h0(18)= h0(29)	0.0118562165103587
h0(19)= h0(28)	0.0511171629772864
h0(20)= h0(27)	−0.0359874077216667
h0(21)= h0(26)	−0.0996990241015380
h0(22)= h0(25)	0.1255024549007690
h0(23)= h0(24)	0.4681455274400170

Figure 3. Normalized magnitude response of the analysis filters for N = 48.

Figure 4. Reconstruction error for filter bank designed using prototype filter of order N = 48.

Table 2. The coefficients of prototype filter after optimization (N = 32).

Filter coefficients	Values
h0(0) = h0(31)	−0.00012935731488
h0(1) = h0(30)	0.000108901554865
h0(2) = h0(29)	0.000094851515419
h0(3) = h0(28)	−0.000031508516407
h0(4) = h0(27)	0.000481881649469
h0(5) = h0(26)	−0.001466461026304
h0(6) = h0(25)	−0.001532163574506
h0(7) = h0(24)	0.006842547779440
h0(8) = h0(23)	0.001455774007123
h0(9) = h0(22)	−0.019595911860164
h0(10)= h0(21)	0.004202987798966
h0(11)= h0(20)	0.044772481396089
h0(12)= h0(19)	−0.026211231502887
h0(13)= h0(18)	−0.098470671706567
h0(14)= h0(17)	0.116648565189399
h0(15)= h0(16)	0.472810386808457

Figure 5. Normalized amplitude response of analysis filters for N = 32.

Figure 6. Reconstruction error.

Table 3. The coefficients of prototype filter after optimization (N = 24).

Filter coefficients	Values
h0(0) = h0(23)	0.00245482339148712
h0(1) = h0(22)	−0.00522474163849697
h0(2) = h0(21)	−0.00194808285430188
h0(3) = h0(20)	0.01294794543225470
h0(4) = h0(19)	−0.00050325273253512
h0(5) = h0(18)	−0.02698100895516620
h0(6) = h0(17)	0.00958630118745679
h0(7) = h0(16)	0.05057204101175600
h0(8) = h0(15)	−0.03408992562872450
h0(9) = h0(14)	−0.09988990318638480
h0(10)= h0(13)	0.12420972429619000
h0(11)= h0(12)	0.46888101218902900

Table 4. Comparison of proposed technique with existing optimization techniques for N = 48.

Techniques	${\epsilon }_R(dB)$	$E_p$	$E_s$	$A_E(dB)$	$A_S(dB)$
DE technique [2]	0.0148	2.00$\times {10}^{-8}$	5.00$\times {10}^{-8}$	48.55	58.97
JADE technique [2]	0.0170	2.49$\times {10}^{-8}$	3.16$\times {10}^{-8}$	49.81	59.31
PSO technique [24]	0.0136	2.20$\times {10}^{-8}$	2.53$\times {10}^{-8}$	48.55	58.97
BCT technique [22]	0.0093	3.16$\times {10}^{-8}$	2.95$\times {10}^{-8}$	55.08	64.15
Proposed HBCT technique	0.00002	3.0$\times {10}^{-11}$	8.4$\times {10}^{-11}$	92.20	99.17

Figure 7. Normalized amplitude response of analysis filters for N = 24.

Figure 8. Reconstruction error.

Table 5. Comparison of proposed technique with existing optimization techniques for N = 32.

Techniques	${\epsilon }_R(dB)$	$E_p$	$E_s$	$A_E(dB)$	$A_S(dB)$
DE technique [2]	0.0166	1.58$\times {10}^{-7}$	3.15$\times {10}^{-6}$	34.73	44.68
Marquard method [18]	0.0270	2.90$\times {10}^{-8}$	5.51$\times {10}^{-6}$	33.93	44.25
Gradient method [19]	0.0160	2.64$\times {10}^{-8}$	3.30$\times {10}^{-6}$	33.60	44.40
Weighted Least Square [14]	0.0160	2.11$\times {10}^{-8}$	1.55$\times {10}^{-6}$	34.00	35.00
PSO based [23]	0.0126	5.27$\times {10}^{-8}$	1.00$\times {10}^{-6}$	34.14	43.50
PSO based [24]	0.0148	2.30$\times {10}^{-8}$	5.97$\times {10}^{-6}$	36.87	44.75
Proposed HBCT technique	0.00036	6.17$\times {10}^{-9}$	2.76$\times {10}^{-8}$	66.99	71.04

Table 6. Comparison of proposed technique with existing optimization techniques for N = 24.

Techniques	${\epsilon }_R(dB)$	$E_p$	$E_s$	$A_E(dB)$	$A_S(dB)$
Marquardt method [18]	0.0251	9.2$\times {10}^{-8}$	8.5$\times {10}^{-5}$	23.03	35.83
PSO based [24]	0.019	1.8$\times {10}^{-7}$	7.9$\times {10}^{-5}$	22.78	34.43
MJADE_pBX technique [2]	0.015	9.1$\times {10}^{-7}$	1.3$\times {10}^{-4}$	20.11	30.94
Levenberg– Marquardt (LM) and Quasi-Newton(QN) method [37]	–	2.1$\times {10}^{-7}$	7.3$\times {10}^{-6}$	24.76	–
BCT technique [22]	0.014	1.1$\times {10}^{-7}$	6.9$\times {10}^{-5}$	24.98	34.70
Proposed HBCT technique	0.011	7.5$\times {10}^{-8}$	5.2$\times {10}^{-6}$	23.61	42.04

Figure 9. Convergence plot for proposed HBCT and BCT techniques.

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