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Applications of Fractional Derivatives in Adaptive Signal Processing Systems

Thesis Info

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Author

Shah, Syed Muslim

Program

PhD

Institute

Capital University of Science & Technology

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Electrical Engineering

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11514/1/Syed%20Muslim%20Shah%20electrical%20engg%202019%20cust%20isb%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727704712

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Adaptive algorithms are mostly optimized using integer order derivatives for error minimization. The Least Mean Squares (LMS) and Recursive Least Squares (RLS) adaptive filters are among the most commonly employed schemes. The LMS algo rithm is simple to implement, has robust tracking performance in nonstationary environments and is less sensitive to floating point precision effects. However, it has the issue of slow convergence especially when the number of weights is large. The RLS achieves faster convergence but is computationally expensive, and prob lematic in nonstationary environments. This study introduces fractional calculus techniques in stochastic gradient algo rithms. In addition to first order derivative, Fractional Order (FO) derivatives are proposed in the optimization of gradient algorithms. Four configurations have been considered based on whether the fractional derivative is applied to the in stantaneous present or posterior error. For evaluation of the FO algorithms, three applications have been considered, that is, (a) adaptive equalization of multi path channels (b) Active Noise Control Systems (ANCS) and (c) tracking of time varying Rayleigh fading sequences. In equalization, both supervised and unsu pervised algorithms are considered. For the supervised case, FO variants of LMS and Normalized LMS (NLMS) are applied in both feed-forward and decision feed back configurations. In the unsupervised case, FO variants of Gordad and con stant modulus algorithms are developed. In ANCS, FO variants of the NLMS, Filtered-x (input) LMS, Modified FxLMS and Filtered-error LMS algorithms are developed. The noises are modelled as binary, Gaussian and impulsive sources characterized by fractional lower order moments. In tracking, the behavior of FO variants is evaluated for nonstationary environments. A Rayleigh channel has also been considered having Doppler frequency shifts of 0.8KHz to 3KHz. The frac tional algorithms are compared with the standard NLMS, RLS and Extended-RLS schemes. The main performance metrics include (1) mean squared error (2) mean squared deviation (3) relative modelling error (4) model accuracy using both frequency and time domain analysis and (5) symbol error rate. The former three performance metrics help compare the convergence speed and steady state performance; the latter two are application specific. Simulation results are shown for different step sizes and fractional orders. It is seen that the fractional variants show superior performance in all the three applications and hold great promise for future use.
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سی حرفی : ۹

سی حرفی۔۹
(ہک بیت وچ اٹھ حرف)
الف
الٰہی، میل ماہی نوں، ’ب‘ برے دن آئے نیں
ت
تلوار برہوں دی لٹکے، ’ث‘ ثواب کمائے نیں
ج
جوانی آخر فانی، ’ح‘حائل غم آئے نیں
خ
خوف حنیف وچھوڑے اندر، ’د‘ دکھاں دے سائے نیں

ذ
ذکر تیرے وچ رہندی، ’ر‘ رخ ویکھاں ماہی دا
ز
زیارت لکھ ثواباں، ’س‘ سوہنا چن چاہی دا
ش
شوخاں دے ناز نہورے، ’ص‘ صفا دل چاہی دا
ض
ضدی سنگ دل حنیف اے، مان حسن دی شاہی دا

ط
طواف کریں دن راتیں، ’ظ‘ ظالم کوئی خبر نہیوں
ع
عشق دے کٹھے عاشق، ’غ‘ غصہ تے جبر نہیوں
ف
فائدہ کی شکویاں سندا، ’ق‘ قسمت وچ اجر نہیوں
ک
کتھے چھڈ گیوں ماہی، کجھ حنیف نوں صبر نہیوں

ل
لیکھاں وچ درد وچھوڑا، ’م‘ ماڑے دا زور نہیوں
ن
نوازش وصل دی ہووے، ’و‘ وسیلہ ہور نہیوں
ہ
ہڈاں وچ درد وچھوڑا، ’لا‘ لہو دا زور نہیوں
ء
آخر حنیف ملے گا، ’ی‘ یاداں وچہ ہور نہیوں
سی حرفی ۔۱۰
(ہک مصرعہ وچ دو حرف)
الف
اللہ نوں سور پیارے، ’ب‘ بس کر کوئی ہور نہیوں
ت
توبہ کر آخر مرنا، ’ث‘ ثابت وچ گور نہیوں
ج
جمع کر عمل دی پونجی، ’ح‘ حاصل کجھ ہور نہیوں
خ
خوف حنیف خدا دا کریے، ’ر‘ رحمت باہجھوں ٹھور نہیوں
د
دوا گناہاں والی، ’ذ‘ ذکر وچ ڈھیندی اے
ر
رحمت وی لا متناہی، ’ز‘ زوراور تھیندی اے
س
سوہنا رب کرم کماسی، ’ش‘ شاہی نت جیندی اے
ص
صدیق حنیف نہ جھورے، آخر سچ منیندی اے

ض
ضعیف ایمانوں ہوئے، ’ط‘ طریقے بھلے نی
ظ
ظرافت رہی نہ مولے، ’ع‘ عمل نال تلے نی
غ
غازی تے ہین مجاہد، ’ف‘ فکراں وچ رُلّے نی
ق
قولاں دے سچے جیہڑے، پاون...

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From the very beginning Islam has given great importance to discipline. In every facet of life discipline has a role to play. Today when we delve deep in to our lives, we are amazed as to how it has always proved its worth. It has brought the tide of revolution in everyone's mind. Similarly, the element of discipline saves a society from disruption and instability. It infuses in life satisfaction and contentment. Contrarily, indiscipline and mismanagement give birth to dejection and dissatisfaction. Time management plays a vital role in the establishment of discipline in a society. Considering the vast importance of time management in the light of discipline, the following article throws a great deal of light on it in the Islamic perspective.

Effect of Allelopathic Plants on Morphoanatomical Features of Wheat

This study was conducted to evaluate the effect of allelopathic plant on growth and morpho-anatomical features of wheat. Three experiments were conducted in order to study the allelopathic effects of root, stem, leaf and fruit of Dodonea viscosa, Eucalyptus camaldulensis, Fumaria indica, Juglans regia, Melia azedarach, Olea ferruginea,Sapindus mukorossi, Tamarix indica and Taraxacum officinale on growth and morpho-anatomical features of Wheat variety Pirsabaq 2005 during 2013-2016 at experimental field and laboratory, Department of Botany, Hazara University Mansehra. The present investigation showed that all the applied allelopathic plants parts have adverse effect on germination, morphological and anatomical parameters of wheat. Results of germination revealed that leaf aqueous extracts > Fruits> Root > Shoot. The degree of sensitivity of wheat in respect of growth to applied applications was Melia azedarach > Sapindus mukorossi > Taraxacum officinale > Juglans regia > Fumaria indica > Eucalyptus camaldulensis > Olea ferruginea > Tamarix indica > Dodonea viscosa. Root, stem, leaf of Olea ferruginea increased the diameter of xylem, phloem, and mesophyll tissue of root, stem and leaf of wheat which directly effect the physio-morphology of wheat. Fumaria indica has stimulatory effect on radical and plumule length, it also increases morpho-agronomic characters and anatomical character of wheat. Fruit of Melia azedarach is least effect of on germination and morpho–agronomic and anatomical character of wheat. The fruit of Sapindus mukorossi is highly harmful for germination, morphology, agronomy,and anatomical features of wheat and partially block the xylem and phloem as result it retard germination, morphology,agronomy of wheat. Dodonea viscosa is less toxic as compare to Tamarix indica and Juglan regia and Eucalyptus camadulensis for wheat growth and anatomical parameters. It is concluded that stem of Eucalyptus camaldulensis is highly toxic for all the morpho-agronomic characters of wheat i-e length of internode,length of spike, grain yield. Soil analysis shows that all allelopathic plants decrease the nitrogen in soil while phosphorus is deficient in Tamarix indica leaf and Melia azedarch treatments. Similarly potassium value increase in all treatments as compare to control. Maximum electric conductivity was observed in Eucalyptus camadulesis stem. pH values do not show significant difference in all treatments. Eucalyptus camaldulensis, Melia azedarach, Sapindus mukorossi,Tamarix indica, Juglans regia decrease the germination, growth and yield of wheat. Olea ferruginea and Fumaria indica show stimulatory effect on germination and other morpho-anatomical features of wheat. This study would be helful to understand the nature of allelopathic plants either they have allopathic effect or allelopathic potentials for different crops. Some allelopathic plants would be benficial and harmful for the growth of different crops due to allelochemicals. Biofertilizers and bioherbicides can be prepared from the allopathic plants for crop improvement.