Fourier and Periodogram Transform Temperature Analysis in Soil

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ISSN (e): 2250 3005 Volume, 05 Issue, 09 September 2015 Iteratioal Joural of Computatioal Egieerig Research (IJCER) Fourier ad Periodogram Trasform Aalysis i Soil Afolabi O.M.

were as iterpreted. Measuremet of 5-miute iterval temperature variatio with 3 LM34DZ sesors was made. The results show that Clay has the highest average Fourier trasform (32.472) followed by loam (30.

1 ISSN (e): Volume, 05 Issue, 09 September 2015 Iteratioal Joural of Computatioal Egieerig Research (IJCER) Fourier ad Periodogram Trasform Aalysis i Soil Afolabi O.M. Adekule Ajasi Uiversity, Akugba Akoko, Odo state Nigeria Abstract Fourier series ad periodogram trasform of three set of temperature data measured with costructed PIC 18F4520 based temperature meter were as iterpreted. Measuremet of 5-miute iterval temperature variatio with 3 LM34DZ sesors was made. The results show that Clay has the highest average Fourier trasform (32.472) followed by loam (30.624) ad sad (29.428). The periodogram aalysis also varied i similar maer with clay havig a mea periodogram , loam ad sad These show that temperature icreasig most i clay caused higher values of Fourier ad periodogram trasforms. The average of the absolute deviatio idicated loam has highest Fourier series chages (1.497) followed by sad (0.678) ad clay (0.598) while the periodogram has deviatio ragig from loam , sad to clay This idicates that loam soil has most sesitive respose to temperature variatios. Keywords: Soil Data, Fourier Trasform,, Periodogram, Variatio. I. Itroductio measuremet o lad ca be affected by sideways or lateral ad subsurface disturbaces ad field soils are heterogeeous i costituets. Samplig of soil ad the temperature measuremet i provides a best approach to elimiate error cotributio from other materials. Time series aalysis is associated with the time domai (i.e. tred compoet) ad the frequecy domai (i.e. periodic compoet). time series maily cosist of Tred compoet i the very short or daily duratio ad log ru comprisig of moths data with ot so obvious periodicity. May years data comprise of seasoal temperature associated with tred or a log term movemet i a time series. It is the uderlyig directio (upward or dowward) ad rate of chage i a time series, whe allowace has bee for radom or chaotic residuals. They ca accout for less tha a year s seasoal or cyclic compoet depedig o the duratio cosidered (Abdullah et al., 2009). II. Material ad Methods The temperature sesor used is LM35DZ, P.I.C used is PIC18F4520 (programmed i C with MPLAB). 9v DC INPUT LM7805 1P3 Fig.1 PIC18F4520 temperature circuit modified from Ope Access Joural Page 21

2 The display is o 20x4 LCD. The whole costructed circuit was eclosed i a PVC case ad the LCD was udereath a trasparet Perspex cover ml each of the 3 soils were mixed with 500ml water ad the solutio were put i a woode box uderlai iside with cellophae paper, each of all the three LM34DZ ICs 3 pis were isulated with thick maskig tape away from the soil solutio to avoid short circuit of the IC before the LM34DZ temperature sesors were immersed 1 cm ito the soils. readigs i cetigrade were take from the costructed temperature meter every 5 miutes from all the soils after switchig with 1-pole 3- throw (1P3) switch (see Fig. 1) to the 3 LM34DZ sesors.. III. Result ad Discussio The temperature data recorded from each soil are i Table 1. Soil temperature data recorded i 7 th March, 2015 were checked ad the data were cosistet ad cotiuous, Tushar ad Keith, 2008 Table 1: Time temperature data for Sad, Loam ad Clay Soils Time Time (MIN) Sad ( o C) Loam ( o C) Clay ( o C) 11: : : : : : : : : : : : : : : : : : : : : : : : Ope Access Joural Page 22

3 0 C Sad Loam Clay Time (miute) Fig.1 time series curves for sad, loam ad clay The temperature data showed Clay reached its maximum temperature of C faster tha the other two soils at pm followed by sad at pm a maximum temperature of C. Loam took logest time to reach its iitial maximum temperature of C at 13.50pm. The average temperatures recorded from the experimet are sad, loam ad clay. The correlatio of the 3 separate data shows that clay ad sad vary similarly with Pearso correlatio coefficiet 0.66 i respose to similar atmospheric coditio while loam ad clay do ot correlate (-0.19). Sad ad loam have low correlatio of The average of the absolute deviatio from each of their mea shows that loam has highest temperature deviatio with average absolute deviatio 1.50 followed by sad 0.68 ad clay This meas that the temperature of loam soil vary the most out of three soils cosidered. Fourier Trasform Fourier trasform (FT) is a mathematical fuctio that ca be used for mappig a time series from the time domai ito the frequecy domai. It decomposes a waveform or a fuctio ito siusoids of differet frequecies which sum to the origial waveform. It distiguishes differet frequecy siusoids ad their respective amplitudes. Fourier trasform is expressed as x(t) X(f) accordig to X f = 1 t() t(0) x(t) e i2πft dt.1. for cotiuous fuctio. The expoetial ivolvig 2πft is θ i radia, simplified i form as e iθ = cosθ+isiθ..2. A graph of the distributio of the Fourier coefficiets i the complex plae is difficult to iterpret (Abdullah et al., 2009). By usig the real compoet of the siusoid, ad usig the discrete form of equatio 1 for a discrete process measured at equal itervals of time legth, t, the discrete Fourier trasform (DFT) is the outcome that is implemeted as 1 t() t(=0) x(t)cosw t.3 Ope Access Joural Page 23

4 For the soil temperature data with a fiite sequece [x] of sample from a series x(t), the discrete Fourier trasform is defied by X(f) = 1 =5 x t cos2π t k k=1 4 Where k is k th frequecy sampled. Periodogram The complex magitude squared of X(f) is called the power or periodogram. This stregth of the periodic compoet is more ofte represeted by the periodogram defied as P(f)= isiw t) 2.5 t(5) 1 t() t(=1) x t (cosw t P f = 1 {x t } 2 {(cosw t t(=1) ) 2 + (siw t) 2 }.6 The real part of equatio 6 ca be implemeted i Microsoft EXCEL as ((H3/SQRT(5))*COS(6.284*5)*(1/5+2/5+3/5+4/5+5/5)+SIN(6.284*5*(1/5+2/5+3/5+4/5+5/5)))^2with the procedure of equatio 5. Equatios 5 ad 6 are calculated ad show i tables 2 to 4 followig. Table 2. Fourier trasform of Sad, Loam ad Clay s temperature Time (MIN) x(fs) x(fl) x(fc) Ope Access Joural Page 24

5 Table 3. Periodogram of Sad, Loam ad Clay s temperature Time (MIN) p(fs) p(fl) p(fc) The Fourier trasform ad Periodogram data from tables 2 ad 3 are geerally higher tha the raw temperature data. They all show similar treds as the data they origiated from. The Fourier trasform correlatio of sad ad loam is low while that betwee loam ad clay is the lowest The highest correlatios of Fourier trasform exist betwee clay ad sad while periodogram correlatios are respectively similar but slightly lower ( , ad ). The trasforms idicate that clay ad sad temperature have similar respose to exteral heat iteractio while loam ad clay do ot have ay similar respose to heat as the egative correlatio is too low for iterpretig opposite respose. This is coversely similar to the respose betwee sad ad loam with too low positive Fourier ad Periodogram trasforms. Fig.2 Fourier trasform time series curves for sad, loam ad clay Ope Access Joural Page 25

6 Fig.3. Periodogram time series curve for sad, loam ad clay The frequecy curves of sad Periodogram data show clear chages due to temperature variatio ad the highest periodogram data occur i loam from 120 th ad 125 th miutes correspodig to a time from to pm. Clay show early icrease i Periodogram ad frequecy i the 30 th miute or pm. The periodogram ad Fourier trasform are useful to check iterpretatio error i the pricipal data ad here they corroborate the earlier iterpretatio of soil, clay ad sad temperature data ad all the resultig curves. IV. Coclusio The 1 pole three throw switch temperature meter permitted the measuremet of temperature i the samples of sad, loam ad clay soils. Clay has the highest average temperature (32.472) followed by loam (30.624) ad sad (29.428). The correlatio of the 3 temperature data shows that clay ad sad vary similarly with Pearso correlatio coefficiet 0.66 i respose to similar atmospheric coditio while loam ad clay do ot correlate (- 0.19). Sad ad loam have poor correlatio of The average of the absolute deviatio idicated loam has highest temperature chages followed by sad ad clay. This result is further cofirmed by the Fourier trasform ad periodogram data that proved useful for ivestigatig the iterpretatios from origial data. Refereces [1] Abdullah, S., C.K.E. Nizwa ad M.Z. Nuawi, A study of fatigue data editig usig the Short Time [2] Fourier Trasform (STFT). Am. J. Applied Sci., 6: [3] ajas pdf. [4] Lough, J.M., variatios i a tropical-subtropical eviromet: Queeslad, [5] Australia, It. J. Climatol., 15: DOI: /joc [6] Tushar S. ad Keith A.C Time Series Aalysis of Soil Freeze ad Thaw Processes i Idiaa [7] Joural of Hydrometeorology Vol. 9 [8] Fraueberger C. ad Gerhard Eckel A. ANALYSING TIME SERIES DATA Proceedigs of the 13 th [9] Iteratioal Coferece o Auditory Display,Motr eal, Caada, Jue26-29, Ope Access Joural Page 26

Chapter 7 z-transform

Chapter 7 z-transform Chapter 7 -Trasform Itroductio Trasform Uilateral Trasform Properties Uilateral Trasform Iversio of Uilateral Trasform Determiig the Frequecy Respose from Poles ad Zeros Itroductio Role i Discrete-Time