Transform analog voltage signals with 'Morlet' wavelets: complex wavelet kernels with \(\pi/2\) phase differences.
Arguments
- freqs
frequency in which
datawill be projected on- srate
sample rate, number of time points per second
- wave_num
desired number of cycles in wavelet kernels to balance the precision in time and amplitude (control the smoothness); positive integers are strongly suggested
- data
numerical vector such as analog voltage signals
- precision
the precision of computation; choices are
'float'(default) and'double'.- trend
choices are
'constant': center the signal at zero;'linear': remove the linear trend;'none'do nothing- signature
signature to calculate kernel path to save, internally used
- ...
further passed to
detrend;- frequency_range
frequency range to calculate, default is 2 to 200
- cycle_range
number of cycles corresponding to
frequency_range. For default frequency range (2 - 200), the defaultcycle_rangeis 3 to 20. That is, 3 wavelet kernel cycles at 2 Hertz, and 20 cycles at 200 Hertz.
Value
wavelet_kernels returns wavelet kernels to be
used for wavelet function; morlet_wavelet returns a file-based array
if precision is 'float', or a list of real and imaginary
arrays if precision is 'double'
Examples
# \donttest{
# generate sine waves
time <- seq(0, 3, by = 0.01)
x <- sin(time * 20*pi) + exp(-time^2) * cos(time * 10*pi)
plot(time, x, type = 'l')
# freq from 1 - 15 Hz; wavelet using float precision
freq <- seq(1, 15, 0.2)
coef <- morlet_wavelet(x, freq, 100, c(2,3))
# to get coefficients in complex number from 1-10 time points
coef[1:10, ]
#> [,1] [,2] [,3]
#> [1,] 0.079415046+0.1186043i 0.09068563+0.1566062i 0.081491686+0.2158995i
#> [2,] 0.070035875+0.1221303i 0.07500284+0.1634681i 0.053901780+0.2204804i
#> [3,] 0.060283009+0.1248344i 0.05994895+0.1687918i 0.028882088+0.2217750i
#> [4,] 0.050308734+0.1270776i 0.04561965+0.1722808i 0.006465297+0.2200116i
#> [5,] 0.040320020+0.1290842i 0.03170361+0.1737074i -0.014214927+0.2154187i
#> [6,] 0.030511839+0.1308505i 0.01765361+0.1729923i -0.034401946+0.2081803i
#> [7,] 0.021003243+0.1321430i 0.00295374+0.1702363i -0.055064443+0.1984321i
#> [8,] 0.011802451+0.1325862i -0.01261945+0.1656932i -0.076370113+0.1862965i
#> [9,] 0.002815931+0.1318068i -0.02884216+0.1596938i -0.097490542+0.1719405i
#> [10,] -0.006100574+0.1295805i -0.04505559+0.1525505i -0.116815194+0.1556303i
#> [,4] [,5] [,6]
#> [1,] 0.09494893+0.2750027i 0.07831753+0.3720973i 0.12207478+0.4939324i
#> [2,] 0.05750818+0.2820133i 0.02066774+0.3739292i 0.02797596+0.5025347i
#> [3,] 0.02137382+0.2835686i -0.03839022+0.3655892i -0.06338145+0.4926330i
#> [4,] -0.01272639+0.2795582i -0.09631336+0.3473318i -0.14782295+0.4650585i
#> [5,] -0.04462781+0.2700548i -0.14979412+0.3199039i -0.22251487+0.4214858i
#> [6,] -0.07452112+0.2553693i -0.19543830+0.2845643i -0.28576091+0.3642318i
#> [7,] -0.10262396+0.2360650i -0.23056759+0.2430175i -0.33649319+0.2960882i
#> [8,] -0.12886351+0.2129196i -0.25385961+0.1972672i -0.37372234+0.2202145i
#> [9,] -0.15269735+0.1868443i -0.26559499+0.1494193i -0.39621446+0.1400774i
#> [10,] -0.17314655+0.1587818i -0.26742333+0.1014823i -0.40256131+0.0593922i
#> [,7] [,8] [,9]
#> [1,] 0.123074822+0.6599417i 0.29512212+0.80541188i 0.481908888+0.9416207i
#> [2,] -0.009155749+0.6693053i 0.11448307+0.86292142i 0.256427228+1.0539577i
#> [3,] -0.145165384+0.6481661i -0.07666951+0.87634575i 0.003848762+1.1080878i
#> [4,] -0.276914090+0.5966316i -0.26706496+0.84258908i -0.259800225+1.0963969i
#> [5,] -0.395405680+0.5168822i -0.44542515+0.76171952i -0.516965687+1.0158346i
#> [6,] -0.491899669+0.4131744i -0.60101658+0.63718253i -0.749713719+0.8684299i
#> [7,] -0.559261739+0.2916004i -0.72409075+0.47574779i -0.940880179+0.6614633i
#> [8,] -0.593079686+0.1596200i -0.80632752+0.28717023i -1.075251460+0.4072578i
#> [9,] -0.592241049+0.0254319i -0.84138227+0.08357185i -1.140798926+0.1225601i
#> [10,] -0.558839977-0.1027219i -0.82555842-0.12141941i -1.129926801-0.1725127i
#> [,10] [,11] [,12]
#> [1,] 0.613101900+1.1134408i 0.97635090+1.0530784i 1.2249333+1.01607740i
#> [2,] 0.334765136+1.2709807i 0.70727330+1.3227400i 0.9577800+1.37094104i
#> [3,] 0.009571603+1.3525786i 0.35680702+1.5176992i 0.5832236+1.65095401i
#> [4,] -0.339798450+1.3449109i -0.05261636+1.6127059i 0.1244914+1.82088077i
#> [5,] -0.685791612+1.2415154i -0.48996174+1.5897704i -0.3844635+1.85322142i
#> [6,] -0.998754323+1.0440711i -0.91824609+1.4408896i -0.9013491+1.73211050i
#> [7,] -1.250209093+0.7628828i -1.29823387+1.1698096i -1.3790479+1.45617616i
#> [8,] -1.416096091+0.4164638i -1.59268785+0.7925254i -1.7700713+1.03991318i
#> [9,] -1.479472041+0.0302225i -1.77058423+0.3363909i -2.0316057+0.51328421i
#> [10,] -1.432301402-0.3656267i -1.81071901-0.1620989i -2.1306221-0.08051831i
#> [,13] [,14] [,15]
#> [1,] 1.35191715+1.1092380i 1.6438580+0.7382753i 1.7838074+0.8809177i
#> [2,] 1.05171585+1.5203370i 1.4613980+1.2524108i 1.5476340+1.4624588i
#> [3,] 0.62185955+1.8432338i 1.1074976+1.7156254i 1.1065426+1.9686555i
#> [4,] 0.09072659+2.0339305i 0.5994499+2.0676584i 0.4901076+2.3258750i
#> [5,] -0.49923444+2.0586474i -0.0239758+2.2552743i -0.2442087+2.4738417i
#> [6,] -1.09487903+1.8989538i -0.7057343+2.2403517i -1.0182161+2.3757749i
#> [7,] -1.63736320+1.5553236i -1.3766049+2.0062461i -1.7437997+2.0248806i
#> [8,] -2.06835794+1.0485209i -1.9633654+1.5613497i -2.3352664+1.4461050i
#> [9,] -2.33684039+0.4185183i -2.3978601+0.9392623i -2.7209735+0.6930609i
#> [10,] -2.40563107-0.2790205i -2.6256561+0.1955671i -2.8523569-0.1590180i
#> [,16] [,17] [,18]
#> [1,] 2.0009513+0.4329820i 2.1021199+0.2082681i 2.1996233-0.01233783i
#> [2,] 1.9174918+1.1055355i 2.0970860+0.9460760i 2.2720675+0.79616457i
#> [3,] 1.5851542+1.7526965i 1.8063605+1.6844114i 2.0168366+1.63061273i
#> [4,] 1.0173950+2.2799182i 1.2368711+2.3078260i 1.4356301+2.35038424i
#> [5,] 0.2667023+2.6022451i 0.4453299+2.7107744i 0.5929527+2.82652712i
#> [6,] -0.5827126+2.6594913i -0.4710104+2.8182421i -0.3962666+2.96917272i
#> [7,] -1.4283910+2.4268260i -1.3921632+2.5997078i -1.3905101+2.74522424i
#> [8,] -2.1661053+1.9187409i -2.1971214+2.0734994i -2.2502131+2.18229890i
#> [9,] -2.7056894+1.1860645i -2.7841260+1.3013198i -2.8633745+1.35905087i
#> [10,] -2.9831216+0.3073068i -3.0850532+0.3752776i -3.1621120+0.38584641i
#> [,19] [,20] [,21]
#> [1,] 2.33506536+0.69246244i 2.4501245+0.06454356i 2.4651997-0.2008947i
#> [2,] 2.13033867+1.47070014i 2.4586723+0.90580237i 2.5679915+0.6772068i
#> [3,] 1.65624738+2.17644382i 2.1613877+1.74592674i 2.3369265+1.5861278i
#> [4,] 0.94257206+2.71395230i 1.5647689+2.47089338i 1.7692572+2.3947690i
#> [5,] 0.05369809+3.00124192i 0.7201751+2.97369766i 0.9166396+2.9778409i
#> [6,] -0.91813743+2.98262143i -0.2820088+3.17148042i -0.1218577+3.2377720i
#> [7,] -1.86402524+2.63782454i -1.3249383+3.01895523i -1.2157197+3.1214414i
#> [8,] -2.67228317+1.98626935i -2.2821121+2.51580286i -2.2242208+2.6285341i
#> [9,] -3.24295902+1.08581531i -3.0352345+1.70700836i -3.0182986+1.8104304i
#> [10,] -3.50081182+0.02629376i -3.4900486+0.67652702i -3.4987714+0.7607290i
#> [,22] [,23] [,24]
#> [1,] 2.471909523-0.4527444i 2.48310828-0.6981176i 2.5095661-0.94233018i
#> [2,] 2.666216373+0.4641936i 2.76812243+0.2656741i 2.8854177+0.08128414i
#> [3,] 2.495334387+1.4436839i 2.65026212+1.3234967i 2.8117075+1.22942650i
#> [4,] 1.947960377+2.3341198i 2.11079621+2.2983096i 2.2642350+2.29364872i
#> [5,] 1.078675508+2.9894106i 1.21106923+3.0197523i 1.3163128+3.07550859i
#> [6,] -0.001040098+3.2969441i 0.08025372+3.3597388i 0.1214682+3.43147302i
#> [7,] -1.143531799+3.1981289i -1.11204588+3.2573230i -1.1230568+3.30240774i
#> [8,] -2.192038298+2.6972275i -2.19056463+2.7272103i -2.2209857+2.72054148i
#> [9,] -3.007503033+1.8574508i -3.00727081+1.8511975i -3.0171371+1.79388797i
#> [10,] -3.489273787+0.7865683i -3.46451735+0.7565802i -3.4226763+0.67477643i
#> [,25] [,26] [,27]
#> [1,] 2.5597193-1.18711960i 2.63878536-1.4304572i 3.0148675-1.1060885i
#> [2,] 3.0256851-0.08753117i 3.19160414-0.2379207i 3.3878024+0.2944070i
#> [3,] 2.9846883+1.16450822i 3.16900539+1.1302563i 3.0822475+1.7566789i
#> [4,] 2.4102669+2.32293010i 2.54688358+2.3848839i 2.1465552+2.9471982i
#> [5,] 1.3942275+3.15792918i 1.44301248+3.2628736i 0.7859895+3.6041443i
#> [6,] 0.1219929+3.51163125i 0.08234455+3.5946085i -0.6990706+3.6061065i
#> [7,] -1.1757939+3.33207870i -1.26614952+3.3417084i -1.9999197+2.9959815i
#> [8,] -2.2801137+2.67692685i -2.36046910+2.5953102i -2.8828051+1.9547400i
#> [9,] -3.0318129+1.68811870i -3.04227376+1.5381390i -3.2425628+0.7364987i
#> [10,] -3.3580842+0.54776108i -3.26310921+0.3851931i -3.1116619-0.4113465i
#> [,28] [,29] [,30]
#> [1,] 3.1947560-1.2840021i 2.7357285-2.1535256i 3.3279779-1.69316530i
#> [2,] 3.6036561+0.2503167i 3.6075091-0.7159399i 3.9045222+0.03994172i
#> [3,] 3.2497482+1.8335520i 3.6868143+1.0097815i 3.5580297+1.86702156i
#> [4,] 2.2070611+3.0870326i 2.9319055+2.5869319i 2.3700070+3.30611634i
#> [5,] 0.7279506+3.7271509i 1.5323865+3.6237602i 0.6599216+3.99466658i
#> [6,] -0.8363473+3.6419389i -0.1533425+3.8883989i -1.1195199+3.79596090i
#> [7,] -2.1415222+2.9114096i -1.7115843+3.3696992i -2.5263419+2.82949495i
#> [8,] -2.9469476+1.7675955i -2.7988815+2.2656636i -3.2632554+1.41731334i
#> [9,] -3.1723278+0.5106685i -3.2375839+0.9062406i -3.2568700-0.03253290i
#> [10,] -2.8981290-0.5882277i -3.0509958-0.3605143i -2.6575718-1.16304982i
#> [,31] [,32] [,33]
#> [1,] 3.5382948-1.81696606i 2.9342194-2.7534552i 3.6709437-2.11524653i
#> [2,] 4.1170473+0.05529752i 4.0583143-1.0410227i 4.3653116-0.06902755i
#> [3,] 3.6894689+1.98786068i 4.1655478+1.0338389i 3.9176700+2.06103587i
#> [4,] 2.3747342+3.45822501i 3.2175047+2.8887649i 2.4613724+3.66616106i
#> [5,] 0.5473364+4.09270239i 1.4931444+4.0163007i 0.4339745+4.31117916i
#> [6,] -1.2882986+3.77727675i -0.5071648+4.1427193i -1.5715019+3.86947823i
#> [7,] -2.6614833+2.67991257i -2.2284436+3.3058789i -3.0036790+2.55163646i
#> [8,] -3.2807407+1.17913353i -3.2405860+1.8271718i -3.5297272+0.81978035i
#> [9,] -3.1119680-0.27367055i -3.3686996+0.1897533i -3.1312408-0.78021222i
#> [10,] -2.3648248-1.30815506i -2.7306361-1.1321286i -2.0876002-1.80792630i
#> [,34] [,35] [,36]
#> [1,] 2.9656105-3.0569928i 3.7645516-2.3299246i 2.9743092-3.2672565i
#> [2,] 4.2366405-1.2268951i 4.5376792-0.1521685i 4.3441257-1.3547779i
#> [3,] 4.3819547+1.0208271i 4.0662217+2.1213930i 4.5107627+1.0105745i
#> [4,] 3.3531106+3.0267251i 2.4977989+3.8164403i 3.4213076+3.1136911i
#> [5,] 1.4668674+4.2151313i 0.3209561+4.4532270i 1.4221781+4.3312898i
#> [6,] -0.7044845+4.2794075i -1.8023022+3.8995938i -0.8611342+4.3361416i
#> [7,] -2.5267656+3.2736807i -3.2598472+2.4036007i -2.7376585+3.1983204i
#> [8,] -3.5138578+1.5806044i -3.6906185+0.4957319i -3.6832633+1.3490076i
#> [9,] -3.4809539-0.2317493i -3.0936787-1.2034105i -3.5104220-0.5793013i
#> [10,] -2.5886061-1.6117542i -1.8081353-2.2006013i -2.4163253-1.9785502i
#> [,37] [,38] [,39]
#> [1,] 3.7988098-2.4735126i 3.7240367-2.5138834i 2.848142-3.3984356i
#> [2,] 4.6218805-0.2154855i 4.5936208-0.2585213i 4.309911-1.4724206i
#> [3,] 4.1349535+2.1437199i 4.1358562+2.1295335i 4.524998+0.9565532i
#> [4,] 2.4966784+3.8864796i 2.4933510+3.9134400i 3.419847+3.1316411i
#> [5,] 0.2307914+4.5049353i 0.1888932+4.5594788i 1.349867+4.3830142i
#> [6,] -1.9543053+3.8661289i -2.0535977+3.9126203i -1.022831+4.3513274i
#> [7,] -3.4069319+2.2469442i -3.5555210+2.2411225i -2.956120+3.1039290i
#> [8,] -3.7500093+0.2272735i -3.9115138+0.1348012i -3.880315+1.1032375i
#> [9,] -2.9989638-1.5200574i -3.1188779-1.7068865i -3.587958-0.9616780i
#> [10,] -1.5386397-2.4671452i -1.5630968-2.7213631i -2.293884-2.4206567i
#> [,40] [,41] [,42]
#> [1,] 3.6828005-2.56395578i 2.761570-3.4309258i 2.697829-3.3602076i
#> [2,] 4.5634751-0.29743251i 4.235487-1.5215883i 4.158175-1.4791826i
#> [3,] 4.1011467+2.09802079i 4.462800+0.8944273i 4.382802+0.9116253i
#> [4,] 2.4456556+3.87300086i 3.369932+3.0551012i 3.292628+3.0538902i
#> [5,] 0.1338267+4.48870468i 1.315826+4.2870903i 1.240975+4.2731209i
#> [6,] -2.0949392+3.79604626i -1.031700+4.2319622i -1.107057+4.2058239i
#> [7,] -3.5519338+2.07986283i -2.925521+2.9637482i -3.002280+2.9199209i
#> [8,] -3.8329611-0.04763826i -3.795239+0.9563227i -3.867757+0.8859368i
#> [9,] -2.9502380-1.86696887i -3.439861-1.0886738i -3.494274-1.1919868i
#> [10,] -1.3152252-2.80677700i -2.088403-2.4929421i -2.105344-2.6265590i
#> [,43] [,44] [,45]
#> [1,] 3.48999786-2.5334368i 2.544442-3.3447075i 2.503186-3.2291193i
#> [2,] 4.37326050-0.3376532i 3.999378-1.5331479i 3.914323-1.4455364i
#> [3,] 3.93967557+1.9972719i 4.253737+0.7902871i 4.142331+0.8351622i
#> [4,] 2.32985616+3.7286539i 3.223722+2.8831189i 3.107003+2.8815253i
#> [5,] 0.07079511+4.3183055i 1.249994+4.0822334i 1.146548+4.0408335i
#> [6,] -2.10460424+3.6135612i -1.018983+4.0280361i -1.097538+3.9598446i
#> [7,] -3.50898242+1.8954576i -2.849549+2.7845623i -2.899753+2.7032421i
#> [8,] -3.73594475-0.2237827i -3.675160+0.8130565i -3.699316+0.7282429i
#> [9,] -2.79644060-2.0193882i -3.290509-1.1934229i -3.292327-1.2775848i
#> [10,] -1.10634136-2.9121420i -1.917747-2.5576987i -1.898682-2.6404538i
#> [,46] [,47] [,48]
#> [1,] 3.22675991-2.4543104i 3.16936731-2.3264494i 2.2516725-3.0681870i
#> [2,] 4.09577799-0.3887969i 3.98687220-0.2996546i 3.6036687-1.4275271i
#> [3,] 3.71405125+1.8257535i 3.57841039+1.8577497i 3.8546040+0.6978704i
#> [4,] 2.20676637+3.4778445i 2.07414913+3.4499581i 2.9188864+2.6214142i
#> [5,] 0.07133675+4.0468121i -0.03262736+3.9715414i 1.1053289+3.7252259i
#> [6,] -1.99250209+3.3786633i -2.05344319+3.2779968i -0.9882566+3.6687562i
#> [7,] -3.32244253+1.7365087i -3.33950329+1.6333746i -2.6785631+2.5032365i
#> [8,] -3.52153063-0.2932601i -3.50422382-0.3824753i -3.4306126+0.6528968i
#> [9,] -2.59439421-2.0090032i -2.55622244-2.0778134i -3.0427537-1.2333857i
#> [10,] -0.94098085-2.8445752i -0.89316702-2.8949780i -1.7164109-2.5121295i
#> [,49] [,50] [,51]
#> [1,] 2.2379272-2.9190328i 2.85429287-2.2382662i 2.81143618-2.0874882i
#> [2,] 3.5200524-1.3000990i 3.65874243-0.3844451i 3.54727221-0.2714689i
#> [3,] 3.7209268+0.7718943i 3.33056664+1.6158565i 3.17914605+1.6616915i
#> [4,] 2.7682154+2.6257722i 1.97751117+3.1148076i 1.82576144+3.0843074i
#> [5,] 0.9734974+3.6637704i 0.04677613+3.6347287i -0.06792398+3.5415542i
#> [6,] -1.0741578+3.5630214i -1.82675016+3.0279505i -1.88161290+2.9026690i
#> [7,] -2.7079351+2.3836157i -3.03541231+1.5262964i -3.02829432+1.4043519i
#> [8,] -3.4102044+0.5474176i -3.20728374-0.3378769i -3.15437937-0.4286765i
#> [9,] -2.9910266-1.3077666i -2.33697987-1.9172329i -2.26425886-1.9646611i
#> [10,] -1.6546948-2.5526402i -0.78812933-2.6809320i -0.72075182-2.6895740i
#> [,52] [,53] [,54]
#> [1,] 1.9383160-2.7660811i 1.9426708-2.6107895i 2.4555550-2.0470860i
#> [2,] 3.1706400-1.3242352i 3.0965977-1.1839021i 3.2094612-0.4271744i
#> [3,] 3.4232113+0.5666487i 3.2892559+0.6534200i 2.9624896+1.3453621i
#> [4,] 2.6118269+2.2916737i 2.4544497+2.3021188i 1.7992355+2.6956284i
#> [5,] 1.0057716+3.2945428i 0.8675359+3.2297530i 0.1048080+3.1933899i
#> [6,] -0.8651598+3.2624640i -0.9504839+3.1464174i -1.5640018+2.6927052i
#> [7,] -2.3880255+2.2297387i -2.4064577+2.0993273i -2.6623290+1.3816534i
#> [8,] -3.0735552+0.5677451i -3.0333545+0.4587325i -2.8430495-0.2765235i
#> [9,] -2.7266438-1.1404415i -2.6523416-1.2052492i -2.0829308-1.7013897i
#> [10,] -1.5186124-2.3052187i -1.4402789-2.3216074i -0.6962802-2.4043565i
#> [,55] [,56] [,57]
#> [1,] 2.426996231-1.8957025i 1.5924708-2.5023348i 1.6099882-2.3571868i
#> [2,] 3.108124733-0.3080825i 2.7274668-1.2787368i 2.6684124-1.1412779i
#> [3,] 2.815939426+1.3985411i 3.0128570+0.3703721i 2.8922162+0.4605267i
#> [4,] 1.649070740+2.6699150i 2.3595781+1.9072059i 2.2122014+1.9245251i
#> [5,] -0.008056067+3.1012499i 0.9872150+2.8387077i 0.8558960+2.7817366i
#> [6,] -1.613890171+2.5663905i -0.6529875+2.8738313i -0.7334973+2.7651930i
#> [7,] -2.646287203+1.2600824i -2.0233135+2.0175419i -2.0381184+1.8939205i
#> [8,] -2.778956175-0.3617870i -2.6769223+0.5753644i -2.6337724+0.4732825i
#> [9,] -2.000647068-1.7356418i -2.4162481-0.9440653i -2.3400021-1.0003659i
#> [10,] -0.626008987-2.3924577i -1.3714346-2.0078161i -1.2936904-2.0129032i
#> [,58] [,59] [,60]
#> [1,] 1.6291827-2.2108769i 2.0223403-1.7778202i 2.00940514-1.6374005i
#> [2,] 2.6094227-1.0017039i 2.6900053-0.4249961i 2.60582161-0.3082213i
#> [3,] 2.7694368+0.5524032i 2.5141609+1.0708392i 2.38223267+1.1286596i
#> [4,] 2.0610187+1.9416360i 1.5615888+2.2280574i 1.42177904+2.2107973i
#> [5,] 0.7207387+2.7217536i 0.1451238+2.6827528i 0.03840881+2.6000226i
#> [6,] -0.8158651+2.6510684i -1.2755371+2.2973690i -1.32243276+2.1793768i
#> [7,] -2.0512769+1.7637738i -2.2354569+1.2098864i -2.21786451+1.0946852i
#> [8,] -2.5850189+0.3656787i -2.4219310-0.1994630i -2.35607314-0.2794580i
#> [9,] -2.2550507-1.0591658i -1.7948811-1.4335548i -1.71031666-1.4614041i
#> [10,] -1.2061895-2.0161519i -0.6114144-2.0609083i -0.54006964-2.0394278i
#> [,61] [,62] [,63]
#> [1,] 1.99615645-1.4968544i 1.2678558-2.0402925i 1.2967606-1.9145942i
#> [2,] 2.52061081-0.1913637i 2.1991014-1.0498766i 2.1580286-0.9234648i
#> [3,] 2.24848437+1.1857940i 2.4355311+0.2844589i 2.3338258+0.3730831i
#> [4,] 1.27999616+2.1914680i 1.9147528+1.5273854i 1.7831541+1.5506623i
#> [5,] -0.06936412+2.5138381i 0.8132340+2.2901611i 0.6925207+2.2435155i
#> [6,] -1.36851454+2.0571926i -0.5167341+2.3371105i -0.5922088+2.2397795i
#> [7,] -2.19708753+0.9756001i -1.6453965+1.6567386i -1.6593624+1.5423422i
#> [8,] -2.28480148-0.3618382i -2.1991041+0.4817950i -2.1564450+0.3855393i
#> [9,] -1.61900711-1.4891160i -1.9989907-0.7748259i -1.9219477-0.8273582i
#> [10,] -0.46219048-2.0148447i -1.1402282-1.6666828i -1.0599476-1.6670697i
#> [,64] [,65] [,66]
#> [1,] 1.3243761-1.7895404i 1.5979588-1.4822203i 1.59880424-1.3624456i
#> [2,] 2.1158495-0.7980021i 2.1613417-0.3987669i 2.09815860-0.2932374i
#> [3,] 2.2310457+0.4603490i 2.0468531+0.8056440i 1.93754470+0.8631279i
#> [4,] 1.6506625+1.5719366i 1.3091894+1.7543641i 1.18867564+1.7466685i
#> [5,] 0.5715532+2.1942551i 0.1826939+2.1592472i 0.08791818+2.0927930i
#> [6,] -0.6668748+2.1395898i -0.9780500+1.8916150i -1.02215946+1.7913973i
#> [7,] -1.6712238+1.4253479i -1.7916812+1.0368446i -1.77874470+0.9357197i
#> [8,] -2.1103542+0.2875044i -1.9826471-0.1094808i -1.92472172-0.1816265i
#> [9,] -1.8404368-0.8802667i -1.4976486-1.1376160i -1.42028952-1.1629936i
#> [10,] -0.9748936-1.6660146i -0.5367500-1.6811993i -0.46989784-1.6597471i
#> [,67] [,68] [,69]
#> [1,] 1.597956538-1.2439231i 0.9398270-1.7105370i 0.9755515-1.6103427i
#> [2,] 2.033836126-0.1894441i 1.7325824-0.9394110i 1.7097660-0.8318992i
#> [3,] 1.827662945+0.9184634i 1.9711685+0.1225555i 1.8938630+0.2032667i
#> [4,] 1.068315148+1.7365732i 1.6082021+1.1354973i 1.5012285+1.1633288i
#> [5,] -0.005889252+2.0240428i 0.7654062+1.7993118i 0.6633980+1.7682818i
#> [6,] -1.064555883+1.6893046i -0.3020929+1.9090847i -0.3695053+1.8333771i
#> [7,] -1.763421178+0.8333433i -1.2527838+1.4199094i -1.2700042+1.3260312i
#> [8,] -1.863810062-0.2541806i -1.7625654+0.4932239i -1.7308873+0.4107738i
#> [9,] -1.339606285-1.1877015i -1.6571842-0.5404754i -1.5934587-0.5878278i
#> [10,] -0.399889022-1.6364752i -0.9931343-1.3063893i -0.9238878-1.3087059i
#> [,70] [,71]
#> [1,] 1.0089647-1.5111580i 1.0396967-1.4129652i
#> [2,] 1.6853703-0.7260948i 1.6590753-0.6222578i
#> [3,] 1.8157876+0.2818265i 1.7368206+0.3578002i
#> [4,] 1.3943741+1.1888105i 1.2877952+1.2115057i
#> [5,] 0.5623614+1.7351103i 0.4626952+1.6995418i
#> [6,] -0.4353651+1.7560649i -0.4991703+1.6771836i
#> [7,] -1.2853483+1.2311652i -1.2983905+1.1356310i
#> [8,] -1.6970941+0.3279551i -1.6609907+0.2452661i
#> [9,] -1.5274355-0.6348679i -1.4592371-0.6810863i
#> [10,] -0.8523360-1.3099889i -0.7789017-1.3098996i
# power
power <- Mod(coef[])^2
# Power peaks at 5Hz and 10Hz at early stages
# After 1.0 second, 5Hz component fade away
image(power, x = time, y = freq, ylab = "frequency")
# wavelet using double precision
coef2 <- morlet_wavelet(x, freq, 100, c(2,3), precision = "double")
power2 <- (coef2$real[])^2 + (coef2$imag[])^2
image(power2, x = time, y = freq, ylab = "frequency")
# The maximum relative change of power with different precisions
max(abs(power/power2 - 1))
#> [1] 6.914835e-05
# display kernels
freq <- seq(1, 15, 1)
kern <- wavelet_kernels(freq, 100, c(2,3))
print(kern)
#> Discrete wavelet kernels
#> number of kernels/frequencies: 15
#> frequency range: 1.00 Hz - 15.00 Hz
#> number of cycles: 2.00 - 3.00
plot(kern)
# }