An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Methods </td><td align="center"><span style="width: 22.2182ptpx;"><svg height="11.576pt" id="M116" style="vertical-align:-3.051021pt" version="1.1" viewbox="-0.0498162 -8.52498 22.2182 11.576" width="22.2182pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.384,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.285,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.172,3.001)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center"><span style="width: 22.2182ptpx;"><svg height="11.576pt" id="M117" style="vertical-align:-3.051021pt" version="1.1" viewbox="-0.0498162 -8.52498 22.2182 11.576" width="22.2182pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.384,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.285,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.172,3.001)"><path d="M414 144C384 79 371 75 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523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.384,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.285,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.172,3.001)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center"><span style="width: 22.2182ptpx;"><svg height="11.576pt" id="M119" style="vertical-align:-3.051021pt" version="1.1" viewbox="-0.0498162 -8.52498 22.2182 11.576" width="22.2182pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.384,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.285,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.172,3.001)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">EMD </td><td align="center">—</td><td align="center">9.2599</td><td align="center">3.8289</td><td align="center">3.8118</td></tr><tr><td align="left">ESMD</td><td align="center">—</td><td align="center">3.9242 </td><td align="center">—</td><td align="center">2.6267 </td></tr><tr><td align="left">BEMD</td><td align="center">3.4426</td><td align="center">7.3495</td><td align="center">2.0984</td><td align="center">1.5690</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The error norms of different methods for <svg height="12.6917pt" id="M115" style="vertical-align:-3.40337pt" version="1.1" viewbox="-0.0498162 -9.28833 21.63 12.6917" width="21.63pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M563 395C563 428 543 451 519 451C500 451 480 438 472 423C468 415 465 403 470 394C477 381 482 368 482 347C482 272 386 136 342 74H340C334 163 323 257 312 337C302 410 290 451 257 451C214 451 160 385 127 338L145 310C169 341 203 373 209 373C219 373 225 369 232 325C249 215 269 62 271 -15C220 -80 135 -165 18 -231L26 -257L142 -230C254 -105 279 -74 342 13C394 85 484 211 526 286C553 334 563 365 563 395Z" id="g50-122"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.633,0)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z" id="g50-41"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.287,0)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.798,0)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z" id="g50-42"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g></svg>.

Mathematical Problems in Engineering

tab2

Table 2

Table 2: An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals 