Fast Extraction for Skewed Source Signals Using Conditional Expectation

<div>The PDF of unimodal continuous skewed distribution, where <svg height="12.2089pt" id="M67" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 5.94546 12.2089" width="5.94546pt" 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="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path></g></svg> denotes the skewness and <span class="nowrap"><svg height="12.2089pt" id="M68" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 27.1322 12.2089" width="27.1322pt" 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="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path></g><g transform="matrix(.013,0,0,-0.013,9.457,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path></g><g transform="matrix(.013,0,0,-0.013,20.72,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg>,</span> <span class="nowrap"><svg height="12.2089pt" id="M69" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 27.1322 12.2089" width="27.1322pt" 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="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path></g><g transform="matrix(.013,0,0,-0.013,9.457,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z" id="g117-91"></path></g><g transform="matrix(.013,0,0,-0.013,20.72,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg>,</span> and <svg height="12.2089pt" id="M70" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 27.1322 12.2089" width="27.1322pt" 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="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path></g><g transform="matrix(.013,0,0,-0.013,9.457,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,20.72,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg> indicate the positively skewed distribution, the negatively skewed distribution, and the symmetric distribution, respectively.</div>

Journal of Sensors

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Figure 1

Figure 1: Fast Extraction for Skewed Source Signals Using Conditional Expectation 