Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

<div>The power spectrum phase-noise <svg height="14.8173pt" id="M89" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 35.4887 14.8173" width="35.4887pt" 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="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.071,3.132)"><path d="M610 0V27L347 666L316 657L46 26V0H610ZM504 54H116L310 537L504 54Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.018,3.132)"><path d="M569 272C569 396 502 451 440 451C377 451 308 398 280 296C262 229 239 121 223 41C163 58 116 110 116 203C116 313 187 386 283 428L269 460C133 413 24 332 24 189C24 85 87 3 215 -10C187 -153 174 -212 164 -249L173 -257C208 -253 245 -243 260 -214L295 -5C427 6 569 118 569 272ZM493 270C493 139 401 42 302 37L357 327C369 388 390 405 412 405C438 405 493 369 493 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.959,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.457,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.809,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> of NAC1 and AR13300 obtained by integration of the resulted Wigner spectrum <span class="nowrap"><svg height="17.427pt" id="M90" style="vertical-align:-5.5289pt" version="1.1" viewbox="-0.0498162 -11.8981 51.7083 17.427" width="51.7083pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="12.7095" x="0" y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.71,3.132)"><path d="M610 0V27L347 666L316 657L46 26V0H610ZM504 54H116L310 537L504 54Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.657,3.132)"><path d="M569 272C569 396 502 451 440 451C377 451 308 398 280 296C262 229 239 121 223 41C163 58 116 110 116 203C116 313 187 386 283 428L269 460C133 413 24 332 24 189C24 85 87 3 215 -10C187 -153 174 -212 164 -249L173 -257C208 -253 245 -243 260 -214L295 -5C427 6 569 118 569 272ZM493 270C493 139 401 42 302 37L357 327C369 388 390 405 412 405C438 405 493 369 493 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.598,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.096,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.529,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.672,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.024,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

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Figure 3

Figure 3: Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution 