Maximally Flat Waveforms with Finite Number of Harmonics in Class-<svg     style="vertical-align:-0.0pt;width:14.0625px;" id="M1" height="14.7" version="1.1" viewBox="0 0 14.0625 14.7" width="14.0625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,14.638)"><path id="x1D439" d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" /></g>

		
	
</svg> Power Amplifiers

<table>Pair of maximally flat waveforms <svg height="17.9625" id="M270" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 40.862499 17.9625" width="40.862499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,5.944,13.688)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g>
<g transform="matrix(.012,-0,0,-.012,18.05,5.525)"><path d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5
q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g>
<g transform="matrix(.012,-0,0,-.012,18.05,17.763)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,23.19,17.763)"><path d="M478 437v-26q-39 -5 -53 -17.5t-35 -57.5q-68 -149 -142 -347h-28q-47 128 -138 350q-17 43 -30.5 54.5t-53.5 17.5v26h205v-26q-40 -4 -46.5 -14.5t6.5 -42.5q41 -115 95 -247q43 101 89 238q12 36 3.5 48.5t-50.5 17.5v26h178z" id="x76"></path></g><g transform="matrix(.012,-0,0,-.012,28.616,17.763)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,33.673,17.763)"><path d="M524 0h-209v26q44 5 55 18t11 65v167q0 114 -91 114q-50 0 -109 -51v-235q0 -50 10 -61.5t55 -16.5v-26h-217v26q51 5 62 17t11 61v206q0 47 -9.5 58.5t-50.5 19.5v23q82 15 139 40v-79l67 47q47 30 83 30q60 0 94.5 -40t34.5 -112v-193q0 -50 10 -61.5t54 -16.5v-26z
" id="x6E"></path></g>
</svg>, <svg height="16.4125" id="M271" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 37.474998 16.4125" width="37.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.162,16.212)"><path d="M257 449q92 0 154 -65t62 -158q0 -112 -67 -175t-150 -63q-98 0 -158.5 66.5t-60.5 154.5q0 59 21 106.5t54.5 75.5t71 43t73.5 15zM244 416q-48 0 -81 -47t-33 -128q0 -96 38 -158t99 -62q51 0 82 43.5t31 139.5q0 91 -36 151.5t-100 60.5z" id="x6F"></path></g><g transform="matrix(.012,-0,0,-.012,18.338,16.212)"><path d="M517 51v-25q-101 -18 -155 -38v65l-61 -36q-50 -29 -78 -29q-68 0 -126.5 58t-58.5 155q0 103 77 175.5t180 72.5q36 0 67 -12v143q0 48 -11.5 58.5t-65.5 14.5v25q79 9 156 34v-597q0 -38 7.5 -48t36.5 -13zM362 85v275q-35 51 -103 51q-20 0 -40.5 -8.5t-42 -28
t-35 -57.5t-13.5 -89q0 -83 42 -130t96 -47q51 0 96 34z" id="x64"></path></g><g transform="matrix(.012,-0,0,-.012,24.62,16.212)"><path d="M517 51v-25q-101 -18 -155 -38v65l-61 -36q-50 -29 -78 -29q-68 0 -126.5 58t-58.5 155q0 103 77 175.5t180 72.5q36 0 67 -12v143q0 48 -11.5 58.5t-65.5 14.5v25q79 9 156 34v-597q0 -38 7.5 -48t36.5 -13zM362 85v275q-35 51 -103 51q-20 0 -40.5 -8.5t-42 -28
t-35 -57.5t-13.5 -89q0 -83 42 -130t96 -47q51 0 96 34z" id="x64"></path></g>
<g transform="matrix(.017,-0,0,-.017,31.525,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> for class-<svg height="11.175" id="M272" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.7 11.175" width="10.7" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
</svg> PA and inverse class-<svg height="11.175" id="M273" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.7 11.175" width="10.7" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
</svg> PA for <svg height="11.425" id="M274" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 42.5625 11.425" width="42.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M857 650l-6 -28q-44 -4 -61.5 -16.5t-29.5 -48.5q-11 -32 -37 -166l-78 -399h-29l-351 537h-4l-56 -276q-24 -120 -24 -164q0 -35 17.5 -46t75.5 -15l-6 -28h-245l7 28q41 2 62 14t31 44q10 30 41 171l53 245q8 44 6.5 60.5t-14.5 33.5q-10 15 -27 19.5t-64 6.5l6 28h153
l350 -516h5l48 257q25 131 25 171q0 34 -17.5 45t-77.5 15l7 28h240z" id="x1D441"></path></g><g transform="matrix(.017,-0,0,-.017,19.628,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,34.332,11.112)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
q53 0 90 28q4 31 4 66q0 51 -9.5 95.5t-39 80.5t-75.5 36z" id="x39"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Maximally Flat Waveforms with Finite Number of Harmonics in Class-<svg     style="vertical-align:-0.0pt;width:14.0625px;" id="M1" height="14.7" version="1.1" viewBox="0 0 14.0625 14.7" width="14.0625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,14.638)"><path id="x1D439" d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" /></g>

		
	
</svg> Power Amplifiers 

Mathematical Problems in Engineering

Maximally Flat Waveforms with Finite Number of Harmonics in Class- Power Amplifiers

Figure 7