Digital Architectures for UWB Beamforming Using 2D IIR Spatio-Temporal Frequency-Planar Filters

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="234263.fig.0022a" src="https://static.hindawi.com/articles/ijap/volume-2012/234263/figures/234263.fig.0022a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>  <svg height="11.175" id="M305" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 31.174999 11.175" width="31.174999" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,0,0,-.017,13.526,11.113)"><path d="M300 253l-14 -55h-229l14 55h229z" id="x2D"></path></g><g transform="matrix(.017,0,0,-.017,19.577,11.113)"><path d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5
q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" id="x1D44C"></path></g>
</svg> view of three 2D Gaussian pulse functions in frequency domain</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="234263.fig.0022b" src="https://static.hindawi.com/articles/ijap/volume-2012/234263/figures/234263.fig.0022b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="11.175" id="M306" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 31.174999 11.175" width="31.174999" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,0,0,-.017,13.526,11.113)"><path d="M300 253l-14 -55h-229l14 55h229z" id="x2D"></path></g><g transform="matrix(.017,0,0,-.017,19.577,11.113)"><path d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5
q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" id="x1D44C"></path></g>
</svg> view of frequency response of 2D 2nd-order filter for Gaussian pulse signals</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="234263.fig.0022c" src="https://static.hindawi.com/articles/ijap/volume-2012/234263/figures/234263.fig.0022c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b><svg height="11.175" id="M307" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 31.174999 11.175" width="31.174999" 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="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g><g transform="matrix(.017,0,0,-.017,13.526,11.113)"><path d="M300 253l-14 -55h-229l14 55h229z" id="x2D"></path></g><g transform="matrix(.017,0,0,-.017,19.577,11.113)"><path d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5
q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" id="x1D44C"></path></g>
</svg> view of frequency response of 2D 3rd-order filter for Gaussian pulse signals</td></tr></table></td></tr></table>

<table>Input and output Gaussian signals in frequency domain.</table>

International Journal of Antennas and Propagation

fig22

Figure 22

Figure 22: Digital Architectures for UWB Beamforming Using 2D IIR Spatio-Temporal Frequency-Planar Filters 