周期卷積循環(huán)卷積與線性卷積

同 4.2,1周期卷積周期卷積與線性卷積的區(qū)別左d加）例|X2Qm)%o） = 丫￡ （加）乙（0-加）m=Q=1x0 + 1x0 + 1x0 + 1x1 + 0x24-0x1 x.(m)5%1）=工左1 （訃2（1-加）m=0=1x1 + 1x0 + 1x0 + 1x0 + 0x14-0x1了 (2尸工元(m)X2(2 - m)m=0=Ix2 + Ixl + IxO + IxO + 0x0 + Oxi =359(3)=左1 (加)焉(3-加)H1 =0=Ixl + Ix2 + Ixl + IxO + 0x0 + 0x0=4y(4)=4%5) = 34-2,1周期卷積一 I II【…⑴【【印???一一ZOZn[i -h，? [1 -,一ZoZ71岳 1UL1c7V — 1/! = 1TV — 1T HHTLNHIT J【【I一zo周期卷積DFT[x(n)] = X(k)0 < n < N - lDFT[yS)] = Y 伙)F(k) = X(k)Y(k)N-l/(zi) = IDFT[F()]二藝兀 O)y(( 〃 -加))顯譏比)m=0x(n) ? y(n) >)他)4.4,3循環(huán)卷積時(shí)域循環(huán)卷積過程4,4,3 循環(huán)卷積N=7I %2 3)4.4,3循環(huán)卷積3c2Q m)乂 2 ((O — W))N 尺 v (m)乂 2((1 —加))“ RNW)兀 2((2 — F))N Rn (m)乂 2 ((3 - w))~ Rz (w)y(0) = [AXm))e((0-m)f]/?7(m) = lxl + Ixl + 1x0 + 0x0 + 0x0 + 0xl + 0xl = w=06y(l) = [Ax(m)x((l-m)7]/3(m) = lxl + lxl + lxl + 0x0 + 0x0 + 0x0 + 0xl = 3 /n=06y(2) = [A(m)洶(2?m?/?(m) = lxl + lxl + lxl + 0xl + 0x0 + 0x0 + 0x0 //7=06y(3) = [A(m))2((3-m?/?

風(fēng)⑺）的長度為M+M-1所以只有當(dāng)/vny+M -咐，乳⑺）以N為周期進(jìn)行周期延拓才無混疊現(xiàn)象即當(dāng)循環(huán)卷積的長度Vny+M-1時(shí)，N點(diǎn)循環(huán)卷積 能代表線性卷積1("產(chǎn)x2Nny n”〃)(〃)Nny+y 10