outlineofchapterseven

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Example 20 DTFT][)(][ nunx n jeX 1)(Example (cont.) ][nx21NkXkExample (cont.) kX][nx21NkmNnn  1 10 1  Nn1m o d, nNn 1n1nNn m o d,取模运算 如果 ， m为整数；则有： 此运算符表示 n被 N除，商为 m，余数为。 是 的解 ,或称作取余数 ,或说作 n对N取模值 , 或简称为取模值 ,n模 N。 取模运算示例 79m od,252792259,251nNnNn59m od,555949,4NnNnCircular Time Shift (圆周移位） 1,1,0  Nn 0 40 4周期延拓 5N],[nxnnCircular Time Shift ]m o d,2[ Nnx ]m o d,2[ Nnx 0 40 4nnTime reversal (时间反转） nn1,1,0  Nn 5N],[nx0 4]m o d,[ Nnx 0 4Linear Convolution (线性卷积） If both and are zero, for and ][nx ][nv 0n Nn 10][][][*][][Niinvixnvnxny is zero for and ][ny 0n 12  NnCircular Convolution (圆周卷积） Because Npoint DFT of will not incorporate the values for , it is necessary to define a convolution operation so that the convolved signal is zero outside the range ][*][][ nvnxny Nn 10]m o d,[][][][][NiNinvixnvnxny1,1,0  Nn ][*][][ nvnxny NExample of linear convolution and circular convolution 3],0[]3[]1[]2[]2[]1[]3[]0[2],3[]3[]0[]2[]1[]1[]2[]0[1],2[]3[]3[]2[]0[]1[]1[]0[0],1[]3[]2[]2[]3[]1[]0[]0[nvxvxvxvxnvxvxvxvxnvxvxvxvxnvxvxvxvx][][ nvnx 46],3[]3[5],2[]3[]3[]2[4],1[]3[]2[]2[]3[]1[3],0[]3[]1[]2[]2[]1[]3[]0[2],0[]2[]1[]1[]2[]0[1],0[]1[]1[]0[0],0[]0[nvxnvxvxnvxvxvxnvxvxvxvxnvxvxvxnvxvxnvx][*][ nvnxThe relationship between linear circular convolution and circular convolution Setting , an Lstep interval linear convolution and circular convolution give the same result, that is ][*][][ nvnxny 12  NL],[][ nvnx 1,1,0  Ln LProperties of the DFT Linearity Circular time shift Time reversal Multiplication by a plex exponential Circular convolution Multiplication in the time domain Parseval’s theorem P331 System analysis via the DTFT and DFT ],[nx],[nhThe (N+Q)point DFT of is The (N+Q)point DFT of is given by Nn 0Qn 0][nx 10)/(2][NnQNknjk enxX][nhQnQNknjk enhH0。