同济大学数字信号处理演示课件第3章节4离散傅里叶变换的性质.ppt

信号处理 四、离散傅里叶变换的性质 DFT正变换和反变换： 1、线性： 2、序列的圆周移位 调制特性： 时域序列的调制等效于频域的圆周移位 3、共轭对称性 其中： 定义： 圆周共轭对称序列满足： 圆周共轭反对称序列满足： 共轭对称性 实数序列的共轭对称性 纯虚序列的共轭对称性 例：设x1(n)和x2(n)都是N点的实数序列，试用一次N点DFT运算来计算它们各自的DFT: 4、复共轭序列 5、DFT形式下的Parseval定理 6、圆周卷积和 圆周卷积过程： 1）补零 2）周期延拓 3）翻褶，取主值序列 4）圆周移位 5）相乘相加 同样，利用对称性 7、有限长序列的线性卷积与圆周卷积 讨论圆周卷积和线性卷积之间的关系： 小结：线性卷积求解方法 时域直接求解 8、线性相关与圆周相关 相关函数的z变换： 圆周相关定理 …-3 -2 -1 … 1 0 0 … 1 1 1 0 1 2 3 4 5 5 4 3 2 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 6 7… 1 1… 1 0… 8 10 12 14 10 6 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 若 则 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 线性卷积： N点圆周卷积： N N Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 对x1(n)和x2(n)补零，使其长度均为N点； 对x2(n)周期延拓： 圆周卷积： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. N Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 补N-N1个零 x(n) N点DFT 补N-N2个零 h(n) N点DFT N点IDFT y(n) = x(n)*h(n) z变换法 DFT法 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 线性相关： 自相关函数： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 相关函数不满足交换率： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2