Generate two signals of different lengths. Compare their circular convolution and their linear convolution. Use the default value forn。

a = [1 2 -1 1]; b = [1 1 2 1 2 2 1 1]; c = cconv(a,b);％圆形卷积cref = conv（a，b）;％线性卷积dif = norm(c-cref)

dif = 9.7422e-16

The resulting norm is virtually zero, which shows that the two convolutions produce the same result to machine precision.

Generate two vectors and compute their modulo-4 circular convolution.

a = [2 1 2 1]; b = [1 2 3 4]; c = cconv(a,b,4)

C =1×414 16 14 16

Generate two complex sequences. UseCCONV计算它们的圆形互相关。翻转并结合第二个操作数以符合互相关的定义。指定输出向量长度为​​7。

a = [1 2 2 1]+1i; b = [1 3 4 1]-2*1i; c = cconv(a,conj(fliplr(b)),7);

将结果与使用的互相关进行比较xcorr。

cref = xcorr(a,b); dif = norm(c-cref)

DIF = 3.3565E-15

生成两个信号：一个五样本三角波形和带有响应的一阶Fir滤波器 $$H(z)=1-z^{-1}$$。

x1 = conv（[1 1 1]，[1 1 1]）

x1 =1×51 2 3 2 1

x2 = [-1 1]

x2 =1×2-1 1

用默认输出长度计算其圆形卷积。结果等效于两个信号的线性卷积。

ccnv = cconv(x1,x2)

ccnv =1×6-1.0000 -1.0000 -1.0000 1.0000 1.0000 1.0000

lcnv = conv(x1,x2)

lcnv =1×6-1 -1 -1 1 1 1

The modulo-2 circular convolution is equivalent to splitting the linear convolution into two-element arrays and summing the arrays.

ccn2 =CCONV(x1,x2,2)

ccn2 =1×2-1 1

nl = numel(lcnv); mod2 = sum(reshape(lcnv,2,nl/2)')

mod2 =1×2-1 1

Compute the modulo-3 circular convolution and compare it to the aliased linear convolution.

ccn3 = cconv（x1，x2,3）

ccn3 =1×30 0 0

mod3 = sum（reshape（lcnv，3，nl/3）'）

mod3 =1×30 0 0

If the output length is smaller than the convolution length and does not divide it exactly, pad the convolution with zeros before adding.

C =5; z = zeros(c*ceil(nl/c),1); z(1:nl) = lcnv; ccnc = cconv(x1,x2,c)

ccnc =1×50.0000 -1.0000 -1.0000 1.0000 1.0000

modc = sum（reshape（z，c，numel（z）/c）'）

modc =1×50 -1 -1 1 1

如果输出长度等于或大于卷积长度，请填充卷积，不要添加。

d = 13; z = zeros(d*ceil(nl/d),1); z(1:nl) = lcnv; ccnd = cconv(x1,x2,d)

ccnd =1×13-1.0000 -1.0000 -1.0000 1.0000 1.0000 1.00000.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000

modd =z'

modd =1×13-1 -1 -1 1 1 1 0 0 0 0 0 0 0

The following example requires Parallel Computing Toolbox™ software. Refer toGPU Support by Release(Parallel Computing Toolbox)看看GPUs are supported.

Create two signals consisting of a 1 kHz sine wave in additive white Gaussian noise. The sample rate is 10 kHz

FS = 1E4;t = 0：1/fs：10-（1/fs）;x = cos（2*pi*1e3*t）+randn（size（t））;y = sin（2*pi*1e3*t）+randn（size（t））;

Putx和yon the GPU usinggpuArray。Obtain the circular convolution using the GPU.

x = gpuarray（x）;y = gpuarray（y）;circ = cconv（x，y，长度（x）+长度（y）-1）;

将结果与x和y的线性卷积进行比较。

linc = conv（x，y）;规范（linc-cir，2）

ANS = 1.4047E-08

Return the circular convolution,cirC，使用Matlab®工作区gather。

circ =聚集（circ）;