如果输入数组为 {0,1,2,3,4,5,6,7}，FFT 后的正确结果是多少
如果输入数组为 {0,1,2,3,4,5,6,7}，谁能告诉我快速傅立叶变换后的正确结果是什么？
我得到了 {28,0,0,0,0,0,0,0}。这不正确吧？
只是想测试 C 中的 FFT 实现。
谢谢， 安德烈
can anyone tell me what is correct result after Fast Furier Transform, if input array is {0,1,2,3,4,5,6,7}.
I got {28,0,0,0,0,0,0,0}. It isn't correct right?
just want to test FFT implementation in C.
thanks,
Andrey
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{0,1,2,3,4,5,6,7}的 FFT 正确答案是The correct answer to a FFT for
{0,1,2,3,4,5,6,7}is不，这是不正确的（单个非零输出元素意味着您的输入由常数值或单个复指数分量组成）。
为什么不使用现有的 FFT 实现（例如 FFTW 来提供参考结果？或者只是实现一个简单的 DFT？
No, it isn't correct (a single non-zero output element implies that your input consists of either a constant value, or a single complex-exponential component).
Why don't you use an existing FFT implementation, such as FFTW to provide a reference result? Or just implement a straightforward DFT?
根据 Wolfram Alpha 它是：
请注意，没有单一的“正确答案”，因为有多个DFT/FFT 的一种定义，每个定义之间的区别在于您为正向变换和反向变换包含的缩放因子。 （这个答案和之前接受的答案之间的区别只是
sqrt(8)的比例因子）。According to Wolfram Alpha it's:
Note that there is no single "correct answer" as there is more than one definition of the DFT/FFT, the difference between each one being what scaling factor you include for forward and inverse transform. (The difference between this answer and the earlier accepted answer is just a scaling factor of
sqrt(8)).Divij 答案假设输入 {0,1,2,3,4,5,6,7} 的大小=8，即：
{0,0i},{1,0i},{ 2,0i},{3,0i},{4,0i},{5,0i},{6,0i}
对于被视为大小 = 4 的二进制复数的输入，即：
{ 0,1i},{2,3i},{4,5i},{6,7i},
结果是：
Divij answer assumes that input {0,1,2,3,4,5,6,7} has size=8, that is:
{0,0i},{1,0i},{2,0i},{3,0i},{4,0i},{5,0i},{6,0i}
for input considered as binary complex with size=4, that is:
{0,1i},{2,3i},{4,5i},{6,7i},
the result is: