The input float range for FFTW depends on the specific implementation and the configuration of the library. However, in general, the input float values should be within the range of -1.0 to 1.0, which represents the normalized range of the input signal.
stackoverflow는 과거 글이긴 한데.. 미묘..
Surprisingly there is no single agreed definition for the FFT and the IFFT, at least as far as scaling is concerned, but for most implementations (including FFTW) you need to scale by 1/N in the forward direction, and there is no scaling in the reverse direction.
Usually (for performance reasons) you will want to lump this scaling factor in with any other corrections, such as your A/D gain, window gain correction factor, etc, so that you just have one combined scale factor to apply to your FFT output bins. Alternatively if you are just generating, say, a power spectrum in dB then you can make the correction a single dB value that you subtract from your power spectrum bins.
A number literal like 37 in JavaScript code is a floating-point value, not an integer. There is no separate integer type in common everyday use. (JavaScript also has a BigInt type, but it's not designed to replace Number for everyday uses. 37 is still a number, not a BigInt.)
For a real-to-complex transform you get N / 2 + 1 complex outputs for N real inputs (the redundant symmetric outputs are not generated).
The 0 Hz component is in bin 0.
Now out contains r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1 , as it is written in the manual.
r0 ,out[0],is the mean value of your data/signal. r1 ,out[1],is the real part of the first element of the DFT. ... i0 is 0 because you're using real data , so it isn't stored in out. i1 ,out[N-1],is the imaginary part of the first element of the DFT. i2 ,out[N-2],is the imaginary part of the second element of the DFT. If N is a even number , then r(N/2) out[N/2] is the Nyquist frequency amplitude.
Im new to fftw library
Remember that FFTW computes only the product of your data by the trigonometric functions, but it don't normalize them. You can find more info about the halfcomplex here.
The reason that the Fast Fourier Transform (FFT) in the library FFTW produces a result of N/2+1 values when applied to real input data of length N is because of the way that the FFT algorithm works. In FFTW, the FFT algorithm used is called the "real-to-complex" FFT, which takes real-valued input data and produces complex-valued output data. When applied to real input data, the algorithm takes advantage of the symmetry properties of the Fourier transform of real-valued signals. Specifically, the Fourier transform of a real-valued signal is complex-conjugate symmetric, meaning that if x(t) is a real-valued signal, then its Fourier transform X(f) satisfies X(-f) = conj(X(f)), where "conj" denotes complex conjugation. Because of this symmetry property, half of the output values of the FFT algorithm are redundant, and can be calculated from the other half. Specifically, the output values for frequencies from 0 to N/2 are unique, while the output values for frequencies from N/2+1 to N-1 can be calculated as the complex conjugate of the corresponding frequency from 1 to N/2-1. Therefore, to save computation time and memory, FFTW only calculates the unique output values for frequencies from 0 to N/2, as well as the value for frequency N/2 (if N is even). This results in a total of N/2+1 output values.
FFTW 라이브러리에서 Fast Fourier Transform (FFT)를 적용하면, 길이가 N인 실수 입력 데이터에 대해 복소수 출력 데이터 N/2+1개가 생성됩니다. 이는 FFT 알고리즘이 동작하는 방식 때문입니다. FFTW에서 사용되는 FFT 알고리즘은 "real-to-complex" FFT라고 불리며, 실수값 입력 데이터를 복소수값 출력 데이터로 변환합니다. 이 알고리즘은 실수값 신호의 푸리에 변환의 대칭성(symmetric) 특성을 활용합니다. 구체적으로, 실수값 신호 x(t)의 푸리에 변환 X(f)은 X(-f) = conj(X(f)) 라는 복소수 공액대칭성(complex-conjugate symmetric)을 만족합니다. 여기서 "conj"는 복소수 공액(conjugate)를 의미합니다. 이 대칭성 특성 때문에 FFT 알고리즘의 출력값 중 절반은 중복되는 값이며, 나머지 절반은 이 중복된 값들로부터 계산될 수 있습니다. 구체적으로, 0부터 N/2까지의 주파수 대역에서는 고유한 출력값이 존재하며, N/2+1부터 N-1까지의 주파수 대역에서는 대응하는 1부터 N/2-1까지의 주파수 대역의 복소수 공액값을 계산하여 구할 수 있습니다. 따라서 FFTW는 연산 시간과 메모리를 절약하기 위해, 0부터 N/2까지의 주파수 대역에 대한 고유한 출력값과, N이 짝수인 경우 주파수 N/2에 대한 출력값을 계산합니다. 이렇게 계산된 출력값의 총 개수는 N/2+1개가 됩니다.
The DFT results are stored in-order in the arrayout, with the zero-frequency (DC) component inout[0].
Size of FFT in 1D is not half of the signal length. It's still the signal length (assuming FFT length was of the signal length). However for real data, due to conjugate symmetry, half of this is redundant and can be dicarded to reduce storage. Note however that, when it's required to process the FFT data, you have to construct the full length from the half and proceed.
This is also the reason why spectral analysis software display only positive frequencies for real data; i.e, negative frequencies will be a mirror copy (of the magnitude) of positive frequencies.
But you don't have to discard the half. You can just retain it.
For image processing, the symmetry of FFT for real input data again exist and if you wish you can also dicard half of the image FFT data. Whether this will be employed or not depends on the intentions of the package.
머 병원에서 주사를 놔야 하는게 당연하긴 한데.. 동물병원이 너무 비싸다 보니 오히려 백신을 안 놓게 되는 일이 발생할 것 같네..
오는 11월 13일부터 동물약국에서 반려견 4종 백신(DHPPi), 반려묘 3종 백신(FVRCP)을 수의사 처방전 없이 판매할 수 없게 됐다. 수의사 처방제가 확대시행됐기 때문이다.
만약 약국에서 개 종합백신, 고양이 종합백신을 처방전 없이 판매하면 약사법 위반으로 1년 이하의 징역 또는 1천만원 이하의 벌금에 처하게 된다.
...
개 5종 백신(DHPPL), 고양이 4종 백신, 5종 백신이 이미 2018년부터 처방대상이었던 점을 고려하면, 사실상 반려견·반려묘의 백신(생물학적제제)의 약국 판매가 금지되는 것이다. 수의사 처방전이 있으면 백신을 구입할 수 있으나, 처방전을 받기 위해서는 동물병원에서 수의사의 진료를 먼저 받아야 한다.
