Fourier transform Fft_generic Halcon

the function of Fourier transform (ft, Fourier Transform) is to transform a signal from time domain to frequency domain. In fact, the data from the horizontal axis time, ordinate sampling value waveform format, converted to horizontal frequency, ordinate amplitude (or phase) of the spectral format. After the transformation can be clearly seen some of the previously imperceptible characteristics. The discrete Fourier transform (DFT) algorithm belongs to the linear transformation. Because each sampling point is to do a weighted sum of all points at once, so when the sampling point is more time, the operation speed is very slow. Fast Fourier transform (FFT) is a fast algorithm for DFT, and the result of operation is equal to DFT. The principle is to use the symmetry of weights and periodicity, the sampling point decomposition into two parts, each part of the original half of the number of points, so that the calculation will be halved. Then you can continue to break down into 4 parts,8 copies, ... In order to continuously improve the efficiency.

Formula for waveform:

Sampling Plant (y) -The vertical axis represents the value of the sample point
time (t) -The horizontal axis represents the time, or represents the current number of sample points
amplitude (A) -also called amplitude, which represents the height of the wave (peak)
round frequency (ω) -ω=2π*f,f Representative frequency
phase (Ω*T) -is an angle, generally expressed in radians, Radian-based 0~2π, representing 0 degrees to 360 degrees



number of sample points (N) -the sampled data is discrete and is often represented by a scatter point, with a total of 20 sample points.

frequency (f) -is the number of times the vibration is completed per unit of time, the number of repetitions of the f= wave/n.



If the graph of a wave is: The number of sample points (N) = 200, amplitude (A) = 3, frequency is 10 waves, i.e. 3*sin (2π*10/200).

After Fourier transform, you can see that there is a vertical line in about 10 of the position, it is easy to see that the frequency of 10 waves . Because the result of the transformation is a symmetric shape , a vertical line appears in the corresponding position on the right 200-10. The transformed data, in addition to these two vertical bars, the other values are approximately 0, is a sparse matrix .


The result of the operation is a complex number, and the output value takes the modulus (absolute value) of complex numbers. Modulus of the complex number = square of the real part + imaginary part squared, then open square = sqrt (real^2+imagine^2)


If you are only extracting features, use the above output values. If you want the standard amplitude and frequency values, then:
amplitude = output value/(N/2) = 300/(200/2) = 3
Frequency = number of repetitions of the wave n = 10/200 = 0.05

Matlab:


N = 200; % number of sample points
A = 3; % amplitude
FV = 10; Number of repetitions of the% wave
f = fv/200; % frequency
t = [1:200]; % Time


y = A * sin (t*2*pi*f); % generate waveform sampled data
Plot (y); % Display Time domain graph


Figure
y = FFT (y, N); % FFT transform
Plot (ABS (Y)); % Display Frequency domain graph


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Introduction to Fourier Transform: http://news.cnblogs.com/n/209014/
The FFT is based on complex numbers, and the actual data of the sampled points is usually real, so it is converted into a plural form. The standard practice is that the real part of the complex number is the real data of the sampling point, and the imaginary part is filled in 0. (However, there are some computational efficiency problems, because the part that fills 0 also participates in the operation, and there are some optimization algorithms.) )

Fourier transform Fft_generic Halcon