Menu
I wanted to use Apache math commons implementation for FFT (FastFourierTransformer class) to process some dummy data whose 8 data samples are contributing to one complete sinusoidal wave. The maximum being amplitude 230. The code snippet that I tried is below :
private double[] transform()
{
double [] input = new double[8];
input[0] = 0.0;
input[1] = 162.6345596729059;
input[2] = 230.0;
input[3] = 162.63455967290594;
input[4] = 2.8166876380389125E-14;
input[5] = -162.6345596729059;
input[6] = -230.0;
input[7] = -162.63455967290597;
double[] tempConversion = new double[input.length];
FastFourierTransformer transformer = new FastFourierTransformer();
try {
Complex[] complx = transformer.transform(input);
for (int i = 0; i < complx.length; i++) {
double rr = (complx[i].getReal());
double ri = (complx[i].getImaginary());
tempConversion[i] = Math.sqrt((rr * rr) + (ri * ri));
}
} catch (IllegalArgumentException e) {
System.out.println(e);
}
return tempConversion;
}
1) Now the data returned by method transform is an array of complex number. Does that array contains the frequency component information about input data? or the tempConversion array that I created will contain the frequency information? The values in tempConversion array is :
2.5483305001488234E-16
920.0
4.0014578493024757E-14
2.2914314707516465E-13
5.658858581079313E-14
2.2914314707516465E-13
4.0014578493024757E-14
920.0
2) I searched a lot but at most of the places there is no clear documentation on what format of data algorithm expects (in terms of sample code to understand better) and how do I use the array of results to calculate the frequencies contained in the signal?
698
The sampling rate or sampling frequency fs of the measuring system (e.g. 48 kHz). This is the average number of samples obtained in one second (samples per second). The selected number of samples; the blocklength BL. This is always an integer power to the base 2 in the FFT (e.g., 2^10 = 1024 samples)
What is FFT Analysis? FFT analysis is one of the most used techniques when performing signal analysis across several application domains. FFT transforms signals from the time domain to the frequency domain. FFT is the abbreviation of Fast Fourier Transform.
Other FFT algorithms Algorithms that recursively factorize the DFT into smaller operations other than DFTs include the Bruun and QFT algorithms.
V The Fast Fourier Transform In the FFT formula, the DFT equation X(k) = ∑x(n)WNnk is decomposed into a number of short transforms and then recombined. The basic FFT formulas are called radix-2 or radix-4 although other radix-r forms can be found for r = 2k, r > 4.
Your output data looks correct. You've calculated the magnitude of the complex FFT output at each frequency bin which corresponds to the energy in the input signal at the corresponding frequency for that bin. Since your input is purely real, the output is complex conjugate symmetric, and the last 3 output values are redundant.
So you have:
Bin Freq Magnitude
0 0 (DC) 2.5483305001488234E-16
1 Fs/8 920.0
2 Fs/4 4.0014578493024757E-14
3 3Fs/8 2.2914314707516465E-13
4 Fs/2 (Nyq) 5.658858581079313E-14
5 3Fs/8 2.2914314707516465E-13 # redundant - mirror image of bin 3
6 Fs/4 4.0014578493024757E-14 # redundant - mirror image of bin 2
7 Fs/8 920.0 # redundant - mirror image of bin 1
All the values are effectively 0 apart from bin 1 (and bin 6) which corresponds to a frequency of Fs/8 as expected.
61
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
