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The remainder of the method and the class

The nested for loops discussed above are included in the code shown in Listing 15 . As suggested above, the outer loop iterates on frequency while the inner loop iterates on the values that make up the incoming samples. The code inthe inner loop computes the sum of the product of the time series and the reference cosine and sine functions.

Listing 15. The remainder of the method and the class.
//Outer loop iterates on frequency // values.for(int i=0; i<dataLen;i++){ double freq = lowF + i*delF;double real = 0.0; double imag = 0.0;double ang = 0.0; //Inner loop iterates on time-// series points. for(int j=0; j<dataLen; j++){ real += data[j]*Math.cos( 2*pi*freq*(j-zero));imag += data[j]*Math.sin(2*pi*freq*(j-zero)); }//end inner looprealOut[i]= real/dataLen; imagOut[i]= imag/dataLen; magnitude[i]= (Math.sqrt( real*real + imag*imag))/dataLen;//Calculate and return the phase // angle in degrees.if(imag == 0.0&&real == 0.0){ang = 0.0;} else{ang = Math.atan(imag/real)*180.0/pi;}if(real<0.0&&imag == 0.0){ang = 180.0;} else if(real<0.0&&imag == -0.0){ ang = -180.0;}else if(real<0.0&&imag>0.0){ ang += 180.0;}else if(real<0.0&&imag<0.0){ ang += -180.0;}angleOut[i] = ang;}//end outer loop }//end transform method}//end class ForwardRealToComplex01

Store results in output array objects

At the end of each iteration of the inner loop, code in the outer loop deposits the real, imaginary, magnitude, and phase angle results in the outputarray objects. To accomplish this, the code:

  • Computes the magnitude or amplitude as the square root of the sum of the squares of the real and imaginary parts.
  • Performs some trigonometry operations to determine the phase angle in degrees based on the values of the real and imaginary parts.

Now you know about the dft algorithm

Now you know about the DFT algorithm. You also know about some of the fundamental aspects of spectral analysis involving the sampling frequency andthe folding frequency.

Future modules will discuss other aspects of spectral analysis including:

  • Frequency resolution versus data length.
  • The relationship between the phase angle and delays in the time domain.
  • The reversible nature of the Fourier transform involving both forward and inverse Fourier transforms.

Spectral analysis using an FFT algorithm

At this point, I will present a similar spectral analysis program that uses an FFT algorithm. I will present this program with very little discussion. I amproviding it in this module for two primary purposes:

  • To allow you to experiment and appreciate the flexibility of the DFT as compared to the FFT.
  • To allow you to experiment and appreciate the speed of the FFT as compared to the DFT.

The program named Dsp030

The program named Dsp030 is very similar to Dsp028 . The major differences are:

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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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