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Implementing the dft algorithm

At this point, I will present and explain two different programs:

  • Dsp028 - Driver program for doing spectral analysis using a DFT algorithm.
  • ForwardRealToComplex01 - Class that implements the DFT algorithm.

In addition, I will present, but will not explain the plotting program named Graph03 .

The program named Dsp028

This driver program is similar in many respects to the program named Dsp029 that I explained earlier. It differs mainly in how it populates the arrayobjects containing the data that is plotted by the plotting program.

The program named Dsp029 simply populates those array objects with five sinusoidal functions. The program named Dsp028 also creates five sinusoidal functions. However, it passes those functions to a static method named transform belonging to the ForwardRealToComplex01 class to perform spectral analysis on those functions. The results of the spectral analysis are used to populate thefive array objects whose contents are plotted by the plotting program.

Because of the similarity of the two programs, my discussion of Dsp028 will be much more brief than was my discussion of Dsp029 .

Computes and displays the magnitude spectrum

The program named Dsp028 computes and displays the magnitude of the spectral content for up to five sinusoids having different frequencies and amplitudes.

(Future modules will discuss other aspects of spectral analysis such as the complex spectrum, zero time, and the phase angle.)

Input parameters

The program gets input parameters from a file named Dsp028.txt . If that file doesn't exist in the current directory, the program uses a set of defaultparameters. As with the program named Dsp029 , each parameter value must be stored as characters on a separate line in the file named Dsp028.txt . The required parameters are shown in Figure 12 .

Figure 12. Required input parameters for Dsp028.
Data length as type int Sample number representing zero time as type intLower frequency bound as type double Upper frequency bound as type doubleNumber of spectra as type int. Max value is 5. List of sinusoid frequency values as type double.List of sinusoid amplitude values as type double.

Don't allow blank lines at the end of the data in the file.

The number of values in each of the lists must match the value for the number of spectra.

Specification of sinusoidal frequencies

As before, each frequency value is specified as a double value representing a fractional part of the sampling frequency. For example, avalue of 0.5 specifies a frequency that is one-half the sampling frequency.

Example contents for dsp028.txt

Figure 13 shows the contents of the file named Dsp028.txt that represent the parameters shown in Figure 10 .

Figure 13. Contents of Dsp028.txt file.
200 00.4 0.65 0.4920.494 0.4960.498 0.590 9090 9090

Performing the spectral analysis

A static method named transform belonging to the class named ForwardRealToComplex01 is used to perform the actual spectral analysis. The method named transform does not implement an FFT algorithm. Rather, it is more general than, but much slower than an FFTalgorithm.

Questions & Answers

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