4.4 Java1485-spectrum analysis using java, forward and inverse  (Page 2/14)

Listings

• Listing 1. The beginning of the class named Dsp035.
• Listing 2. Beginning of the constructor.
• Listing 3. Compute the complex spectrum.
• Listing 4. Perform the inverse Fourier transform.
• Listing 5. Beginning of the class named InverseComplexToReal01.
• Listing 6. The inverse transform computation.
• Listing 7. Some code from Dsp036.
• Listing 8. Beginning of the class for Dsp037.
• Listing 9. Beginning of the constructor.
• Listing 10. Compute the Fourier transform.
• Listing 11. Apply the filter to the frequency data.
• Listing 12. Re-compute the magnitude.
• Listing 13. Compute the inverse Fourier transform.
• Listing 14. Dsp035.java.
• Listing 15. InverseComplexToReal01.hava.
• Listing 16. Dsp036.java.
• Listing 17. InverseComplexToRealFFT01.java,
• Listing 18. Dsp037.java.
• Listing 19. Dsp038.java.

Preview

In this module, I will present and explain the following new programs:

• Dsp035 - Illustrates the reversible nature of the Fourier transform. This program transforms a real time series into a complexspectrum, and then reproduces the real time series by performing an inverse Fourier transform on the complex spectrum. This is accomplished using a DFTalgorithm.
• InverseComplexToReal01 - Class that implements an inverse DFT algorithm for transforming a complex spectrum into a real timeseries.
• Dsp036 - Replicates the behavior of the program named Dsp035 but uses an FFT algorithm instead of a DFT algorithm.
• InverseComplexToRealFFT01 - Class that implements an inverse FFT algorithm for transforming a complex spectrum into a real timeseries.
• Dsp037 - Illustrates filtering in the frequency domain. Uses an FFT algorithm to transform a time-domain impulse into the frequencydomain. Modifies the complex spectrum, eliminating energy within a specific band of frequencies. Uses an inverse FFT algorithm to produce the filteredversion of the impulse in the time domain.

In addition, I will use the following programs that I explained in the module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm and other previous modules.

• ForwardRealToComplex01 - Class that implements a forward DFT algorithm for transforming a real time series into a complexspectrum.
• ForwardRealToComplexFFT01 - Class that implements a forward FFT algorithm for transforming a real time series into a complexspectrum.
• Graph03 - Used to display various types of data. (The concepts were explained in an earlier module.)
• Graph06 - Also used to display various types of data in a somewhat different format. (The concepts were also explained in an earliermodule.)
• GraphIntfc01 - An interface that is required by Graph03 and Graph06 .

Discussion and sample code

Description of the program named Dsp035

The program named Dsp035 illustrates forward and inverse Fourier transforms using DFT algorithms.

The program performs spectral analysis on a time series consisting of pulses and a sinusoid. Then it passes the resulting real and complex parts of thespectrum to an inverse Fourier transform program. This program performs an inverse Fourier transform on the complex spectral data to reconstruct theoriginal time series.