Spectrum (Fourier Transform) Theory

The Fourier Transform is a mathematical method that converts an input signal from the time domain to the frequency domain. The time domain is displayed as a waveform of voltage versus time, whereas the frequency domain is shown as a spectrum of magnitude or power versus frequency. Daqarta uses the Spectrum button or ALT+S to toggle between the time and frequency domains.

This discussion of Fourier Transform methods will begin with the original "continuous" Fourier Transform, which is the basis for several types of analog instruments, then proceed to the Discrete Fourier Transform (DFT) needed for digital systems, and finally the Fast Fourier Transform (FFT), which is the streamlined version of the DFT in common use.

Unlike the usual "textbook" treatment of these subjects, there are no integrals or summations, no complex or imaginary numbers, and no "compact" notational tricks. No math is used beyond the high school level, yet nothing has been "watered down". Instead, the focus is on a deeper understanding of fundamental principles... the "gut-level" kind of knowledge that is often missing from academic engineering formalism.

• Fourier Series - Sine Wave Synthesis
• Sine Wave Analysis
• Sine Wave Multiplication Experiment
• Conceptual Spectrum Analyzer
• Practical Spectrum Analyzer
• Spectrum Analysis Frequency Resolution
• Sampled Data for the Discrete Fourier Transform
• Sampled Data Aliasing
• Aliasing Demonstration
• Discrete Sine and Cosine References
• DFT Frequency Resolution
• Fast Fourier Transform (FFT)
• Fundamental Time - Frequency Domain Concepts