The Scientist and Engineer's Guide to
Digital Signal Processing
By Steven W. Smith, Ph.D.
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Table of contents
- 1: The Breadth and Depth of DSP
- 2: Statistics, Probability and Noise
- 3: ADC and DAC
- 4: DSP Software
- 5: Linear Systems
- 6: Convolution
- 7: Properties of Convolution
- 8: The Discrete Fourier Transform
- 9: Applications of the DFT
- 10: Fourier Transform Properties
- 11: Fourier Transform Pairs
- 12: The Fast Fourier Transform
- 13: Continuous Signal Processing
- 14: Introduction to Digital Filters
- 15: Moving Average Filters
- 16: Windowed-Sinc Filters
- 17: Custom Filters
- 18: FFT Convolution
- 19: Recursive Filters
- 20: Chebyshev Filters
- 21: Filter Comparison
- 22: Audio Processing
- 23: Image Formation & Display
- 24: Linear Image Processing
- 25: Special Imaging Techniques
- 26: Neural Networks (and more!)
- 27: Data Compression
- 28: Digital Signal Processors
- 29: Getting Started with DSPs
- 30: Complex Numbers
- 31: The Complex Fourier Transform
- 32: The Laplace Transform
- 33: The z-Transform
- 34: Explaining Benford's Law
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Chapter 9: Applications of the DFT
The Discrete Fourier Transform (DFT) is one of the most important tools in Digital Signal Processing. This chapter discusses three common ways it is used. First, the DFT can calculate a signal's frequency spectrum. This is a direct examination of information encoded in the frequency, phase, and amplitude of the component sinusoids. For example, human speech and hearing use signals with this type of encoding. Second, the DFT can find a system's frequency response from the system's impulse response, and vice versa. This allows systems to be analyzed in the frequency domain, just as convolution allows systems to be analyzed in the time domain. Third, the DFT can be used as an intermediate step in more elaborate signal processing techniques. The classic example of this is FFT convolution, an algorithm for convolving signals that is hundreds of times faster than conventional methods.