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.
Spectral Analysis
CHAPTER
Applications of the DFT
9

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 p