文档介绍：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 mon 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 ponent 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 of Signals
It is mon for information to be encoded in the sinusoids that form
a signal. This is true of naturally occurring signals, as well as those that
have been created by humans. Many things oscillate in our universe. For
example, speech is a result of vibration of the human vocal cords; stars
and s change their brightness as they rotate on their axes and revolve
around each other; ship's propellers generate periodic displacement of the
water, and so on. The shape of the time domain waveform is not important
in these signals; the key information is in the frequency, phase and
amplitude of ponent sinusoids. The DFT is used to extract this
information.
An example will show how this works. Suppose we want to investigate the
sounds that travel through the ocean. To begin, a microphone is placed in the
water and the resulting electronic signal amplified to a reasonable level, say a
few volts. An analog low-pass filter is then used to remove all frequencies
above 80 hertz, so that the signal can be digitized at 1