TABLE OF CONTENTS In this chapter, the discrete Fourier transform (DFT) will be discussed. The Fourier transform discussed in the previous chapter is quite useful, but the applications will be limited for two reasons. First, the function in the time domain must be representable in closed form so that the Fourier integral can be performed. Thus, unless the input function can be written in closed form, it is impossible to evaluate the integral. Second, even if the time function can be written in closed form, it might also be difficult to find a closed-form solution to the integral.
In a digital receiver, the input data are obtained from digitizing the input signal. In an electronic warfare (EW) environment, the input signal represented by a function in the time domain is usually unknown. Even if the input is known (such as simulated data generated from a sine or cosine function to test a signal processing algorithm), the signal is digitized before it is processed. When the input signal is in digitized form, the DFT is used to implement the Fourier transform discussed in the previous chapter. Unlike the Fourier transform, the DFT can be performed on any kind of digitized input data; therefore, its usage is not limited.
It is important to know that DFT does not provide the same result as the Fourier transform. It only provides an approximate solution. Sometimes these results can be very close to the desired result, but it rarely happens for short data lengths. At other...
