This book discusses digital signal processing schemes that are potentially applicable to electronic warfare (EW) receivers. These receivers must have very wide instantaneous input bandwidth (about 1 GHz) to fulfill their operational. However, communication bandwidth is increasing because the wider the bandwidth, the more information per unit time can be transmitted from one point to another.

In this chapter, both the Fourier transform and Fourier series will be discussed. The properties of the Fourier transform will be presented and the concept of impulse function will be introduced. The definition of convolution and its relation with Fourier transform will be presented. Examples of some commonly used Fourier transforms are given and the results are presented in a table for quick reference. There are many good books on this subject. A few of the books are listed at the end of this chapter. Readers with a background in this area can skip this chapter. However, Examples 3.10 and 3.11 may be of interest, because the former one is related to the radar pulse train and the latter will be used in the Hilbert transform.

In this chapter, the operations discussed will be related to the Fourier transform and especially to the discrete Fourier transform (DFT) or fast Fourier transform (FFT). Some of these operations are useful to receiver design and some of these techniques can improve the results of the FFT. The discussion includes zero padding, better localization of FFT peaks, digital convolution, parallel FFT operations to increase overall speed, performing real FFT by using complex FFT operations, and a phase sampling scheme to increase the bandwidth of the receiver.

The main purpose of this chapter is to present an optimum way to match the radio frequency (RF) amplifier with the ADC. The word optimum means to obtain a certain sensitivity and dynamic range, desired by the designer, within the limits of the amplifier performance and the ADC. The important parameters for the ADC are the number of bits, maximum sampling frequency, and input power level. It is assumed that the performance of the ADC is ideal. The lower limit of the dynamic range is the noise level rather than the spur levels because the spur levels are difficult to predict, as discussed in the Chapter 6. This same approach can be used to design with nonideal ADCs. For nonideal ADCs, the lower limit of the dynamic range should be considered as limited by the spur's response rather than the noise level.

This chapter discusses different types of detection schemes. The difference between the detection schemes of analog and digital receivers will be emphasized. The possible advantages of a digital receiver from a detection point of view will be discussed. The detection based on one data sample will be discussed first. The one sample case will be extended to multiple samples. Finally, frequency domain detection, which can be applied to digital receivers, will be examined. Examples with computer programs are used to illustrate some of the detection schemes.

Channelization is one of the most important operations in building digital electronic warfare (EW) receivers. The equivalent analog operation is the filter bank. Therefore, digital channelization can be considered a digital filter bank. It can also be considered as an N-port network with one input and N-1 outputs. An input signal will appear at a certain output according to its frequency. By measuring the outputs from the filter bank, the frequency of the input signal can be determined. The design of a specific digital filter bank will be presented. This specific example is used to illustrate the design procedure while avoiding the unnecessary mathematical complexity of a general design. In this example the concepts of polyphase filter and multirate operation will be introduced. In order to understand these concepts, decimation and interpolation are discussed first.

This chapter describes how, after the frequency channelization, further processing is performed to determine the number of frequencies and the frequencies themselves. The frequency data resolution (or frequency bin width) calculated through an FFT operation determines the frequency precision measured on the input signal. It is often desirable to obtain better frequency precision than the FFT operation can provide. Another problem with such a wide frequency bin is that when two signals fall into one frequency output channel, the receiver cannot effectively separate them.The traditional way to separate signals by frequency is through an analog filter bank. Although the main emphasis of this book is digital, one still can consider the analog filtering approach. In an analog channelized receiver, after the filter bank and amplifier, crystal video detectors are used to convert the radio frequency (RF) into video signals. The video signals are digitized by ADCs and are further processed to determine the number of signals and their frequencies. In converting RF into video signal, some information is lost. If two signals fall into one channel, it is difficult to separate them.

The angle of arrival (AOA) is the most valuable information that can be obtained from an enemy radar because the radar cannot change its position drastically in a very short time frame (i.e., a few milliseconds). Unfortunately, the AOA information is also the most difficult information to obtain. It requires several antennas with receivers. The two common approaches to measure AOA are based on amplitude and phase comparisons. Another approach is to use the Doppler frequency shift generated by the aircraft movement. However, this approach is closely related to the phase measurement system. If the requirement is to measure AOA on simultaneous signals, the problem becomes even more complicated because receivers with multiple signal capability are needed.