From Fourier Transform in Radar and Signal Processing

6.4 Simple Example of Amplitude Equalization

It has already been remarked that the problem of delay equalization as considered here has been covered in Section 5.3 under the subject of sampled waveform delay, so no further illustrations are given here. However, the subject of amplitude equalization has not been illustrated before, so a simple example, using the results of Section 6.3 above, is presented in this section, showing how effective the method is and with how little computation if there is a degree of oversampling. We take the simple case of a linear amplitude distortion with an unweighted squared error function over the bandwidth (equivalent to a rect function power spectrum). The response to be matched is of the form G( f) = 1 + af over the bandwidth (taken to be unity), or G( f) = rect f + ( a/2) ramp f. The Fourier transforms of G required for the components of a will include a transform of the ramp function, that is, a snc 1 function, as well as a snc 0 from the rect function. As we require the transform of G 2( f) to determine the elements of B, we also have a ramp 2 function with its transform snc 2. There is an important detail to notice in that they are actually inverse Fourier transforms that are required [see (6.6) and (6.7)]. In many cases (using...

Products & Services
IC Electronic Filters
IC electronic filters are frequency-selective circuits that consist of devices such resistors, capacitors, inductors, transistors, or operational amplifiers coupled with reactive components.
Active Band Pass Filters
Active band pass filters are used to attenuate frequencies below and above a range of frequencies (i.e., the bandwidth or passband of the filter).
Computer Based Instruments
Computer-based instruments are part of a computer (a board, for example), or need to be connected to a computer in order to measure and display data.
Audio Analyzers
Audio analyzers measure the noise and audio spectrum of output from an amplifier or a stereo.
Accelerometers are instruments for measuring, displaying, and analyzing acceleration and vibration.

Topics of Interest

6.5 Equalization for Broadband Array Radar Many antennas for use in radio, radar, or sonar systems consist of an array of simple elements, rather than, in some radio cases, a single element or, for...

6.1 Introduction In this chapter we consider the problem of compensating for some known frequency distortion over a given band. One form of distortion is an unwanted delay, and the resulting...

6.8 Summary In this chapter we have looked at equalization of both linear phase variation (due to delay error) and polynomial amplitude error across the band of interest. In the latter case, we saw...

2.1 Introduction In this chapter we present the basic tools and techniques for carrying out Fourier transforms of suitable functions without using integration. In the rest of the book the definitions...

The illustrations of the use of the rules and pairs technique in Chapters 3 to 7 show a wide range of applications and how some quite complex problems can be tackled using a surprisingly small set of...