Chirp Filters Research Articles

Relation between i.f. and baseband chirp filtering

Extracting the modulus output for a complex signal convolved with a complex chirp impulse response requires four real filters at baseband plus components for summing, differencing, squaring and square rooting. Modulating the signal onto a carrier allows the equivalent processing to be performed to a good approximation by a single i.f. filter.

Network analyser employing surface-acoustic-wave discrete Fourier-transform processor

The design and experimental performance of a novel i.f. network analyser is reported. The network is excited with a line spectrum and a real time discrete Fourier transform is performed on the output, using surface-acoustic-wave chirp filters. The amplitude and phase of the network transfer function are displayed on a conventional oscilloscope.

A linear filtering approach to the computation of discrete Fourier transform

It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \log_{2} N</tex> for any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N, N</tex> being the number of points in the array that is transformed. Another proposed implementation of the chirp filter requires N to be a perfect square. The number of operations required for this algorithm is proportional to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N^{3/2}</tex> .

View of Digital Filtering

Use of the term digital is motivated by today's increasingly common use of digital computers; use of the term “filtering” by today's widespread knowledge of techniques for programming a computer to carry out operations similar to those performed by ordinary electrical filters. Techniques for using a computer to perform filtering include the z transform, which has both standard and bilinear forms. One of the newer techniques for digital filtering is the fast-convolution application of the Fast Fourier Transform (the FFT is a recently developed method of computing discrete approximations to Fourier transforms). This technique makes efficient use of computation time and often provides an unusually simple procedure for designing the computer program. Specification of the filtering operation can be as simple as supplying a numerical or algebraic statement of its frequency response. Filters useful in spectrum analysis are most easily specified in this manner. These filters include Taylor weighting and Kaiser's windows. Other filters that are expressed most easily as an algebraic frequency response are chirp filters and Hilbert transform filters. Digital filtering appears to offer the advantages of easier maintainability due to elimination of the need for adjustments, more compactness (as large-scale integrated circuits become available), fewer constraints and modeling uncertainties, and greater possibility of using the same hardware to perform several functions. Implementations involving floating-point computations on general-purpose digital computers have a reputation for programming ease and filter accuracy.

Synthesis of Transfer Functions in a Prescribed Frequency Band

A signal-processing system for synthesizing complicated transfer functionisn a prescribed frequency band is described. The system consists of a multiplier followed by a closed loop containing a delay line and phase modulator in series. One of the inputs to the multiplier is the signal to be filtered. The second input to the multiplier is periodic, the period being equal to the loop delay. One cycle of the periodic waveform is identicatlo the real part of the transfer function overa prescribed frequency band of width equatlo the reciprocal of the loop delay. The imaginary componeonf t the transfer functionis the negative of the Hilbert transform of the real part, as in all physically realizable filters. Two applications of the system are discussed. It is shown how a continuously variable delay line and chirp filter can be synthesized using these techniques.