A New Twist to Fourier Transforms
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.
The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs.
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amplitude antenna Artech House beamwidth Blackman-Harris calculated Cartesian centre Chapter characteristic function complex conjugate convention convolution correlation Cosine wave cosine waveform curve decibels delta function discrete Fourier transform echo signals Equation example filter characteristic finite impulse response Fourier series helical waveform helix input integration inverse Fourier transform inverse transform kurtosis lowpass filter Massachusetts minor signal Modern Radar Systems modulation multiplied negative phase sequence Norwood number of samples output parameters phase sequence component plotted polyphase probability distribution function processing gain Rayleigh distribution rectangular pulse representing root mean square rotating sampling frequency Scalloping loss Section shown in Figure sidelobe level sidelobes signal processing Signal ratio signal-to-noise ratio sinc function sine wave skew Source spatial spiral spectral leakage spectrum standard deviation statistics Table tapering functions Twist to Fourier two-tone characteristics values variable variance vector voltage waveform width Worst case loss zero