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DISCRETE FOURIER TRANSFORMATION
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aliasing approximately autocorrelation average power spectrum bandlimited bandlimited function bandlimited to f bias circular circular convolution circular shift complex conjugation complex Fourier series convolution correlation cosine-tip dB/oct decreases digital phase modulated direct method discrete data window discrete Fourier transform discrete lag window discrete spectral window DOU8LE PRECISION energy spectrum evaluated example exp(-j2TTft FFT algorithms finite energy folding frequency Fortran Fortran IV Fourier series frequency f given in Fig harmonic Hence IDFT indirect integer interval Kaiser window l/At leakage linear main lobe main-lobe width method using DFT N-term sequence obtained optimal discrete spectral Papoulis parameter sets plotted Power dB power spectra estimation Prob process x(t pulses radix-2 real sequence rectangular window sampling period shift theorem short-time spectral estimation sidelobe level spectrograms spectrum S f stationary process subroutine Table 3.l Table B.3 taking DFT time-limited transform counterpart variance waveform wide-sense stationary x(nAt