Useful Information: Algorithms ------------------------------ INTERPOLATION USING FFTS The FFT of the signal is taken. It is assumed that the signal is well within the Nyquist criterion (the sample rate is greater than twice the maximum frequency within the signal). This implies that the values of the real and imaginary arrays of the FFT tend to zero toward their centres. The centres of these arrays are expanded in length by the 'interpolation factor' This factor must be a power of two in order to meet the length requirements of the FFT. The inverse FFT is then taken giving a time domain array which is interpolated by the specified factor. ref. DSPlink Issue 13 (1997), Loughborough Sound Images -------------------------------------------------------------------------------- TIME WINDOWING FOR FFT Hanning w(n) = 0.5 - 0.5*cos(2*PI*n/N) Hamming w(n) = 0.54 - 0.46*cos(2*PI*n/N) 3 Term Blackman-Harris w(n) = 0.42323 - 0.49755*cos(2*PI*n/N) + 0.07922*cos(4*PI*n/N) 4 Term Blackman-Harris w(n) = 0.35875 - 0.48829*cos(2*PI*n/N) + 0.14128*cos(4*PI*n/N) - 0.01168*cos(6*PI*n/N) Nuttall w(n) = 0.3635819 - 0.4891775*cos(2*PI*n/N) + 0.1365995*cos(4*PI*n/N) - 0.0106411*cos(6*PI*n/N) -------------------------------------------------------------------------------- SPECTRAL CHARACTERISTICS OF TIME WINDOWS 3dB bandwidth scalloping sideband level sideband rolloff (dB/octave) Rectangular 0.89 3.92dB -13dB 6 Bartlett (Triangular) 1.27 1.82dB -27dB 12 Cosine 1.24 2.10dB -23dB Hanning (cos^2) 1.44 1.42dB -32dB 18 cos^3 1.66 1.08dB -39dB 24 cos^4 1.85 0.86dB -47dB 30 Hamming 1.30 1.75dB -43dB 6 3 Term Blackman-Harris 1.62 1.13dB -67dB 6 4 Term Blackman-Harris 1.90 0.83dB -92dB 6 Nuttall 1.87 0.82dB -98dB 6 100dB Chebyshev 1.84 0.88dB -100dB 0 -------------------------------------------------------------------------------- COMPENSATION OF ZERO-ORDER HOLD FIR: (-z + 18z^-1 - z^-2) / 16 IIR: (9/8)/(1 + (1/8)z^-1) ref. The DSP Handbook, Andrew Bateman & Iain Paterson-Stephens, 2002