Matlab listing: zpfmin.m
function [zpmin] = zpfmin(window,MT,freqBiasMax); % [zpmin] = zpfmin(window,MT,freqBiasMax) % returns the minimum zero-padding factor to achieve prescribed % tolerances in sinusoidal peak parameters measured using the QIFFT % method with the window. % % INPUTS: % window = 'rect', 'hamming', 'hann', or 'blackman' % MT = window length (seconds) % freqBiasMax = max frequency bias allowed in peak frequency (Hz) % ampBiasMax = max peak-magnitude bias allowed (relative fraction) % % If ampBiasMaxPct is not specified, amplitude bias is not considered. % % RETURNED: % zpmin = minimum zero-padding factor (1 means no zero padding) % % EXAMPLE % Assuming the window contains one cycle of a sinusoid whose % frequency f must be estimated to within 0.1% accuracy, we have % zpfmin('blackman',1/f,0.001*f) = 1.9 for min zero-padding factor. % Similarly, % 2 cycles under the Blackman window yields zpf > 1.5 % 4 cycles under the Blackman window yields zpf > 1.2 % 6 cycles under the Blackman window yields zpf > 1.02 % % Reference: % "Design Criteria for Simple Sinusoidal Parameter Estimation % based on Quadratic Interpolation of FFT Magnitude Peaks", by % Mototsugu Abe and Julius O. Smith, % Audio Engineering Society Convention preprint 6256", NY, 2004. %!test %! assert(zpfmin('blackman',1,0.001),2.3609,0.001); % disp(sprintf('%s window',window)); switch window case 'rect' c0 = 0.4467; r0 = -0.3218; c1 = 0.8560; r1 = -0.2366; case 'hamming' c0 = 0.2456; r0 = -0.3282; c1 = 0.4381; r1 = -0.2451; case 'hann' c0 = 0.2436; r0 = -0.3288; c1 = 0.4149; r1 = -0.2456; case 'blackman' c0 = 0.1868; r0 = -0.3307; c1 = 0.3156; r1 = -0.2475; otherwise error(sprintf('Window type %s unknown - say help zpfmin',window)); end zpmin = c0*(MT*freqBiasMax)^r0; if nargin>3 zpminamp = c1*(MT*freqBiasMax)^r1; zpmin = max(zpmin,zpminamp); end if strcmp(window,'rect') zpmin=max(1.7,zpmin); % See Abe & Smith 2004, Fig. 2 re. why this else zpmin=max(1,zpmin); end
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