Testing the Flat-Top Windowing Function

December 14, 2011 Coded in Matlab

The following code is for testing the Flat-Top Windowing Function, used for the Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

%    Code for testing the 'Wind_Flattop(Spec)' function in
%    reducing 'scalloping loss' errors in time signal amplitude
%    estimation.
%
%    Generates a time-domain sinusoid, computes its FFT, and passes
%    that FFT sequence to the 'Wind_Flattop(Spec)' function.
%
%    The maximum output sample of the 'Wind_Flattop(Spec)' function
%    is used to estimate the peak amplitude of the original
%    sinusoidal time-domain test signal.
%
%    The user controls the values for the test sinusoid's
%    'Test_Freq' and peak amplitude 'Peak_Amp' near lines 23 & 24.
%
%    Richard Lyons [December, 2011]

clear all, clc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Define test parameters
Test_Freq = 7.22; % Test tone's freq. Must be less that N/2
Peak_Amp = 5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

N = 64; % Number of time samples
Index = (0:N-1);

X = Peak_Amp*cos(2*pi*(Test_Freq)*Index/N + pi/3);

figure(1), clf
subplot(2,1,1)
plot(X,':ko', 'markersize', 4)
title('Original time signal'), grid on, zoom on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   FFT the input 'X' sequence and call 'Wind_Flattop()' function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Spec = fft(X);
[Windowed_Spec] = Wind_Flattop(Spec);

subplot(2,1,2), plot(abs(Spec),'ko', 'markersize', 3)
title('SpecMag of unwindowed time signal'), grid on, zoom on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Display results accuracy (error)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp(' ')
disp(['Test Freq = ',num2str(Test_Freq),...
',  True Peak Amplitude = ',num2str(Peak_Amp)])

Mag_peak_unwindowed = max(abs(Spec));
Unwindowed_Amp_Estimate = 2*Mag_peak_unwindowed/N;
Unwindowed_Amp_Estimate_Error_in_dB = ...
20*log10(Unwindowed_Amp_Estimate/Peak_Amp);
disp(' ')
disp(['Unwindowed Peak Amplitude Estimate = ',...
num2str(Unwindowed_Amp_Estimate)])
disp(['Unwindowed Estimate Error in dB = ',...
num2str(Unwindowed_Amp_Estimate_Error_in_dB),' dB'])

M_peak_windowed = max(abs(Windowed_Spec));
Windowed_Amp_Estimated = 2*M_peak_windowed/N;
Windowed_Amp_Estimation_Error_in_dB = ...
20*log10(Windowed_Amp_Estimated/Peak_Amp);
disp(' ')
disp(['Windowed Peak Amplitude Estimate = ',...
num2str(Windowed_Amp_Estimated)])
disp(['Windowed Estimate Error in dB = ',...
num2str(Windowed_Amp_Estimation_Error_in_dB),' dB'])