# Correlation between frequency and initial phase estimates using FFT

Why is there a high negative correlation between frequency estimation errors and initial phase estimation errors when measured using FFT? I have a simple code showing this negative correlation. is there a known explanation for that? here is the code

clear all;clc;close all; %% T = 0.2; fs = 500; f = 200; ts = 1/fs; snr = 5; n = fs*T; t = linspace(0,T-ts,n); theta = 0.1; y = exp(1i*2*pi*(f.*t + theta)); for count = 1:2000 count; yy = awgn(y,snr,'measured'); NFFT = 2^16; fVals = fs/NFFT.*[0:NFFT-1]; X = fft(yy,NFFT)./n; plot(abs(X)) [~,M] = findpeaks(abs(X),'MinPeakheight',0.8); measuredAngle = angle(X(M))/2/pi; errfreq(count) = fVals(M) - f; errph(count) = measuredAngle - theta; end cov(errfreq,errph) corrcoef(errfreq,errph)

ans = 1.0000 -0.8506 -0.8506 1.0000