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5th November 2016, 20:13 #1
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FFT alternates '0' for a quantized SIN wave
Hello,
Doing FFT exercises in Matlab I've discovered that for some frequencies (defined by k) the FFT of quantized SIN wave alternates '0'.
For k I used primary numbers.
With k = 11, 13, 17, 19, 23, 29, 31, 37 it's Ok
With K = 3, 5, 7, 41, 53, 67, 101, 127 FFT alternates '0'.
Any ideas ?
Thanks in advance.
Pavel.
Code:close all; % clear all; L = 2^14; res = 10; A = 1; Fs = 1e+5; k = 41; f1 = k/L*Fs; t = (0:L1)/Fs; y = A*sin(2*pi*f1*t); % Display Original Signal figure(1) plot(t, y); grid on; % Quantization dA = (2*A)/2^res; partition = (A+dA:dA:AdA); codebook = (0:2^res1); [index,yq] = quantiz(y,partition,codebook); yq = (yq  2^(res1))/2^res*2*A; % Display Quantized Signal figure(2); plot(t,yq); grid on; % Display Quantization Error figure(3); plot(t, yyq); grid on; P2 = abs(fft(yq, L))/L; P1 = P2(1:L/2+1); P1(2:end1) = 2*P1(2:end1); f = Fs*(0:(L/2))/L; % Display FFT figure(4); plot(f, mag2db(P1)); grid on;

5th November 2016, 20:13

6th November 2016, 12:00 #2
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6th November 2016, 12:00

7th November 2016, 15:24 #3
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Re: FFT alternates '0' for a quantized SIN wave
Resolved.
The problem was in erroneous quantization.
Here is the correct quantization code:
% Quantization
dy = (2*A)/(2^res1);
partition = (A+A/2^res:dy:AA/2^res);
codebook = (0:2^res1);
[index,yq] = quantiz(y,partition,codebook);
yq = 2*A*yq/(2^res1)A;
where:
y  SIN waveform values
A  amplitude of SIN waveform
res  resolution of quantizer
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