# I would like to quantize a Sinewave correctly, and identify where the issues is with my code

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Dan Lardner on 21 Jun 2024
Commented: Les Beckham on 24 Jun 2024
Hi,
With the code below, I am trying to Quantize the Sinewave by varying the quantity of bits from 16-bits down via Bit Shifting, and then play a sound.
The waveform is normalised, however I am not replicating the waveform correctly and I just cannot seem to find where my error is.
I have attached some .jpg files at nBits = 1, 8 and 15.
Any help or guidance would be very appreciated.
% Sampling Frequency
fs = 8000;
% Sample Period
Ps = 1/fs;
% Sample Time from zero to two seconds in 125us steps (Ps)
t = 0:Ps:2;
% Waveform Frequency
waveFreq = 2;
% Sinewave signal
waveSignal = sin(2*pi*waveFreq*t);
waveInt = int16(waveSignal*2^15);
% Quantize waveform via truncation. (Reduce the least significant bit - LSB)
nBits = 1;
quantWave = bitshift(waveInt,nBits);
% Cast waveform back into a double data type
quantWaveDub = double(quantWave)/2^(16-nBits);
% Normalise the waveform due to bit change
quantWaveDub = quantWaveDub/max(abs(quantWaveDub));
% Plot Sinewave signal
figure(1);
plot(t,waveSignal);
ylim([-1.5 1.5]);
sound(waveSignal,fs);
pause(1);
% Plot Quantized signal
figure(2);
plot(t,quantWaveDub);
ylim([-1.5 1.5]);
sound(quantWaveDub,fs);

Les Beckham on 21 Jun 2024
Edited: Les Beckham on 21 Jun 2024
You were so close! But bitshift shifts left by the specified number of bits. Use a minus sign to shift right.
% Sampling Frequency
fs = 8000;
% Sample Period
Ps = 1/fs;
% Sample Time from zero to two seconds in 125us steps (Ps)
t = 0:Ps:2;
% Waveform Frequency
waveFreq = 2;
% Sinewave signal
waveSignal = sin(2*pi*waveFreq*t);
waveInt = int16(waveSignal*2^15);
% Quantize waveform via truncation. (Reduce the least significant bit - LSB)
nBits = 1;
quantWave = bitshift(waveInt, -nBits); % <<<<< minus sign to shift right!
% Cast waveform back into a double data type
quantWaveDub = double(quantWave)/2^(16-nBits);
% Normalise the waveform due to bit change
quantWaveDub = quantWaveDub/max(abs(quantWaveDub));
% Plot Sinewave signal
figure(1);
plot(t,waveSignal);grid on
ylim([-1.5 1.5]);
% sound(waveSignal,fs);
% pause(1);
% Plot Quantized signal
figure(2);
plot(t,quantWaveDub); grid on
ylim([-1.5 1.5]);
% sound(quantWaveDub,fs);
Dan Lardner on 22 Jun 2024
Hi Les,
Of course, thanks for pointing that out.
It was drivig me crazy.
Les Beckham on 24 Jun 2024
You are quite welcome.

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