Hi Benjamin,
To handle varying sample times accurately in your real-time Fourier analysis, you need to dynamically adjust the buffer size and ensure that your calculations remain accurate regardless of the sample time. Here are a few suggestions to improve your implementation:
1. Dynamic Buffer Size Adjustment: Calculate the buffer size based on the sample time and fundamental frequency to ensure it covers exactly one period of the fundamental frequency.
2. Windowing Technique: Apply a windowing technique to reduce spectral leakage, which can be significant when the buffer size is not an integer multiple of the signal period.
3. Accurate Phase Calculation: Ensure the phase calculation handles the quadrant correctly by using `atan2` instead of `atand`.
Here's a revised version of your function incorporating these suggestions:
function [magnitude, phase] = RealTimeFourier(inputSignal, fundamentalFreq, harmonicN, sampleTime, initialMagnitude, initialPhase)
%#codegen
persistent signalBuffer cosBuffer sinBuffer bufferSize bufferIndex hasCompletedCycle
if isempty(signalBuffer)
% Calculate buffer size to cover exactly one period of the fundamental frequency
bufferSize = round(1 / (fundamentalFreq * sampleTime));
signalBuffer = zeros(1, bufferSize);
cosBuffer = cos(2 * pi * harmonicN * (0:bufferSize-1) * sampleTime);
sinBuffer = sin(2 * pi * harmonicN * (0:bufferSize-1) * sampleTime);
bufferIndex = 1;
hasCompletedCycle = false;
end
% Update the signal buffer
signalBuffer(bufferIndex) = inputSignal;
% Check if the buffer has completed a cycle
if bufferIndex == bufferSize
hasCompletedCycle = true;
end
% Update the buffer index
bufferIndex = mod(bufferIndex, bufferSize) + 1;
if hasCompletedCycle
% Apply a windowing function (Hann window) to reduce spectral leakage
window = hann(bufferSize)';
windowedSignal = signalBuffer .* window;
% Perform the Fourier analysis
a_n = 2 / bufferSize * sum(windowedSignal .* cosBuffer);
b_n = 2 / bufferSize * sum(windowedSignal .* sinBuffer);
magnitude = sqrt(a_n^2 + b_n^2);
phase = atan2(b_n, a_n); % Use atan2 to handle the quadrant correctly
else
magnitude = initialMagnitude;
phase = initialPhase;
end
end
Explanation
1. Dynamic Buffer Size Calculation: The buffer size is calculated using `round` to ensure it covers exactly one period of the fundamental frequency, regardless of the sample time.
2. Windowing Function: A Hann window is applied to the signal buffer to reduce spectral leakage. This is particularly useful when the buffer size is not an integer multiple of the signal period.
3. Accurate Phase Calculation: The phase is calculated using `atan2(b_n, a_n)` to handle the correct quadrant of the phase angle.
Usage
You can use this function in a loop to process your real-time signal data:
% Example usage
fs = 1e5; % Sample rate
T = 1/fs; % Sample time
f0 = 50; % Fundamental frequency
harmonicN = 1; % Harmonic number
initialMagnitude = 0;
initialPhase = 0;
% Simulate a signal
t = 0:T:1; % Time vector
inputSignal = sin(2 * pi * f0 * t);
% Initialize output arrays
magnitude = zeros(size(t));
phase = zeros(size(t));
% Process the signal in real-time
for i = 1:length(t)
[magnitude(i), phase(i)] = RealTimeFourier(inputSignal(i), f0, harmonicN, T, initialMagnitude, initialPhase);
end
% Plot the results
figure;
subplot(2, 1, 1);
plot(t, magnitude);
title('Magnitude');
subplot(2, 1, 2);
plot(t, phase);
title('Phase');
This revised function should handle varying sample times more robustly and provide accurate Fourier analysis for your real-time signal processing needs.
Thank you.
