How do I calculate Savitzky-Golay 1st Derivative?

Hi, I'm quite new to MATLAB.

I want to use Savitzky-Golay 1st Derivative over a 5-point window and second polynomial order, to smooth my NIR data.

Could I simply use the sgolayfilt function and compute it like this:

dx1 = sgolayfilt(x1, 2, 5)

Or do I need a different code?

Answer 1

[Abhishek Kumar Singh]

Hi @Hannah,

I don't think you can use sgolayfilt to compute the first derivative. It is used to apply the Savitzky-Golay filter to smoothen it. The output you get is a filtered signal, not any derivative. Refer to the documentation: https://www.mathworks.com/help/signal/ref/sgolayfilt.html

To compute the first derivative, you need to use the sgolay function to get the filter coefficients and then apply them to your data using convolution.

Refer to a sample code here:

% Generate sample data: a noisy sine wave
x = linspace(0, 2*pi, 100); % 100 points from 0 to 2*pi
y = sin(x) + 0.1*randn(size(x)); % sine wave with added noise

% Parameters for Savitzky-Golay filter
polynomialOrder = 2; % Second polynomial order
frameSize = 5;       % 5-point window (should be odd)

% Calculate Savitzky-Golay filter coefficients
[b, g] = sgolay(polynomialOrder, frameSize);

% Compute the sampling interval
dt = x(2) - x(1); % Sampling interval

% Compute the first derivative
p = 1; % First derivative
dy = conv(y, factorial(p) / -1*dt^p * g(:, p+1), 'same');

% Plot the original data and the first derivative
figure;
subplot(2, 1, 1);
plot(x, y, 'b.-');
title('Original Data (Noisy Sine Wave)');
xlabel('x');
ylabel('y');
subplot(2, 1, 2);
plot(x, dy, 'r.-');
title('First Derivative (Savitzky-Golay)');
xlabel('x');
ylabel('dy/dx');

Refer to this example for more accurate implementation and understanding of sgolay function for your use case: https://www.mathworks.com/help/signal/ref/sgolay.html#mw_564d68d7-239a-4145-9508-eb6dfcfaf8ae

[Hannah]

Thank you so much!