Sliding window for polynomial fitting of a function

I have a function that I would like to assess using a sliding window to fit a polynomial. Ideally this routine would have the following characteristics:

• Function is Pn (below)
• Need to calculate a polynomial fit within a sliding window (see poly_order)
• Output should be the y-value of the fit calculated at the midpoint of the window, iterated over each window (see poly_fit) stored as an vector for future analyses

I am assuming this will need to be reformatted into a loop of some sort perhaps, but I am puzzled about how to make this happen. If I can better clarify this request, please let me know. Thanks, in advance.

Here is my code thus far:

% Define Constants
po = 0.009982;  % Density of water, g/m3
f = 650000;     % Frequency, in Hz
c = 1481;       % Speed of sound, m/s
Uo = 0.1;       % Max velocity of source surface
w = 2*pi*f;     % Angular frequency of source acoustic field
k = w/c;        % Acoustic wave number
a = 0.005;      % Radius of source, in m
r = 10*a;       % Distance from center of source

% Define Array and Formulas
theta = (-pi/2:0.0001:pi/2)';           % Time step array for discretization,'x-vector'
A = 0.5*po*c*Uo*(a/r)*(k*a);            % Amplitude of pressure fluctuation at distance r along centerline
J1 = besselj(1,k*a*sin(theta));         % Bessel function of the first kind, order 1
H_theta = abs(2*J1./(k*a*sin(theta)));  % Shape function

% Pressure function
Pn = A.*H_theta; 

%Polynomial fitting to Pressure Function
poly_order = polyfit(theta,Pn,20)        % Determines coeffients of best fit equation
poly_fit = polyval(poly_order,theta);    % y-values of poly fit at different values of theta (x)

Answer 1

[TADA]

What you describe is a stavisky golay filter if I understand correctly

windowSize = 10; 
polyOrder = 20;
poly_fit = smooth(theta,Pn,windowSize,'sgolay',polyOrder);