different way to do what hann function does in matlab

The Hann window is a commonly used window in signal processing. It is used to improve the frequency domain analysis of a signal by tapering the edges of the signal toward zero, which reduces the frequency leakage caused by the sharp drop-offs at the edges.

Here are a few different ways to implement the Hann window function in MATLAB:

1. Using the hann() function built into MATLAB:

main.m
% create a 10-point Hann window
w = hann(10)

% apply the Hann window to a signal
x = randn(10,1);
x_hann = x .* w;
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2. Manually defining the Hann window using the formula w(n) = 0.5 * (1 - cos(2*pi*n/(N-1))), where n is the index of the sample in the window and N is the total number of samples in the window:

main.m
% create a 10-point Hann window
N = 10;
n = (0:N-1)';
w = 0.5 * (1 - cos(2*pi*n / (N-1)));

% apply the Hann window to a signal
x = randn(10,1);
x_hann = x .* w;
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3. Using the window() function in MATLAB with the 'hann' argument:

main.m
% create a 10-point Hann window
w = window(@hann, 10);

% apply the Hann window to a signal
x = randn(10,1);
x_hann = x .* w;
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All of these methods will produce the same output: a Hann window with N points, which can be applied to a signal using element-wise multiplication.