SineTransformForward

Fast Discrete Sine Transform (DST-I).

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Parameters

• t input argument t
• x input argument x
• varargin input argument varargin

Returns

• xbar output value xbar
• f output value f

Discussion

SineTransformForward Fast Discrete Sine Transform (DST-I) xbar is returned in the same units as x. This is the finite length definition of a Fourier transform. f is returned in units of cycles, and only contains the potentially nonzero frequency i.e., the zero and nyquist are not included, because they must be zero. The following relationship is satisfied: [f, xbar] = SineTransformForward(t,x); S = T(xbar . conj(xbar)); x_sum = (1/T)sum(x.x)dt; S_sum = sum(S)df; x_sum == S_sum Using, N=33; % total points T=1.0; % total time length t=T(0:(N-1))’/(N-1); This definition of t *includes the end points which must be zero.