CosineTransformForward

Fast Discrete Cosine Transform (DCT-I).

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Declaration

 [xbar, f] = CosineTransformForward( t, x, varargin )

Parameters

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

Returns

• xbar output value xbar
• f output value f

Discussion

CosineTransformForward Fast Discrete Cosine Transform (DCT-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. The cosine series would have the following sum, x(t) = xbar(1)/2 + sum( xbar(i)cos(ipi/T) ) So note that the first coefficient double the average of the function. From this, Parseval’s theorem is, x_sum = (1/T)(sum(x(2:end-1).x(2:end-1))dt+x(1)x(1)dt/2 + x(end)x(end)dt/2); S_sum = ( S(1)/2 + sum(S(2:end-1)) + 2S(end))*df; Where we’ve taken care to integrate only to the endpoints (and not beyond) in the x_sum. The S_sum includes a correction for the Nyquist.