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Math Help - question on ratio of trigonometric series

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    question on ratio of trigonometric series

    Consider following ratio of trigonometric series

    H_{special}(\omega) = \frac{\sum_{n=1}^N a_n\sin(n\omega)}{1+\sum_{n=1}^N a_n\cos(n\omega)}

    where the coefficients a_n in the numerator and denominator are equal. N is any positive integer. This is a special case of the general form

    H_{generic}(\omega) = \frac{\sum_{n=0}^N c_n\sin(n\omega)}{\sum_{n=0}^N d_n\cos(n\omega)}

    Does anyone know if it is possible to quantify in anyway what 'shapes' H_{special}(\omega) is constrained to in comparison to H_{generic}(\omega). Any pointers to relevant literature is very much appreciated. I have read about finite Fourier series, but so far that has not provided much insight.

    niaren
    Last edited by niaren; May 29th 2012 at 04:39 AM.
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