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Coefficient LTI Transfer

When transferring coefficients of a fourier series through an LTI system, each value of $ a_k\ $ is multiplied by $ H(\jmath \omega)\ $ in the system output. Therefore...

$ \displaystyle a_k \rightarrow a_k \cdot H(\jmath \omega) $

The image below illustrates the process of taking the value of the frequency response function at each frequency of the coefficients and then multiplying by that value to yield the transformed coefficient values.

ECE 301 Fall 2007 mboutin Fourier Coefficients.png

Note that when $ H(\jmath \omega) $ is negative, the sign of the value of the coefficient is flipped.

Types of Filters

Types of Filters

ECE 301 Fall 2007 mboutin Lowpass.png Low Pass
ECE 301 Fall 2007 mboutin Highpass.png High Pass
ECE 301 Fall 2007 mboutin Bandpass.PNG Band Pass
ECE 301 Fall 2007 mboutin Bandreject.PNG Band Reject

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