FIR transfer function: Difference between revisions

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h(<math>\tau</math>) is a transfer function of an impulse response to the input. The [[Convolution#Visual explanation|convolution]] allows the filter to only be activated when the input recorded a signal at the same time value. This filter returns the input values (x(t)) if k falls into the support region of function h. This is the reason why this filter is called finite response. If k is outside of the support region, the impulse response is zero which makes output zero. The central idea of this h(<math>\tau</math>) function can be thought of as a quotient of two functions <ref> Nagai, N. (1990). Linear circuits, systems, and signal processing: Advanced theory and applications. New York: M. Dekker.</ref>.

According to Huang (1981)<ref>Huang, T. S. (1981). Topics in applied physics: Two-Dimensional Digital Signal Processing I (3rd ed., Vol. 42, Topics in Applied Physics). Berlin: Springer.</ref> Using this mathematical ground workmodel, there are four methods of designing non-recursive linear filters with various [[Finite impulse response#Filter design|concurrent filter designs]]:

# [[#Window design method|Window design method]]

# Frequency Sampling method