FIR Filter Implementation

Given a sampled signal s [n], the output of an FIR filter would be given by the following code :

		output [n] = b0 * s [n] + b1 * s [n-1] + ... + b9 * s [n - 9] ; 

In order to filter the signal s, the above relationship is calculated for each sample s [n], resulting in a filtered output with the same number of samples as the input signal. For values of n where the signals is not defined, the value of s[n] can be assumed to be zero.

The filter above has 10 coefficients (b0..b9) and operates on only 10 samples of the input at any one time. Hence Finite Impulse Response.

The coefficients are usually constants but they don't have to be. Time varying filters are possible.

DSP people often refer to the 'order' of an FIR filters. An FIR filter with N+1 coefficients is an Nth order filter.

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