ASN8 - FIR filters

Return to Homepage

Problem Statement

Make a page about interpolating FIR filters. Note how many multiply/add operations

Response

In progress

Interpolating a sample can be useful if for example you have a sampler that happens to be faster than the incoming rate of your data. For this example let’s assume that the sampler rate is twice the speed of the data. Using this sampler to sample the data results in only half of the samples being the data that we want and the other half, the zero value samples, are useless and can be discarded. Here is where using an interpolating finite impulse response (FIR) filter is useful. The interpolating FIR filter eradicates the problem of extraneous samples because we can implement the filter to sample at half the original sampler rate. The sample rate is now in sync with the rate of the incoming data. The result of this interpolating sampler contains now only the data of the input.

$\sum _{m=-M}^{m}a_{m}x[(r-m)T/2]=y(r)$

The number of add/multiply operations is half the limits of the sumation above. Half results from only needing to perform calculations on half the data.

$(2M+1)(1/2)\!$

Substitute

$r/2=n=m/2\!$

in y(r) to get the result of the interpolating filter

$y(t)=\sum _{r=-\infty }^{\infty }y(r)\delta (t-rT/2)$