How to test and implement FIR filters?

　　Here are a few methods:

　　Impulse Test: A very simple and effective test is to put an impulse into it (which is just a "1" sample followed by at lest N - 1 zeroes.) You can also put in an "impulse train", with the "1" samples spaced at least N samples apart. If all the coefficients of the filter come out in the proper order, there is a good chance your filter is working correctly. (You might want to test with non-linear phase coefficients so you can see the order they come out.) We recommend you do this test whenever you write a new FIR filter routine.

　　Step Test: Input N or more "1" samples. The output after N samples, should be the sum (DC gain) of the FIR filter.

　　Sine Test: Input a sine wave at one or more frequencies and see if the output sine has the expected amplitude.

　　Swept FM Test: From Eric Jacobsen: "My favorite test after an impulse train is to take two identical instances of the filter under test, use them as I and Q filters and put a complex FM linear sweep through them from DC to Fs/2. You can do an FFT on the result and see the complete frequency response of the filter, make sure the phase is nice and continuous everywhere, and match the response to what you'd expect from the coefficient set, the precision, etc."

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