The Engineer's Guide to Standards Conversion - Snell

clairvoyant powers. Shortening the impulse from infinity gives rise to the name of
Finite Impulse Response (FIR) filter. An FIR filter can be thought of an an ideal
filter of infinite length in series with a filter which has a rectangular impulse
response equal to the size of the window. The windowing causes an aperture effect
which results in ripples in the frequency response of the filter.
Ideal filter
-infinite window
Frequency
Practical filter
-finite window
Premature roll-off
Frequency
Ripples
Fig 2.7.2
The effect of a finite window is to impair the ideal frequency
response as shown here.
Fig 2.7.2 shows the effect which is known as Gibbs’ phenomenon. Instead of
simply truncating the impulse response, a variety of window functions may be
employed which allow different trade-offs in performance. A digital filter simply has
to create the correct response to an impulse. In the digital domain, an impulse is one
sample of non-zero value in the midst of a series of zero-valued samples.
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