Publisher Summary Finite impulse response (FIR) filters get their name from the way they respond to an impulse. These filters are essentially sophisticated versions of the simple moving average filter. In general, the idea behind FIR filter design is to define the transfer function as a function of frequency. This function of frequency, generally named H(ω), is then transformed into a sequence that is a function of time: h[n]. The transformation is accomplished by the inverse discrete Fourier transform (IDFT). A filter is implemented by convolving h(n) with the input sequence x[n]. The resulting sequence, y[n], is the output of the filter. This process works for either a real-time process or an off-line processing system. This chapter explains the filter-design process for an FIR filter, demonstrates the design of a typical digital-signal-processing (DSP) application, and use of the accompanying DSP Calculator software. The FIR filter has a number of significant advantages. It is unconditionally stable, easily designed, and easily implemented. It is possible to design an FIR filter with a linear phase delay. The one major disadvantage of the FIR is that it can require a large number of computations to implement. A general rule is that an FIR filter should not make use of more than about 30 taps. Beyond this, the response of the filter can get mushy and the noise caused by truncations can become a problem. However, like all rules of thumb, this one needs to be applied with some caution.