## Lowpass Filter Design Specifications

Typical design parameters for a lowpass filter are shown in Fig.4.2.

The design parameters are defined as follows:

- stop-band ripple ( dB is common)
- pass-band ripple ( dB typical)
- stop-band edge frequency
- pass-band edge frequency
- TW: transition width
- SBA: stop-band attenuation

^{5.4}For a stop-band gain down around dB, keeping the pass-band ripple at dB, the pass-band ripple becomes around 100 times larger than the stop-band ripple, on a linear scale, but again the stop-band ripple is more likely to yield audible error in typical situations. In summary, the pass-band ripple is an allowed

*gain*deviation, while the stop-band ripple is an allowed ``leakage'' level.

In terms of these specifications, we may define an *optimal FIR
lowpass filter* of a given length to be one which minimizes the
stop-band and pass-band ripple (weighted relatively as desired) for
given stop-band and pass-band edge frequencies. Such optimal filters
are often designed in practice by *Chebyshev* methods, as we
encountered already in the study of *windows* for spectrum
analysis (§3.10,§3.13). Optimal Chebyshev FIR
filters will be discussed further below (in §4.5.2), but
first we look at simpler FIR design methods and compare to optimal
Chebyshev designs for reference. An advantage of the simpler methods
is that they are more suitable for interactive, real-time, and/or
signal-adaptive FIR filter design.

### Ideal Lowpass Filter Revisited

The ideal lowpass filter of Fig.4.1 can now be described by the following specifications:

- The transition width TW is zero ( in Fig.4.2).
- The pass-band and stop-band ripples are both zero

( in Fig.4.2, and ).

**Next Section:**

Optimal (but poor if unweighted) Least-Squares Impulse Response Design

**Previous Section:**

The Ideal Lowpass Filter