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
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 ).
Optimal (but poor if unweighted) Least-Squares Impulse Response Design
The Ideal Lowpass Filter