The filtering system response plays a major role in determining the overall system response. For this reason familiarity with the fundamental aspects of filter responses is not only a must for the filter designer, but it is advantageous for the system designer and those who specify and use filters. Appreciation of the factors affecting the various responses results in more realistic system and filter requirements. Consequently design time, cost, and problems are reduced.

Chapter Contents:

• 3.1 Ideal Low-Pass Responses
• 3.1.1 Rectangular Magnitude with Linear Phase
• 3.1.2 Impulse Response
• 3.1.3 Step Response
• 3.1.4 Gaussian Magnitude with Linear Phase
• 3.1.5 Impulse Response
• 3.1.6 Step Response
• 3.1.7 Summary of Results
• 3.1.8 Paley-Wiener Condition
• 3.1.9 Minimum-Phase Functions
• 3.1.10 Realizable Networks
• 3.1.11 Minimum-Phase Network with Rectangular Magnitude Response
• 3.1.12 Minimum-Phase Network with Linear Phase Response
• 3.2 Mathematical Approximations
• 3.2.1 Taylor Approximation
• 3.2.2 Chebyshev Approximation
• 3.2.3 Least-Squares Approximation
• 3.3 Realizable Low-Pass Response Characterization
• 3.3.1 The Normalized Low-Pass Response
• 3.3.2 All-Pole Networks
• 3.3.3 Group Delay Function
• 3.4 Rectangular Magnitude Response Approximations
• 3.4.1 Maximally Flat (Butterworth)
• 3.4.2 Equiripple (Chebyshev)
• 3.4.3 Legendre
• 3.4.4 Least Squares
• 3.5 Constant Group Delay Approximations
• 3.5.1 Maximally Flat (Bessel) Delay
• 3.5.2 Equiripple (Chebyshev) Delay
• 3.5.3 Least-Squares Delay
• 3.6 Ideal Time-Domain Approximations
• 3.6.1 Gaussian Response
• 3.6.2 Equiripple Transient Response Overshoots
• 3.6.3 Monotonic Step Response with Minimum Rise Time
• 3.7 Special Cases
• 3.7.1 Transitional Responses
• 3.7.2 Specific Pole Locations
• 3.7.3 Synchronous Response
• 3.7.4 Cauer Filters
• 3.8 Rise Time and Noise Bandwidth
• 3.8.1 Rise Time
• 3.8.2 Noise Bandwidth
• 3.8.3 Relationship Between Noise Bandwidth and Impulse Response Energy
• References
• Problems

Inspec keywords: linear systems; filtering theory

Other keywords: linear system response; filtering system response

Subjects: Signal processing theory; Filtering methods in signal processing