filters12(2)

# filters12(2) - ECE-600 Phil Schniter November 5 2010 Filter...

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Unformatted text preview: ECE-600 Phil Schniter November 5, 2010 Filter design: • Filtering is one of the most common forms of signal processing. • A filter can be equivalently described by h [ n ] , H ( z ) , H ( e jω ) = | H ( e jω ) | e j ∠ H ( e jω ) in magnitude & phase, or H ( e jω ) = A ( ω ) e jφ ( ω ) for “signed-magnitude” A ( ω ) ∈ R and “continuous-phase” φ ( ω ) ∈ R . • When designing a filter H ( e jω ) , we are concerned with 1. filtering performance: – want magnitude response | H ( e jω ) | close to target, – want phase response ∠ H ( e jω ) to be agreeable. 2. implementational issues: – complexity, – memory, – robustness to quantization effects. • There are two main classes of digital filter 1. recursive or “ IIR ” (infinite impulse response), and 2. non-recursive or “ FIR ” (finite impulse response). We will see advantages and disadvantages to each. 1 ECE-600 Phil Schniter November 5, 2010 Desired magnitude response: • The desired magnitude response | D ( e jω ) | is often a LPF, HPF, BPF, or notch filter, though sometimes it is more complicated, e.g., a differentiator, raised-cosine, or Hilbert transformer. • The error between actual & desired magnitude responses can be measured in different ways: – peak deviations { δ p ,δ s } in passband and stopband: or A p- 20 log 10 (1- δ p ) , A s- 20 log 10 δ s in dB. – squared error , integrated over ω and possibly weighted: E = π- π W ( ω ) ( | H ( e jω ) | - | D ( e jω ) | ) 2 dω Beware: different error criteria lead to different “optimal” filter designs. 2 ECE-600 Phil Schniter November 5, 2010 Desired phase response: • Sometimes, we want that H ( e jω ) matches a desired response D ( e jω ) in both magnitude and phase. • Other times, we want H ( e jω ) giving “minimum” delay. • More often, we desire a “ linear phase ” response φ ( ω ) =- dω for some d ∈ Z , because the resulting filter H ( e jω ) = A ( ω ) e- jdω alters the signed-magnitude response by A ( ω ) and delays...
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filters12(2) - ECE-600 Phil Schniter November 5 2010 Filter...

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