filters12(2)

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

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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 j ) = | H ( e j ) | e j H ( e j ) in magnitude & phase, or H ( e j ) = A ( ) e j ( ) for signed-magnitude A ( ) R and continuous-phase ( ) R . When designing a filter H ( e j ) , we are concerned with 1. filtering performance: want magnitude response | H ( e j ) | close to target, want phase response H ( e j ) 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 j ) | 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 { p , s } in passband and stopband: or A p- 20 log 10 (1- p ) , A s- 20 log 10 s in dB. squared error , integrated over and possibly weighted: E = - W ( ) ( | H ( e j ) | - | D ( e j ) | ) 2 d 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 j ) matches a desired response D ( e j ) in both magnitude and phase. Other times, we want H ( e j ) giving minimum delay. More often, we desire a linear phase response ( ) =- d for some d Z , because the resulting filter H ( e j ) = A ( ) e- jd alters the signed-magnitude response by A ( ) and delays...
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filters12(2) - ECE-600 Phil Schniter November 5, 2010...

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