Digital Filters

• Designed to have certain characteristics in the frequency domain
• Advantages over analog filters:
  • Linear phase response
  • Robust to environmental changes (temperature)
  • Can be modified if implemented with a microprocessor or digitized
• Disadvantages over analog filters:
  • Speed limitation at high RF frequencies
  • Noise generated from sampling and quantization

FIR Vs IIR Filters

• Can find more at FIR and IIR Filters

FIR

• Linear phase
• Always BIBO stable
• More robust to quantization of filter coefficients
• Difficult to design without CAD tools

IIR

• Nonlinear phase, especially at the edges of bands
• Not guaranteed to be BIBO stable
• Can be designed from analog filters (less difficult to design)
• Can process signals more quickly to meet higher frequency specifications

Recommended Use Cases

• FIR is recommended when you have a small number of filter coefficients and the phase distortion needs to be minimized
• IIR is recommended when sharp band edges are needed and the frequency is very high

Filter Design Steps

1. Specify filter requirements
   • Frequency domain specs
   • Processing time
   • Implementation method
   • Cost of filter
2. Calculate filter coefficients
   • FIR coefficients determined using windowing, frequency sampling, or Parks-McClellan optimization method
   • IIR coefficients determined by transforming analog filters or using zero-pole placement
3. Verify the design meets specifications
4. Realize the design using a computer
5. Analyze the effect of finite word length on the performance
   • Check that the specifications met with filter coefficient quantization
6. Implement the filter in hardware/software
   • Need memory to store filter coefficients and present/past inputs/outputs, multipliers, and adders

FIR Low Pass Filter Design Example

IIR Low Pass Filter Design Example

References