DSP Blockset

Designing Discrete-Time Special IIR and FIR Filters

The Remez FIR Filter Design, Yule-Walker IIR Filter Design, and Least Squares FIR Filter Design blocks design and implement IIR or FIR filters with arbitrary magnitude responses, including multiband responses.

The Yule-Walker IIR Filter Design block designs recursive IIR digital filters by fitting a specified frequency response based on arbitrary piecewise linear magnitude responses. For more on the Yule-Walker algorithm, see the description of the yulewalk function in the Signal Processing Toolbox.

The Remez FIR Filter Design and Least Squares FIR Filter Design blocks design FIR filters using the Parks-McClellan and least-squares techniques, respectively. These techniques reflect two error minimization schemes that provide optimal fits to a desired frequency response, each using a different definition of "optimal fit":

• The Remez FIR Filter Design block implements the Parks-McClellan algorithm, which uses the Remez exchange algorithm and Chebyshev approximation theory to design filters with optimal fits between the desired and actual frequency responses. The filters are optimal in the sense that they minimize the maximum error between the desired frequency response and the actual frequency response over the designated bands. Filters designed in this way exhibit an equiripple behavior in their frequency response, and hence are also known as equiripple filters.
• The Least Squares FIR Filter Design block minimizes the integral of the squared error between the desired frequency response and the actual frequency response. This technique provides a better response over most of the passband and stopband than does the Parks-McClellan algorithm. At the band edges, however, the least-squares technique provides a poorer fit than does an equiripple filter designed to fit the same response.

For more on the Parks-McClellan and least squares design techniques, see the descriptions of the remez and firls functions in the Signal Processing Toolbox.

The following four sections provide more information about the parameters provided by these blocks:

• Frequency and Magnitude Parameter Overview
• Frequency and Magnitude Parameters: Yule-Walker IIR Filter Design
• Frequency and Magnitude Parameters: Remez and Least Squares FIR Filter Design
• Weight Parameters

The final section, Example: Least Squares Multiband Filter, provides an example that uses the Least Squares FIR Filter Design block.

Designing Continuous-Time Classical IIR Filters

Frequency and Magnitude Parameter Overview