page_title: Parks–McClellan filter design algorithm
hierarchical_section_title: Parks–McClellan filter design algorithm
caption_attribution_description: English: H(ω)
context_page_description: The Parks–McClellan algorithm, published by James McClellan and Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite impulse response filter. The Parks–McClellan algorithm is utilized to design and implement efficient and optimal FIR filters. It uses an indirect method for finding the optimal filter coefficients.
  The goal of the algorithm is to minimize the error in the pass and stop bands by utilizing the Chebyshev approximation. The Parks–McClellan algorithm is a variation of the Remez exchange algorithm, with the change that it is specifically designed for FIR filters. It has become a standard method for FIR filter design.
context_section_description: The Parks–McClellan algorithm, published by James McClellan and Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite impulse response (FIR) filter. The Parks–McClellan algorithm is utilized to design and implement efficient and optimal FIR filters. It uses an indirect method for finding the optimal filter coefficients.
  The goal of the algorithm is to minimize the error in the pass and stop bands by utilizing the Chebyshev approximation. The Parks–McClellan algorithm is a variation of the Remez exchange algorithm, with the change that it is specifically designed for FIR filters.  It has become a standard method for FIR filter design.
caption: Pass and stop bands of a filter designed by the Parks–McClellan algorithm
   The y-axis is the frequency response H(ω) and the x-axis are the various radian frequencies, ωi. It can be noted that the two frequences marked on the x-axis, ωp and ωs. ωp indicates the pass band cutoff frequency and ωs indicates the stop band cutoff frequency. The ripple like plot on the upper left is the pass band ripple and the ripple on the bottom right is the stop band ripple. The two dashed lines on the top left of the graph indicate the δp and the two dashed lines on the bottom right indicate the δs. All other frequencies listed indicate the extremal frequencies of the frequency response plot. As a result, there are six extremal frequencies, and then we add the pass band and stop band frequencies to give a total of eight extremal frequencies on the plot.
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