What kind of function is the Parks–McClellan filter used?

I designed a low pass Parks–McClellan filter in Matlab. But how does Matlab create this filter mathematically? What is the transfer function?

Answer 1

[Meet]

Hi Zaref,

The Parks–McClellan filter is a type of finite impulse response (FIR) filter designed using the Remez exchange algorithm. It works by minimizing the maximum error between the desired and actual frequency responses, resulting in a filter that has ripples of equal height in both the passband and stopband. This is achieved through an iterative process that adjusts the filter coefficients to best match the desired specifications.

MATLAB uses the concept of Chebyshev approximation, as mentioned in the references section of the documentation: https://www.mathworks.com/help/signal/ref/firpm.html.

You can also view the implementation details of the "firpm" function by right-clicking on the function name and selecting the "Open 'firpm'" option.

I hope this resolves your query!