create an IIR digital filter from an analog prototype
Digital filter design methods.
This method obtains a finite impulse response (FIR) from a given prototype filter specification in the frequency domain by means of the inverse discrete-time Fourier transform.
Define a zero-phase ideal lowpass filter with a cutoff frequency of 1.2 radians per sample.
The impulse response is obtained by taking the inverse discrete-time Fourier transform of the filter specification:
Evaluating this expression for integer values of from to will return a filter of length .
Create a lowpass FIR filter of length 15 with a cutoff frequency of 1.2 radians per sample:
This method minimizes the mean-squared error between the ideal specification and the resulting FIR filter:
The least-squares method is also known as the window-based method. The mean-squared error can be diminished by applying a smoothing window to the FIR returned by LeastSquaresFilterKernel.
Create a Hann window of length 15:
Apply the window to the lowpass FIR filter h:
Different windows return different attenuations. Select a window type by the degree of the desired attenuation.
Compare attenuation levels of four selected windows
Frequency Sampling Method
Frequency sampling allows the creation of an FIR filter by specifying the filter's amplitude spectrum on the interval at a finite number of uniformly spaced frequency locations.
Sample an ideal lowpass filter at for from 0 to 5:
Create an odd-length, even-symmetry lowpass filter:
Show the ideal lowpass filter, amplitude samples, and the resulting filter:
The Parks–McClellan–Rabiner (1979) algorithm is one of the most popular methods of designing linear-phase FIR filters. It minimizes the maximum deviation from the desired ideal frequency response and results in filters with equal ripples in each of the bands of the filter.
Create a multiband filter of length 55:
Plot the magnitude response of an equiripple multiband filter:
Create a Digital Filter from an Analog Prototype
A popular method of creating digital filters is to transform analog prototypes to their digital equivalents using the bilinear transformation. The result is an infinite impulse response (IIR) filter, represented as a TransferFunctionModel.