Length-15 equiripple lowpass kernel:

Magnitude plot of the filter:

A Bode plot of the filter's frequency spectrum:

An equiripple highpass FIR filter:

Bode plot of the frequency response of the filter:

Create an equiripple bandpass kernel:

Specify different band weights:

Create an even-length, full-band differentiator:

Create a Hilbert transformer:

Phase plot of a Hilbert transformer:

Create an equiripple half-band lowpass filter:

Magnitude plot of the filter and the half-band frequency :

Convert the half-band lowpass filter to highpass:

Magnitude plots of the two half-band filters:

Create a differentiating filter and apply to a sinusoidal sequence:

Create a differentiating filter and calculate the gradient of an image:

Row derivatives (enhanced):

Column derivatives (enhanced):

The gradient image:

Create an orthogonal sequence to x using a Hilbert transformer:

Show that the two sequences are orthogonal:

Create a list of Nyquist filters:

Compare the stopband frequency response behavior of an equiripple (blue) and least-squares (red) realization of a filter:

In a half-band filter of length , coefficients at positions for positive integer values of have zero values:

In a -band filter, coefficients at positions have zero values:

Neighboring bands cannot have the same amplitudes:

Edge frequencies of neighboring bands should be distinct:

Filter design using the equiripple method does not always converge:

Substantially uneven transition bands in the Hilbert transformer will lead to an excessive ripple:

Substantially uneven transition bands in multiband filters will lead to undesirable ripples: