Signal Processing Toolbox

Frequency and Magnitude Specifications Region:
Hilbert Transformer

Select the units for frequency specifications from the Frequency units list:

• Hz
• kHz
• MHz
• Normalized (0 to 1), where 1 corresponds to the Nyquist frequency

For all units except Normalized, specify the sampling frequency, Fs.

Specify the following parameters in the text boxes:

• Freq. vector - A vector defining the frequency points at which the response magnitude is specified, in ascending order. Must have an even length the same as Mag. vector.
• Mag. vector - A vector defining the response magnitudes at the specified frequencies. Must have an even length the same as Freq. vector.
• Weight vector - A vector defining the relative weight that should be given to each frequency band. Must be half the length of Freq. vector.

Each odd-indexed frequency-amplitude pair defines the left endpoint of a line segment representing the desired magnitude response in that frequency band. The corresponding even-indexed frequency-amplitude pair defines the right endpoint. Between the frequency bands specified by these end-points, there may be undefined sections of the specified frequency response. These are called "don't care" or "transition" regions, and the magnitude response in these areas is a by-product of the optimization in the other (specified) frequency ranges.

The Weight vector specifies the emphasis to be placed on minimizing the error in certain frequency bands relative to others, one weight per band. In most cases, Hilbert transformers have only a single band, so the weight is a scalar value that does not affect the final filter. However, the Weight vector is useful when designing an antisymmetric multiband filter, such as a Hilbert transformer with stopbands.

See Multiband FIR Filter Design with Transition Bands and remez for more information.

Frequency and Magnitude Specifications Region: Differentiator

Frequency and Magnitude Specifications Region: Multiband