90 Degree Phase Shift Filter Design

90 degree phase shifters are used to shift the phase of the signal by 90 degrees while applying a constant gain to the magnitude. They are commonly used in Hilbert filters and differentiators. Conceptually, 90 degree phase shifters could treat the entire frequency spectrum as one pass band. However, a better fit is obtained by having transition bands on the edges, especially on the low frequency side. A 90 degree phase shifter is characterized by the limits and characteristics of its pass band and by a few overall characteristics.

The pass band extends over the frequencies of interest, and is characterized by a desired gain value (usually +0 dB or x1) and a ripple value which measures the maximum desired deviation from that gain value. Transition bands may exist above and below the pass band; they represent unspecified regions within which no constraints are placed on the filter. Narrow or non-existent transition bands, especially on the low frequency side, will generally force either a poorer fit or a longer filter.

In addition to the limits and characteristics of each band, an FIR filter design depends on the sampling frequency of the input data. In fact, the usable frequency range is between DC (0 Hz) and half the sampling frequency, which is called the folding frequency. A filter designed for data sampled at one frequency will not behave the same with data sampled at a different rate: the band characteristics remain the same, but the band limits change proportionally with the change in sampling frequency.

Two additional characteristics of an FIR filter are its length and symmetry. The length refers to the number of “taps” or coefficients; increasing the length generally improves the fit at the expense of design speed, execution speed and sample delay. Even length and odd length filters display significantly different behavior. Filter symmetry (even, odd or none) refers to the symmetry of the coefficients and is independent of the evenness or oddness of filter length, although there is some interplay between the two characteristics.

90 degree phase shifters are designed to have odd symmetry to produce the 90 degree phase shift. Even or odd length may be used depending on whether the gain at the folding frequency should be non-zero or zero and whether an integer sample delay is desired.

As an example, consider the following 90 degree phase shifter designed with odd symmetry and a sampling frequency of 10 KHz:

When this filter is generated with 7 taps, the coefficients and frequency response amplitude graph are as follows:

Taps: 0.127288 0 0.601376 0 -0.601376 0 -0.127288

If you need to design a 90 degree phase shift filter, please contact us today!