filter.sq

Design of analog and digital filters

Different filters, defined in continuous time or discrete time. Low-pass, high-pass, band-pass and band-stop can be adjusted interactively in the frequency magnitude diagram.

First contact

A two-by-two array of figures is displayed. The top row represents a continuous-time filter, while the bottom row represents the same filter converted with the bilinear transform. The left column shows the magnitude of the frequency response of the filter; the right column shows the zeros (as circles) and the poles (as crosses) of the filters in the complex plane of the Laplace transform for the continuous-time filter and of the z transform for the discrete-time filter. Initially, the filter is a Chebyshev filter, whose bandwidth (vertical blue line) and bandwidth ripples (horizontal red line) can be manipulated.

Figures

Frequency Response Magnitude

The magnitude of the frequency response of the continuous-time filter is displayed in black. The limits of the bandwidth (lower and/or higher, depending on the kind of filter) are displayed as vertical blue lines and can be manipulated; if the Shift key is held down, both lines are moved together to keep their ratio constant. If the upper limit is moved to the left of the lower limit, or if the lower limit is moved to the right of the upper limit, bandwidth filters become bandstop and vice-versa. For Chebyshev filters, the lower or upper limit of the ripples is displayed as a horizontal red line and can be manipulated.

Frequency Response Phase

The phase of the frequency response of the continuous-time filter is displayed in black.

Poles

In the complex plane of the Laplace transform, the poles of the continuous-time filter are displayed as crosses, and the zeros as circles.

Frequency Response Magnitude (discrete-time)

The magnitude of the frequency response of the discrete-time filter is displayed in black. The limits of the bandwidth (lower and/or higher, depending on the kind of filter) are displayed as vertical blue lines and can be manipulated. For Chebyshev filters, the lower or upper limit of the ripples is displayed as a horizontal red line and can be manipulated.

Frequency Response Phase (discrete-time)

The phase of the frequency response of the discrete-time filter is displayed in black.

Poles (discrete-time)

In the complex plane of the z transform, the poles of the discrete-time filter are displayed as crosses, and the zeros as circles.

Settings

Kind of filter

The kind of filter can be chosen between Butterworth, Chebyshev (ripples of the magnitude in the bandwidth), or Inverse Chebyshev (ripples of the magnitude outside the bandwidth).

Lowpass Filter

High frequencies are filtered out.

Highpass Filter

Low frequencies are filtered out.

Bandpass Filter

Low and high frequencies are filtered out, leaving medium frequencies.

Bandstop Filter

Medium frequencies are filtered out, leaving low and high frequencies.

Filter Order

The order of the filter can be entered in a dialog box. Note that large orders (>10) often result in inaccurate figures, because of numeric problems.

Transition Frequencies

The lower and upper limits of the bandwidth can be entered in a dialog box as a vector of two elements. If the lower limit is 0, the filter is low-pass; if the upper limit is inf, the filter is high-pass. If the lower limit is larger than the upper limit, the filter is bandstop.

Sampling Period

The sampling period can be entered in a dialog box.