Designs a digital IIR Elliptic filter.
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ELLIPTIC( |
type, order, rate, pb1, pb2, ripple, attn, sb1, sb2) |
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type |
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An integer, the filter type.
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order |
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Optional. An integer, the filter length. If not specified, the filter order is automatically estimated. | ||||||||
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rate |
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A real, the sample rate of the filter in Hertz. | ||||||||
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pb1 |
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A real, the first passband edge in Hertz. | ||||||||
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pb2 |
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A real, the second passband edge in Hertz. | ||||||||
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ripple |
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A real, the passband ripple in dB. | ||||||||
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attn |
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A real, the stopband attenuation in dB. | ||||||||
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sb1 |
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Optional. A real, the first stopband
edge frequency in Hertz. Defaults to | ||||||||
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sb2 |
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Optional. A real, the second stopband
edge frequency in Hertz. Defaults to |
A series, the Elliptic filter coefficients in multi-stage cascade format.
W1: elliptic(1, 1000.0, 100.0, 3, 40)
W2: 20*log10(filtmag(W1, 1024));sety(-80, 10)
W1 creates an Elliptic lowpass filter with a sample rate of 1000 Hz, a passband ripple of 3 dB and a stopband attenuation of 40 dB. The stopband frequency defaults to 150 Hz. W2 displays the frequency response of the resulting filter.
W1: elliptic(1, 1000.0, 100.0, 3, 40)
W2: gsin(1000, 1/1000, 3) + gsin(1000, 1/1000, 250)
W3: iirfilter(W2, W1)
Creates the same IIR lowpass filter as the previous example. W2 contains a series with two sinusoids and W3 applies the filter to recover the lower frequency sinewave.
W2: elliptic(1, 1000.0, 100.0, 3.0, 50.0, 130.0)
Creates a similar filter except the stopband attenuation is set to 50 dB and the stopband edge is set to 130 Hz.
W3: elliptic(3, 18, 1000.0, 200.0, 300.0)
Creates an Elliptic bandpass filter with a sample rate of 1000 Hz, a filter order of 18 and a passband that extends from 200 Hz to 300 Hz.
W4: elliptic(3, 24, 1000.0, 200.0, 300.0, 2.0, 50.0, 180.0, 320.0)
Creates a similar Elliptic bandpass filter as above except the order is set to 24 (resulting in 121 coefficients), the desired passband ripple is set to 2 dB and the desired stopband attenuation is set to 50 dB. The first stopband edge is 180 Hz and the last stopband edge is set to 320 Hz.
The generic ELLIPTIC filter specifications are depicted as follows:
Type = 1, Lowpass
Type = 2, Highpass
Type = 3, Bandpass
Type = 4, Bandstop
For filter type 1 and 2 (lowpass and highpass), the band frequencies pb2 and sb2 are omitted.
The ripple and attn parameters are required.
ELLIPTIC uses the Bilinear Transform Method to compute the coefficients by converting an analog filter prototype to the digital domain. The filter order refers to the number of resulting poles (2X poles result for type 3 and type 4) and is not equivalent to the number of filter coefficients.
The bands edges must lie between 0.0 and 0.5 * rate (the Nyquist frequency). Overlapping band edges are not permitted.
The filter coefficients are produced in multi-stage bi-quad form suitable for processing by the CASCADE function.
An ELLIPTIC filter has ripple in both the passband and stopband but generally results in fewer coefficients than other IIR filter types for a given filter specification.
See BANDPASS, BANDSTOP, HIGHPASS and LOWPASS to design linear phase FIR filters using the Remez Exchange method.
ELLIPTIC requires the DADiSP/Filters Module.
Oppenheim and Schafer
Discrete Time Signal Processing
Prentice Hall, 1989
Digital Signal Processing Committee
Programs for Digital Signal Processing
I.E.E.E. Press, 1979
Bateman & Yates
Digital Signal Processing Design
Computer Science Press, 1989