Generates filter coefficients for a digital or analog Chebyshev Type I filter.

Syntax

Num, Den = Cheby1(Order,Fc,PassMag)

Num, Den = Cheby1(Order,Fc,PassMag,Type)

Num, Den = Cheby1(Order,Fc,PassMag,Band,Type)

Num, Den = Cheby1(Order,Fc1,Fc2,PassMag)

Arguments

Name

Description

Order

A positive integer specifying the order of the filter.  For band pass and band stop filter, the order is twice this value.

Fc

The corner frequency in Hz of a low pass or high pass filter, or a vector of two corner frequencies for a band pass or band stop filter.  For a digital filter, Fc is normalized by the Nyquist frequency and has values in the interval (0,1).  For an analog filter, Fc has positive value(s).

Band

(optional)

The filter band specifier.  When Fc is a value, Band can be either ‘low’ (default) or ‘high.’  When Fc is a vector, Band is omitted for a band pass filter and ‘stop’ for a band stop filter.

Type

(optional)

The digital/analog flag.  For analog, set to ‘s.’  For digital, set to ‘z’ (default).

Fc1, Fc2

For the Templex™ style convention, Fc1 and Fc2 are the normalized corner frequencies in Hz of a digital filter.  For a low pass filter, Fc1 = 0. For a high pass filter Fc2 = 0 or 1. For a band pass filter, Fc1 < Fc2. For a band stop filter, Fc1 > Fc2.

PassMag

Magnitude attenuation in decibels (dB) at the nonzero corner frequencies specified by Fc.  This is also called the passband ripple. Must be negative.

Outputs

Name

Description

Num

Vector of numerator coefficients in descending power of s or z.  Its length is one more than the filter order.

Den

Vector of denominator coefficients in descending power of s or z.  Its length is one more than the filter order.

Example 1

A low-pass second order Chebyshev I filter with a corner frequency at 250 Hz and a corresponding magnitude of -3 dB, where the data sampling frequency is 1000 Hz.

Syntax

b, a = Cheby1(2,0,250/500,-3)

Result

b = 0.2130    0.4260    0.2130

a = 1.0000   -0.2483    0.4518

Example 2

A band-pass second order Chebyshev I filter with low corner and high corner frequencies of 150 Hz and 300 Hz, respectively, with corresponding magnitude responses of -3 dB, where the data sampling frequency is 1000 Hz.

Syntax

b, a = Cheby1(2,150/500,300/500,-3)

Result

b = 0.0860 0 -0.1721 0 0.0860

a = 1.0000   -0.5406    1.1609   -0.3881    0.5655

Comments

For digital filters, the Nyquist frequency is half the sampling frequency.  All frequency arguments are to be normalized with this value.

See Also:

Butter

Cheby2

Ellip