Digital FIR Raised Cosine Filter Design (DSP Blockset)

Design and implement a raised cosine FIR filter.

Library

Description

The Digital FIR Raised Cosine Filter Design block uses the firrcos function in the Signal Processing Toolbox to design a lowpass, linear-phase, digital FIR filter with a raised cosine transition band. The block applies the filter to a discrete-time input using the Direct-Form II Transpose Filter block.

An M-by-N sample-based matrix input is treated as M*N independent channels, and an M-by-N frame-based matrix input is treated as N independent channels. In both cases, the block filters each channel independently over time, and the output has the same size and frame status as the input.

The frequency response of the raised cosine filter is

where H(f) is the magnitude response at frequency f, f_n0 is the normalized cutoff frequency (-6 dB) specified by the Upper cutoff frequency parameter, and R is a rolloff factor in the range [0,1] determining the passband-to-stopband transition width.

The Square-root raised cosine filter option designs a filter with magnitude response . This is useful when the filter is part of a pair of matched filters.

When the Design method parameter is set to Rolloff factor, the secondary Rolloff factor parameter is enabled, and R can be directly specified. When Design method is set to Transition bandwidth, the secondary Transition bandwidth parameter is enabled, and the transition region bandwidth, f, can be specified in place of R. The transition region is centered on f_n0 and must be sufficiently narrow to satisfy

The Upper cutoff frequency and Transition bandwidth parameter values are normalized to half the sample frequency.

The Window type parameter allows you to apply a variety of different windows to the raised cosine filter. See the Window Function block reference for a complete description of the available options.

Algorithm

The filter output is computed by convolving the input with a truncated, delayed, windowed version of the filter's impulse response. The impulse response for the raised cosine filter is

which has limits

and

The impulse response for the square-root raised cosine filter is

which has limits

and

Dialog Box

Filter order: The order of the filter. The filter length is one more than this value.
Upper cutoff frequency: The normalized cutoff frequency, f_n0. A value of 1 specifies half the sample frequency. Tunable.
Square-root raised cosine filter: Selects the square-root filter option, which designs a filter with magnitude response . Tunable.
Design method: The method used to design the transition region of the filter, Rolloff factor or Transition bandwidth. Tunable.
Rolloff factor: The rolloff factor, R, enabled when Rolloff factor is selected in the Design method parameter. Tunable.
Transition bandwidth: The transition bandwidth, f, enabled when Transition bandwidth is selected in the Design method parameter. Tunable.
Window type: The type of window to apply. See the Window Function block reference. Tunable.
Stopband attenuation in dB: The level (dB) of stopband attenuation, R_s, for the Chebyshev window. Tunable.
Beta: The Kaiser window parameter. Increasing widens the mainlobe and decreases the amplitude of the window sidelobes in the window's frequency magnitude response. Tunable.
Initial conditions: The filter's initial conditions, a scalar, vector, or matrix. See the Direct-Form II Transpose Filter block reference for complete syntax information.

References

Proakis, J. G. Digital Communications. Third ed. New York, NY: McGraw-Hill, 1995.

Proakis, J. G. and M. Salehi. Contemporary Communication Systems Using MATLAB. Boston, MA: PWS Publishing, 1998.

See Also

Digital FIR Filter Design
DSP Blockset

Digital IIR Filter Design
DSP Blockset

Direct-Form II Transpose Filter
DSP Blockset

Least Squares FIR Filter Design
DSP Blockset

Remez FIR Filter Design
DSP Blockset

Window Function
DSP Blockset

Yule-Walker IIR Filter Design
DSP Blockset

firrcos
Signal Processing Toolbox

Digital FIR Filter Design	DSP Blockset
Digital IIR Filter Design	DSP Blockset
Direct-Form II Transpose Filter	DSP Blockset
Least Squares FIR Filter Design	DSP Blockset
Remez FIR Filter Design	DSP Blockset
Window Function	DSP Blockset
Yule-Walker IIR Filter Design	DSP Blockset
`firrcos`	Signal Processing Toolbox

See Filter Designs for related information.

Digital FIR Filter Design Digital IIR Filter Design