DESIGN AND IMPLEMENTATION OF TWO BAND DIGITAL CROSS OVER SYSTEM

                                   ABSTRACT           

In audio system, there is often a situation where the application requires the entire audible range of frequencies, but this is beyond the capability of any single speaker driver. So we combine several drivers such as the speaker cones and horns, each covering different frequency range, to reproduce the full audio frequency range.

A typical two band digital cross over can be designed with the help of low pass and high pass filters. There are two speaker drivers. The woofer responds to low frequencies and the tweeter responds to high frequencies. The incoming digital audio signal is split into two bands by using a low pass filter and high pass filter in parallel. We then amplify the separated audio signals and send them to their respective corresponding speaker driver. Hence the objectives is to design the low pass filter and high pass filter so that their combined frequency response is flat, while keeping the transition as sharp as possible to prevent audio signal distortions in transition frequency range. Although traditional cross over systems are designed using active circuits or passive circuits, the digital cross over system provides a cost effective solution with programmable ability, flexibility, and high quality.

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Objectives:   

(a) Load, display and manipulate of speech signals.

(b) Compute and plot the spectrum of speech signals.

(c) Design of low pass and high pass filter for given specifications.

(d) Design of the FIR and IIR filters.

Basic Theory:

In audio system, there is often a situation where the application requires the entire audible range of frequencies, but this is beyond the capability of any single speaker driver. So we combine several drivers such as the speaker cones and horns, each covering different frequency range, to reproduce the full audio frequency range.

A typical two band digital cross over can be designed with the help of low pass and high pass filters. There are two speaker drivers. The woofer responds to low frequencies and the tweeter responds to high frequencies. The incoming digital audio signal is split into two bands by using a low pass filter and high pass filter in parallel. We then amplify the separated audio signals and send them to their respective corresponding speaker driver. Hence the objectives is to design the low pass filter and high pass filter so that their combined frequency response is flat, while keeping the transition as sharp as possible to prevent audio signal distortions in transition frequency range. Although traditional cross over systems are designed using active circuits or passive circuits, the digital cross over system provides a cost effective solution with programmable ability, flexibility, and high quality.

Task1:

Design a digital FIR cross over system using the following specifications.

Windows:  (a) Rectangular window (b) Hamming window (c) Hanning window  

Sampling rate    :  44,100 Hz

Cross over frequency   :  1000 Hz

Transition band    :  600 to 1400 Hz

Low pass filter:  

Pass band frequency    :  0 to 600 Hz

Pass band ripple    :  0.02 dB 

Stop band edge     :  1400 Hz

Stop band attenuation    :  50 dB

From these specifications determine the cut-off frequency and filter length.

Task2:

Design a IIR digital cross over system using the following specifications.

Type of filter:     IIR Filter

Sampling rate    :  44,100 Hz

Cross over frequency   :  1000 Hz

High Pass Filter:

Third order Butterworth filter

Cut-off frequency    :  1000 Hz

Low Pass Filter:

Third order Butterworth filter

Cut-off frequency    :  1000 Hz

Determine

(a) The transfer functions and difference equation for the high-pass and low-pass filters.

(b) Frequency responses for the high-pass and low-pass filters.

(c) Combined frequency response for both filters.