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NHE2404 DSP Applications Assignment

Parametric Equalizer

Weighting: 30%

Outcomes Being Assessed

(d), (e), (f).

Introduction

Bi-quad filters have two poles and two zeros arranged in the Z-plane as shown in figure 1.

Figure 1. Bi-quad Filter

These filters are widely used in the audio industry because they can either amplify or attenuate certain frequency components in a signal. If the Pole radius (R) is greater than the Zero radius (r) the filter will amplify components around the centre frequency and if r is greater than R then the filter will attenuate components around the centre frequency.

A practical application of the bi-quad filter is in parametric equalizers, where the filter behaviour is specified using the parameters: centre frequency, gain/attenuation and bandwidth (EQ or Q factor) – see figure 2.

Figure 2 Parametric Equalizer Controls

Commercial parametric equalizers commonly have a number of independent filters.

Tasks

Design bi-quad filters to meet the following specifications:

Centre Frequency Gain/Attenuation Q
Filter 1 500 Hz -10 dB 3.5
Filter 2 1000 Hz -10 dB 5
Filter 3 2000 Hz +10 dB 6

Simulate the filters independently and in combination with each other using a tool such as MATLAB in order to verify that they perform as specified.
Represent the filters you design in the following formats:
Z-transfer function.
Z-Plane diagram.
Signal flow-graph.
Magnitude response.
Difference equation.

Develop a Flowcode program to implement your EQ digital filter(s) on the dsPIC development boards, and evaluate EQ real-time performance.
Record your assignment work in an logbook on Unilearn.
Your logbook should be presented in a standard format, e.g. Date/time, Objectives, Equipment, Procedure, Results, and Discussion.