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Module Code: UFMFH8-15-3
Module Name: Digital Signal Processing
Academic Year: 2023/2024
Coursework
Page 1 of 3
Coursework
Implementing a 7-Band Equaliser
1. Task
Design and implement a 7-band equaliser using the Cypress FM4 board subject to the design
requirements given below. This an individual work.
2. Equaliser Primer
An n-band equaliser is a device used to correct the frequency response characteristic of a signal
processing system. Equalisers can be implemented using digital or analogue filters. The whole
bandwidth of the equaliser is divided into n frequency bands, which can be individually amplified (a
7-band equaliser is shown in Figure 1). Thus, any desired frequency characteristic can be
approximated. Very simple 3-band or 7-band equalisers are found in nearly every modern hi-fi system.
Basically, an n-band equaliser is implemented using a low pass filter, a high pass filter and a set of
n-2 band pass filters.
+ Signal in Signal out
Gain
Frequency
Low Pass
Gain
Frequency
Band Pass
Gain
Frequency
Band Pass
Gain
Frequency
High Pass
Figure 1: 7-Band Equaliser
3. Filters’ Design Requirements:
Low Pass Filter
High pass Filter
Five Band pass Filters
It is suggested that the filters (Low pass filter, Band Pass filters and High pass filter) have equal
bandwidths. Is this the best distribution Refer to deliverable 5(f).
Module Code: UFMFH8-15-3 Academic Year: 2022/2023
Module Name: Digital Signal Processing Coursework
Page 2 of 3
Design seven filters. A low pass filter, 5 band pass filters and a high pass filter according to the
following requirements:
Equalizer bandwidth: 24 kHz
It is suggested that the filters (Low pass filter, Band Pass filters and High pass filter) have equal
bandwidths.
Pass band ripple: max. 5%.
Stop band rejection: min 40 dB.
Mild phase distortions are acceptable.
Sampling frequency is 48 kHz.
The passband ripples apply also to the combination of the seven filters. It is expected that the
frequency response of the 7 combined filters falls into a band of 0.95 to 1.05 (assuming a
normalised response). To achieve this, it will be necessary to scale the individual filters.
NB: The sampling frequency of the Wolfson audio card for this work is 48 KHz.
4. Design Hints
Finite impulse response filters (FIR) should be adopted.
Any type of window can be used. However, it might be a good idea to think about a filter with a
Hamming Window, a Hann Window or a Kaiser Window.
Any software tool can be used to determine the filters’ coefficients (e.g. Matlab’s filterDesigner
[1] or Excel).
5. Deliverables
You must submit an individual report containing the following (12 A4 sheets Max):
a. Derivation of the filter coefficients (using the theory covered in the lectures).
You don’t have to calculate all the coefficients. Three coefficients per filter will
be enough. Be careful, when calculating the coefficients for both the bandpass
and the high pass filters.
b. The frequency response of each filter based on the generated coefficients (must
be labelled using meaningful units). The diagrams must prove that each filter
fulfils the requirements.
c. A diagram showing that the combination of the seven filters can be scaled such
that the frequency response stays in at 0db plus minus 5% for all relevant
frequencies.
d. All diagrams require a short description how they were obtained, together with
relevant equations where applicable.
e. Proof that the filters actually work, e.g. plots of a buffer, showing a signal made
up of two frequencies (one in the stop band and one in the pass band) before
and after filtering.
f. Discuss the borders of the frequency bands with respect to the hearing abilities
of the average human and the likely frequency content of music. Propose and
discuss an improved distribution of the bandwidth into seven bands (a single A4
sheet Max).
g. Briefly discuss your choice of the window function (approx. 200 words). Think
about comparing different windows.
Module Code: UFMFH8-15-3
Module Name: Digital Signal Processing
Academic Year: 2023/2024
Coursework
Page 3 of 3
6. Marks Breakdown
Task Marks
1. Working equaliser 25
2. Filter design
Design description and equations (a)
Frequency response diagrams (b)(c) and (d)
Functionality proof of the filters (e)
15
24
21
4. Frequency band discussion (f) 8
5. Window function discussion (g) 7
Total 100
Please submit a digital copy of the report (Blackboard Submission).
Demonstrate your working code to your lab tutor
7. References
[1]
[2]
Introduction to the Filter Designer
https://uk.mathworks.com/help/signal/examples/introduction-to-filter-designer.html
P.A. Lynn & W. Fuerst, “Introductory Digital Signal Processing”, 2
nd Edition, John Wiley
& Sons, 1998