1. DSP [Digital Signal Processing]
l -4 [Digital Filters]
Vo
A.H.M. Asadul Huq, Ph.D.
asadul.huq@ulab.edu.bd
http://asadul.drivehq.com/students.htm
February 3, 2013 A.H. 1

2. Digital Filters
• A digital filter is a system that implements DSP algorithms using
hardware and/or software.
• The filter input/output signals are generally discrete signals
• Normally input signals are sample values of the signals to be
operated by the filters.
• The input signal may come out of a digital storage device or
sampled in real time.
x(n) Digital Filter y(n)
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February 3, 2013 A.H. 2

3. Classes of Digital Filter Structures
• FIR (Finite Impulse Response
• IIR (Infinite Impulse Response)
General Equations of digital filters -
∝
IIR : y (n) = ∑ h(k ) x(n − k ) Eq Ef . 5.1
k =0
M −1
FIR : y (n) = ∑ h(k ) x(n − k ) Eq. Ef . 5.2
k =0
February 3, 2013 A.H. 3

4. Difference equation of the
digital filter [564]
M N
y (n) = ∑ bk x(n − k ) − ∑ ak y (n − k ) Eq. 9.1.1
k =0 k =1
Here, {ak} and {bk} are filter coefficients and
these parameters determine the frequency
response of the filter.
x(n) {ak}, {bk} y(n)
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February 3, 2013 A.H. 4

5. System Function Equation of the Filter
M
∑b z k
−k
H ( z) = k =0
N
Eq. 9.1.2
1 + ∑ ak z − k
k =1
• System function H(z) equals to the ratio of 2
polynomials in z-1
• Poles and zeros of H(z) depend on the coefficients
filter {ak} and {bk}.
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February 3, 2013 A.H. 5

6. FIR Equations [565]
• FIR Difference Equation -
M −1
y (n) = ∑ bk x(n − k ) Eq. 9.2.1
k =0
• And System Function -
M −1
H ( z ) = ∑ bk z − k Eq. 9.2.2
k =0
• Impulse response h(n) is equal to the coefficient {bk}; Hence,
bk 0 ≤ k ≤ M − 1
h( n) = 
0, otherwise Eq. 9.2.3
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February 3, 2013 A.H. 6

7. Types of FIR Filter Structures
• Direct [566]
• Cascade [567]
• Frequency-Sampling Structure [569]
• Lattice Structure [574]
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February 3, 2013 A.H. 7

8. Basic Components required to Build Filter structures
x1[n]
ADDER
Σ
x1[n]+x2[n]
x2[n]
a
MULTIPLY x[n X ax[n]
]
DELAY x[n] Z-1 x[n-1]
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February 3, 2013 A.H. 12
Of 8

9. Direct-Form Structure of FIR Filter [503]
Direct-form structure is realized by putting {bk} = h(k) in the
equation 9.2.1-
M −1
y (n) = ∑ h(k ) x(n − k ) Eq. 9.2.4
k =0
= h(0) x(n) + h(1) x(n − 1) + ... + h(m − 1) x(n − m + 1)
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February 3, 2013 A.H. 9

10. Cascade form FIR [P.567]
• The system function H(z) is factored into 2nd order (no. of
coefficients=3) sections. The sections are then attached in
series.
February 3, 2013 A.H. 10

11. Cascade form equations
K
H ( z) = ∏ H k ( z)
k =1
• K is the no of 2nd order sections. And b’s are the FIR
coefficients.
February 3, 2013 A.H. 11

12. DSP Lecture
DIGITAL FILTER
THE END
THANK YOU
This ppt may be downloaded from my web site:
http:// asadul.drivehq.com/students.htm
Password (email address): dsp.ete@ulab.edu.bd
This password does not live long !
03:06 PM
February 3, 2013 A.H. 12