FIR filters
ELG6163
Miodrag Bolic
1
Outline
• FIR filters
–
–
–
–
Structures
Polyphase FIR filters
Parallel polyphase FIR
Decimated FIR
• Implementations of FIR filters
2
Sequential application specific
processor
• A processor tuned only for a particular
application
• Can be used for low-power implementations
• Word lengths can be adjusted to the current
problem.
• Example: FIR filter
3
Direct form FIR filter
4
Copied from [Wanhammer99]
Transposed FIR
5
Copied from [Wanhammer99]
Assignment
• Design an N-tap transposed linear-phase
FIR filter as a sequential application
specific processor. Use only one multiplier
and show how processing time can be
decreased twice.
Hint: design a transposed FIR filter
structure as in the previous slide but allow
for generating the sums in reversed order
PSN-1, PSN-2, …, PS1, y(n).
6
Copied from [Wanhammer99]
General purpose processor
architecture
• FIR example
• We will study RISC architectures
• Single-cycle processor
– Implementation of add and load instructions
• Pipelined implementation
– Why do all instructions have the same number
of cycles
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Example: Digital Filtering
• The basic FIR Filter equation is
y[n]   h[k ].x[n  k ]
Where h[k] is an array of constants
y[n]=0;
In C language
For (n=0; n<N;n++)
{
For (k = 0;k<N;k++)
//inner loop
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y[n] = y[n] + h[k]*x[n-k];}
Copied from Rony Ferzli: http://www.fulton.asu.edu/~karam/eee498/
Only Multiply and
Accumulate
(MAC) is needed!
MAC using General Purpose Processor (GPP)
R0
11
12
3
11
X
R1
1
3
Loop
9

44
9
2
Copied from Rony
Ferzli:
http://www.fulton.as
u.edu/~karam/eee49
8/
24
R2
Clr
A
;Clear Accumulator A
Clr
B
; Clear Accumulator B
Mov
*R0, Y0 ; Move data from memory location 1 to register Y0
Mov
*R1,X0
; Move data from memory location 2 to register X0
Mpy
X0,Y0,
A
;X0*Y0 ->A
Add
A,B
;A + B -> B
Inc
R0
;R0 + 1 -> R0
Inc
R1
;R1 + 1 -> R1
Dec
N
;Dec N (initially equals to 3)
Tst
N
;Test for the value
Jnz
Loop
;Different than zero loop again
MAC using DSP
• Harvard Architecture allows multiple
memory reads
11
12
3
11
X
R2

24
1
44
9
2
3
Clr
A
;Clear Accumulator A
Rep
N
; Rep N times the next instruction
MAC
*(R0)+, *(R1)+, A
; Fetch the two memory locations pointed by R0 and R1, multiply
them together and add the result to A, the final result is stored back
in A
Mov
A, *R2
; Move result to memory
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Copied from Rony Ferzli: http://www.fulton.asu.edu/~karam/eee498/
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Copied from [DSPPrimer-Slides]