FIR filters

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FIR filters

• ELG6163
• Miodrag Bolic

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Outline

• FIR filters
• Structures
• Polyphase FIR filters
• Parallel polyphase FIR
• Decimated FIR
• Implementations of FIR filters

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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

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Direct form FIR filter
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Transposed FIR
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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).

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7
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
• Where hk is an array of constants

yn0 For (n0 nltNn) For (k
0kltNk) //inner loop yn yn
hkxn-k
Only Multiply and Accumulate (MAC) is needed!
In C language
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MAC using General Purpose Processor (GPP)
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12
3
R0
11
24
9
R2
44
X
R1
1
2
3
Clr A Clear Accumulator A
Clr B Clear Accumulator B
Loop 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 X0Y0 -gtA
Add A,B A B -gt B
Inc R0 R0 1 -gt R0
Inc R1 R1 1 -gt R1
Dec N Dec N (initially equals to 3)
Tst N Test for the value
Jnz Loop Different than zero loop again
Mov B,R2 Move result to memory
Copied from Rony Ferzli http//www.fulton.asu.edu
/karam/eee498/
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MAC using DSP

• Harvard Architecture allows multiple memory reads

11
12
3
11
24
9
R2
44
X
1
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
Copied from Rony Ferzli http//www.fulton.asu.edu
/karam/eee498/
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Copied from DSPPrimer-Slides