1. Dr. Elwin Chandra Monie Department of ECE, RMK Engineering College
VLSI Signal Processing 1
Dr. Elwin Chandra Monie
Department of ECE, RMK Engineering College
Dept. of ECE

2. 256K Memory Chip
Dept. of ECE, RMK Engineering College

3. Applications
Dept. of ECE, R M K Engineering College

4. Syllabus
Anna University syllabus for VL9253 VLSI Signal processing Text Keshab K. Parhi, ‘VLSI Digital Signal Processing Systems, Design and implementation’, Wiley India Pvt. Ltd., 2009
Dept. of ECE, RMK Engineering College

5. Processors for DSP system
Need for VLSI DSP System
Processors for DSP system
General Purpose Microprocessors/Microcontrollers
General Purpose DSPs
Custom Processors in VLSI- FPGA, ASIC
Real time throughput
Sampling rates from 20KHz to 500 MHz
Present sample is to be processed before the arrival of the next sample; if not buffered
Processing rate upto 100 GOPs/sec is required
Dept. of ECE, R M K Engineering College

6. Need for VLSI DSP system ….
Data Driven property
Systems are synchronized by data and not by clock
Asynchronous operation possible
Reduced size
For portable and mobile applications
High density circuits available - 90MnTr/cm2
Increases according to Moore’s Law
Submicron fabrication technology feasible 0.07µm
Dept. of ECE, R M K Engineering College

7. Typical DSP Algorithms
Filtering
FIR, IIR filters
y(n) = ∑kak y(n-k) + ∑kbk x(n-k)
With (Recursive) and without feedback
Convolution and Correlation
y(n) = ∑ x(k) h (n-k)
y(n) = ∑ a(k) x (n+k) n= 1 to ∞
Non-terminating programs – Execute the same code repetitively
Adaptive Filters –LMS Algorithm
Dept. of ECE, R M K Engineering College

8. Typical DSP Algorithms …
Transforms
FFT, DCT, DWT
FFT : X(k) = ∑n x(n) e -j2πkn/N Real and imaginary components
Decomposition
SVD, LU Matrix factorization, QR decomposition
Operations involved
Arithmetic – Multiplication, Addition
MAC operation
Logic – Shifting, barrel shifiting – Delay
Dot Product/ Matrix-Vector operations
Dept. of ECE, R M K Engineering College

9. Data Flow Graph
A DSP program is often represented using a Data Flow Graph (DFG), which is a directed graph that describes the program
Consider the following IIR filter
y[n] = x[n] + a y[n − 1]
Dept. of ECE, RMK Engineering College

10. Data Flow Graph ….
In the DFG, nodes represent the tasks or computations (Multiplication/Addition)
Each task is associated with its corresponding execution time
The edges represent the communications between the nodes A → B
Associated with each edge is a non-negative number representing the delay
An iteration of the node is the execution of the node, exactly once
Dept. of ECE, RMK Engineering College

11. Data Flow Graph ….
Each edge describes a precedence constraint between two nodes
The precedence constraint is an intra-iteration constraint if the edge has zero delays
(i.e. computations at nodes connecting the edge occur in the same clock cycle)
The precedence constraint is an inter-iteration constraint if the edge has one or more delays
(i.e. computations at nodes connecting the edge occur in different clock cycles)
A1 → B1 => A2 → B2 => A3 …
Dept. of ECE, RMK Engineering College

12. Data Flow Graph …. x(n) Critical Path
the path with the longest computation time among
all paths that contain zero delays
Critical path length is 26 units
Critical path: the lower bound on clock period
To achieve high-speed, the length of the critical path should be reduced
x(n) D D D D 10 10 10 10 10
y(n) 4 4 4 4 14 26 18 22 26
Dept. of ECE, RMK Engineering College

13. Loop Bound
A recursive DFG has one or more loops
A loop bound for the L-th loop is defined as tL / wL
tL is the loop computation time
wL is the number of delays in the loop
Iteration bound T∞
Iteration bound is the maximum loop bound of all loops in the DFG
The loop that gives the iteration bound is called the critical loop
The iteration bound determines the minimum critical path of a recursive system represented by that DFG structure!
In other words, no matter how you pipeline or retime the DFG, you cannot get a circuit with lower critical path than the iteration bound!
Dept. of ECE, RMK Engineering College

14. Example of Iteration Bound
(1)
Loops
Loop 1: ADBA
Loop bound = 4/2
Loop 2: AECBA
Loop bound = 5/3
Loop 3: AFCB
Loop bound = 5/4
Critical Loop
Loop 1
Iteration Bound
Max{4/2,5/3,5/4} = 4/2 = 2
T∞=2 units of time. A 2D
(1)
(2) B D D
(1)
(2) C E D
(2) F
That is the minimum clock period (max frequency) this circuit can operate at after pipelining and retiming
Dept. of ECE

15. Longest path matrix algorithm-1
Let d be the number of delays in DFG. Define K = [1, 2, · · · , d] Form the matrix L(1) as follows max tqd i → dj if at least one path exists L(1)i,j = q -1 if no such path exists where max tqd i → dj is the maximum of the longest computation time between delay element di to delay element dj
Dept. of ECE, RMK Engineering College

16. Longest path matrix algorithm-2
Compute the successive matrices L(m+1)i,j = max ( -1, L(1)i,k + L(m)k,j ) kS in which Si,j = { k  K |(li,j  -1) & (lk,j  -1)} The iteration bound is computed from L(m)i,i T∞ = max i,mK m
Dept. of ECE, RMK Engineering College

17. Longest path matrix algorithm-3
L(1) =
L2,1(2) = max ( -1, L(1)2,k + L(1)k,1)
k{1,2,3,4}
Dept. of ECE, RMK Engineering College

18. Longest path matrix algorithm-4
L2,1(2) = max( -1, L(1)2,k + L(1)k,1) k{1,2,3,4} = max( -1,0+5) = 5 L2,2(2) = max( -1, L(1)2,k + L(1)k,2) = max( -1,4+0 ) = 4 L2,3(2) = max( -1, L(1)2,k + L(1)k,3) = max(-1) = -1 L2,4(2) = max ( -1, L(1)2,4 + L(1)k,4) = max(-1,0+0) = 0
Dept. of ECE, RMK Engineering College

19. Longest path matrix algorithm-5
L(2) = L(3) = T∞ = max 4/2, 4/2, 5/3, 5/3, 5/3, 8/4, 8/4, 5/4, 5/ = L(4) =
Dept. of ECE, RMK Engineering College

20. Data Independence Graph
x’=x y x0 x1 x2 x3 x4 x5 b
b’=b
y’= y+bx x b2 2 b1 1 b0 y1 y2 y3 y4 y5 y0 1 2 3 4 5 6
y(n)= b0 x(n) + b1 x(n-1) + b2 x(n-2)
Dept. of ECE, RMK Engineering College
Dept. of ECE

21. Pipelining in FIR filters
Reduce the critical path
Increase the clock speed or sample speed
Reduce power consumption
Introduce pipelining latches along the data path
Dept. of ECE, RMK Engineering College

22. Pipelining in FIR filters
Critical path : TM+2TA => TM+TA
Dept. of ECE, RMK Engineering College

23. General Method of Pipelining
Pipelining latches can only be placed across any feed-forward cutset of the graph without affecting of the structure
Cutset: A cutset is a set of edges of a graph such that if these edges are removed from the graph, the graph becomes disjoint.
Feed-forward cutset: A cutset is called a feed- forward cutset if the data move in the forward direction on all the edges of the cutset
Limitations of Pipelining
Increase in Latency : The difference in the availability of the first output
Increase in the number of latches
Dept. of ECE, RMK Engineering College

24. General Method of Pipelining
Critical path: 4
Feed forward cutset
Not Correct !
Critical Path: 2
Dept. of ECE, RMK Engineering College

25. Transposition Theorem
x(n) c b a
Z-1
Z-1
y(n)
Reverse the direction of all edges in a given SFG and interchanging the input and output ports preserve the functionality of the system
Critical Path : TM+2TA => TM+TA
Dept. of ECE, RMK Engineering College

26. Fine-Grain Pipelining
Multiplier with processing time of 10 is split into two units with processing times 6 and 4
Critical path: 12 => 6
Dept. of ECE, RMK Engineering College

27. Parallel processing FIR Filters
y(n)= ax(n)+bx(n-1)+cx(n-2)
y(3k) = ax(3k)+bx(3k-1)+cx(3k-2)
y(3k+1)= ax(3k+1)+bx(3k)+cx(3k-1)
y(3k+2)= ax(3k+2)+bx(3k+1)+cx(3k)
Sample speed is increased since multiple samples are processed at the same time. Clock speed remains the same
Dept. of ECE, RMK Engineering College

28. Parallel processing FIR Filters
Iteration Time= 1/3 (TM+2TA )
Used 3 sets of resources for 3-parallel system
Dept. of ECE, RMK Engineering College

29. Pipelining for Low Power
Ccharge V0
Propagation delay =
k(V0- Vt)2
Power consumption = Ctotal V02 f
For M Level pipelining Ccharge is reduced by 1/M
Keeping f same reduce V0 by β V0 where β 0 to 1
Ppip = Ctotal β2 V02 f = β2 Pseq
Ccharge/M β V0
Propagation delaypip =
k(βV0- Vt)2
If the clock period is kept the same
Ccharge V Ccharge/M β V0 =
k(V0- Vt) k(βV0- Vt)2
(βV0- Vt) = β (V0- Vt) Solve for β
Dept. of ECE, RMK Engineering College

30. Example on Pipelining
Consider an original 3-tap FIR filter and its fine- grain pipeline. Assume TM=10 ut, TA=2 ut, Vt=0.6V, Vo=5V, and CM=5CA.In fine-grain pipeline filter, the multiplier is broken into 2 parts, m1 and m2 with computation time of 6 u.t. and 4 u.t. respectively, with capacitance 3 times and 2 times that of an adder, respectively.
(a) What is the supply voltage of the pipelined filter if the clock period remains unchanged?
(b) What is the power consumption of the pipelined filter as a percentage of the original filter?
Dept. of ECE, RMK Engineering College

31. Solution
Solution: Original : C charge = CM + CA = 6 CA Pipelining : C charge = 3 C A (5 β - 0.6)2 = β ( )2 β = or ( not valid) Vpip = V0 Ppip = Pseq
Dept. of ECE, RMK Engineering College

32. Parallel System for Low power
Power consumption :
Ppar = (L Ctotal) (β V0)2 f / L = P seq for L- Parallel System
Propagation delay:
Ccharge V0 Ccharge β V0
Tseq = Tpar =
k(V0- Vt) k(βV0- Vt)2
L Tseq = Tpar
β(V0- Vt)2 = L (βV0- Vt)2
Solve for β
Dept. of ECE, RMK Engineering College

33. Example on Parallel system
Consider a 4-tap FIR filter shown in Fig. 3.18(a) and its 2-parallel version in 3.18(b). The two architectures are operated at the sample period 9 u.t. Assume TM=8, TA=1, Vt=0.45V, Vo=3.3V, CM=8CA
(a) What is the supply voltage of the 2-parallel filter?
(b) What is the power consumption of the 2- parallel filter as a percentage of the original filter?
Dept. of ECE, RMK Engineering College

34. Solution 2- parallel: Ccharge = CM + 2CA = 10CA
9 (β )2 = 5 β ( )2
β = or (not valid)
Vpar = Vo
Ppar = P
Dept. of ECE, RMK Engineering College

35. Problems & Assignments
Prob (a)
Prob
Assignment
Design a Low pass filter with sample rate of 48KHz and order 40 with cut off frequency of 10KHz. Write VHDL/Verilog code and simulate
Hint: Use Matlab to find the coefficients and test the filter functionality by testing the impulse response
2) Implement a 4-tap filter in direct form and in transpose form. Introduce pipelining and compare the performance
Dept. of ECE, RMK Engineering College