24-12-2012, 12:41 PM
CIRCULAR CONVOLUTION
AIM:
Write a program in C and MATLAB to compute the response of a discrete LTI system with input sequence x(n) and impulse response h(n) by using Circular convolution. Verify the same on TMS320C6711 DSP kit, MATLAB.
TOOLS REQUIRED :
2.1 TMS 320C 6711 Kit,
2.2 Full version CCS s/w,
2.3 DSK 6711 s/w,
2.4 MATLAB s/w.
THEORY:
Convolution is a special operation, operated between two signals and which includes the following operations.
Folding.
Shifting.
Multiplication.
Addition
Convolution sum is useful to obtain the response of discrete LTI system with input x(n) and impulse response h(n).
COMPUTATION:
Following steps are required to compute the response of discrete LTI system with input x(n) and impulse response h(n)
Convert the input sequence x(n) duration N1 to N1+N2 –1 by padding with N2 –1 number of zeros.
Convert the impulse response sequence h(n) duration N2 to N1+N2 –1 by padding with N1 –1 number of zeros
Keep the input sequence x(m) as it is and fold the impulse response h(m).
Shift the folded version sequence, h(-m) by n units to get h(n-m).
Multiply the input sequence x(m) and h(n-m).
Finally compute the sum over the range 0 to N1+N2 –2.