24-01-2013, 11:26 AM
TO IMPLEMENT LINEAR CONVOLUTION OF TWO GIVEN SEQUENCES
TO IMPLEMENT LINEAR.docx (Size: 12.38 KB / Downloads: 21)
Theory:
Convolution is an integral concatenation of two signals. It has many
applications in numerous areas of signal processing. The most popular application is the
determination of the output signal of a linear time-invariant system by convolving the
input signal with the impulse response of the system.
Note that convolving two signals is equivalent to multiplying the Fourier Transform of
the two signals.
Mathematic Formula:
The linear convolution of two continuous time signals x(t) and h(t) is defined by
For discrete time signals x(n) and h(n), is defined by
Where x(n) is the input signal and h(n) is the impulse response of the system.
In linear convolution length of output sequence is,
length(y(n)) = length(x(n)) + length(h(n)) – 1
Graphical Interpretation:
• Reflection of h(k) resulting in h(-k)
• Shifting of h(-k) resulting in h(n-k)
• Element wise multiplication of the sequences x(k) and h(n-k)
• Summation of the product sequence x(k) h(n-k) resulting in the convolution
value for y(n)