Convolution of Two Rectangular Pulses

Example 2.2.2: Convolution of two rectangular pulses

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http://s-mat-pcs.oulu.fi/~ssa/ESignals/em2_22-1.htm

Example 2.2.2: Convolution of two rectangular pulses Let A, -T0 < t < T0

f(t) =

0, |t| > T0

= g(t) .

f(u) g(t-u) du

(f*g)(t) =

A · A du,

-2T0 < t < 0

A · A du,

0 < t < 2T0

=

=

A2 (t+2T0 ),

-2T0 < t < 0

A2 (2T0 -t),

0 < t < 2T0

0,

| t | > 2T0

.

The convolution of two rectangular pulses = triangular pulse The Fourier transform of f * g i.e. of f * f is [F(v)]2, where F(v) is the Fourier transform of f, that is 2 (F(v))2 = 2AT0 sin(2 T0v) / 2 T0v

= A2sin2(2 T0v) / 2v2.

03/09/2014 04:37 p.m.

Example 2.2.2: Convolution of two rectangular pulses

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http://s-mat-pcs.oulu.fi/~ssa/ESignals/em2_22-1.htm

Thus

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03/09/2014 04:37 p.m.