Page 458 - Numerical Methods for Chemical Engineering

Convolution and correlation 447

2

t
2

1 1 2
t

1
w a
2w a w i w a
w i w a
w
2

1 1 2 2
w
Figure 9.3 Power spectrum of time signal showing aliasing due to incorrectly-sampled high-frequency
component.

tre t
saed t
2

1
t

1
2

1 1 2
t
Figure 9.4 Comparison of the “true” f (t) signal to the sampled signal showing the incorrect sampling
of the high-frequency component that leads to aliasing.

Convolution and correlation

Convolution of two signals
The convolution of two functions g(t) and f (t) is the function of t

+∞
'
1
∗
[g f ](t) = √ g(τ) f (t − τ)dτ (9.68)
2π
−∞