# Aliasing in Time Series Analysis

Aliasing in Time Series Analysis

The relationship between two sinusoidal signals =cos(2πf+ϕ) and =cos(2π(f+m)+ϕ) is shown for and The signals are assumed to be observed at times and the observed points are indicated. When is an integer the points on the curve coincide and the signals are said to be aliased. Considering all frequencies in the range , the largest value of so that all signals may be identified from the observed points is called the Nyquist frequency. It is well known that =0.5.

a

t

b

t

|f|≤0.5,

|ϕ|≤π/2,

|m|≤3.

t=0,1,…,6

m

|f|≤

f

m

f

m

f

m