Question about Nyquist frequency and noise

[bert2002]

Homework Statement

A time series is sampled at 250 Hz. What is the sampling interval and Nyquist frequency of the original signal, before digitising was contaminated with noise at about 300 Hz. At what frequency would this noise appear in the spectrum of the digitised sequence ? Repeat the calculation for noise contamination at 475 Hz.

The Attempt at a Solution

[/B]
I can calculate the sampling interval and Nyquist frequency fine but I don't understand the noise part of the question at all. Any help is appreciated, thanks.

 

[Hesch]

At what frequency would this noise appear in the spectrum of the digitised sequence ?

Look at the upper curve here:

The dots are the sampled values.

Say the curve is the 300 Hz noise. If you sketch a ( low frequency ) curve through the dots, what will the frequeny of the sketched curve be ?

 

[rude man]

Homework Statement

A time series is sampled at 250 Hz. What is the sampling interval and Nyquist frequency of the original signal, before digitising was contaminated with noise at about 300 Hz. At what frequency would this noise appear in the spectrum of the digitised sequence ? Repeat the calculation for noise contamination at 475 Hz.

The Attempt at a Solution

[/B]
I can calculate the sampling interval and Nyquist frequency fine but I don't understand the noise part of the question at all. Any help is appreciated, thanks.

The noise is well above the Nyquist frequency so you will get aliasing. How does the noise spectrum fold about the Nyquist frequency when its spectrum is above the Nyquist frequency?
A little hint: cos(w₁t)cos(w₂t) = ?