• Represent sampled signals in the time and frequencydomains
and explain the equivalence between domains.
• Explain the significance of Nyquist’s criteria and
recognise the effects aliasing distortion has on a signal.
• Utilise MATLAB to simulate the operation of an analogue
to digital conversion system
Task 1 – Identifying the Nyquist Rate for Signals
Create a 10 second time vector in MATLAB. Use a simulation accuracy of:
Ts = 1/16000; %Time-step for simulation
Using the formulae for a chirp from lectorial 4 slides 5 and 6, create a chirp
signal from this time vector that starts at the frequency f0= 100 Hz and has a
modulation index of μ = 5.
Plot this signal in both the time and frequency domains. Note how the
spectrum looks when displayed on the graph and the frequencies present.
Also use soundsc() to listen to the chirp signal if you’d like.
What frequency range does this signal have? What is the single-sided
bandwidth of this signal? Calculate this exactly using the formula for
instantaneous frequency in lecture 4.
- From Nyquist’s first criterion what is the absolute minimum
sampling rate that could be used to sample this signal?
at the signal’s spectrum and determine where most of the energy
lies. What is the approximate maximum frequency contained in these
- At what sampling frequency did the audio start to noticeably distort?
How did this relate to the frequencies in the original signal (look at the
spectrum you generated)?
- Discuss how aliasing occurs and why.
- Contrast the effect reducing the sampling rate had on speech as
opposed to the music files.