2 Assessing time varying signals

Question 1

Why digital signal processing?

Answer 1

• digital equipment is more flexible

(reprogrammable equipment can be customized)

• digital equipment is more reliable

(no drift of electronic components in varying environment)

• detection of signals

(for example a carrier wave)

• coding and decoding of information

(for example in mobile phone communication)

Question 2

What is a time series?

Answer 2

A time series is defined as a signal which is a function of time x(t)

• x: measurement variable / often in V
• t: time / s
• TS or Δt or : sampling time interval / s
• T: total time interval of the measurements / s

Question 3

Parameters required for a time series?

Answer 3

Two parameters need to be chosen, typically

• sampling time interval T_s = Δt = t_n+1 - t_n
• total time interval of the measurements T

Question 4

Standard fixed time series parameters?

Answer 4

• sampling frequency f_s = 1/Δt
• total number of samples N = T/Δt
• discrete time t_n = n Δt , where n = 0, 1, 2, … N-1

Question 5

What is a signal?

Answer 5

A signal is defined as that part of a time series which is wanted

Question 6

What is noise?

Answer 6

Noise is defined as that part of a time series which is unwanted

Question 7

A periodic signal is characterized by …

Answer 7

• f: frequency of the signal / Hz
• T_P = 1/f: period of the signal / s

Question 8

What is a discrete sinusoid?

Answer 8

A discrete sinusoid is defined as a periodic harmonic signal.

Question 9

The three parameters that characterise a discrete sinusoid?

Answer 9

A discrete sinusoid is characterised by three parameters:

• Amplitude of the sinusoid / often in V
• frequency of the sinusoid / Hz
• Φ: phase of the sinusoid / rad or deg

Question 10

Amplitude, period, frequency and phase of a signal?

Answer 10

• The amplitude A is half the peak-to-peak value of the signal
• The period TP is the time after which the signal repeats
• The frequency f of the signal is the inverse of its period TP
• The phase Φ of the signal describes the relative start time

Question 11

Discrete sinusoids are described by the cosine function?

Answer 11