Chapter 8

Question 1

What is the euler formula?

Answer 1

e^{j \theta} = cos \theta + j sin \theta

Question 2

What are properties of response of LTI system to sinusoidal excitations?

Answer 2

• Response is also sinusoidal
• Excitation and response have same frequency
• The response amplitude and the response phase delay are different

Question 3

What is the frequency response function?

Answer 3

It relates the input and output of LTI system

Question 4

What kind of signals is the Fourier transform defined for?

Answer 4

Continuous, infinite signals

Question 5

How must the signals from fourier transform be adjusted for digital computers?

Answer 5

– Continuous signals must be discretized

– Infinite signals must be truncated

– Only finite number of frequencies can be computed.

Question 6

What can be used to reconstruct the continuous signal of a fourier transform to and infinite discrete sequence?

Answer 6

Discrete Time Fourier Transform

Question 7

What are the differences between Discrete Time Fourier Transform and Discrete Fourier Transform?

Answer 7

DTFT is infinitely long, DFT has finite length

DTFT has continuous frequency, DFT has discrete frequency

Question 8

What are the main things to remember about DFT? (5)

Answer 8

• DFT is suited for computation by computers (finite, discrete time signal sequence)
• The DFT evaluates at a discrete frequency set 𝑓𝑘 as integer multiples of the first
  harmonic frequency 𝑓𝐻.
• The window/ observation length 𝑇𝑤 affects the frequency resolution, i.e. the minimum frequency difference that can be distinguished given by 𝑓𝐻
• For periodic excitation signals, the window 𝑇𝑤 should contain full signal cycles as this avoids any leakage !
• For periodic signals with period 𝑇𝑤 only a finite time sequence of 𝑥(𝑛𝑇𝑠) is necessary to exactly calculate the DTFT
  and hence reconstruct the FT, which would otherwise require an infinite time sequence of 𝑥(𝑡)

Question 9

What is Empirical Transfer Function Estimate?

Answer 9

• The ETFE is a non-parametric Frequency Response Function
• no other assumption than linearity is made

-

Question 10

How can variance of ETFE be decreased?

Answer 10

• calculating the averaged ETFE

Question 11

What is the crest factor?

Answer 11

▪ measures the “peakiness” or dynamic range of a signal

▪ A high Crest factor indicates a signal with high peaks and wide dynamic range (spiky shape)

▪ A low Crest factor indicates a relatively flat signal with fewer peaks.