What is the euler formula?
e^{j \theta} = cos \theta + j sin \theta
What are properties of response of LTI system to sinusoidal excitations?
- Response is also sinusoidal
- Excitation and response have same frequency
- The response amplitude and the response phase delay are different
What is the frequency response function?
It relates the input and output of LTI system
What kind of signals is the Fourier transform defined for?
Continuous, infinite signals
How must the signals from fourier transform be adjusted for digital computers?
– Continuous signals must be discretized
– Infinite signals must be truncated
– Only finite number of frequencies can be computed.
What can be used to reconstruct the continuous signal of a fourier transform to and infinite discrete sequence?
Discrete Time Fourier Transform
What are the differences between Discrete Time Fourier Transform and Discrete Fourier Transform?
DTFT is infinitely long, DFT has finite length
DTFT has continuous frequency, DFT has discrete frequency
What are the main things to remember about DFT? (5)
- 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)
What is Empirical Transfer Function Estimate?
- The ETFE is a non-parametric Frequency Response Function
- no other assumption than linearity is made
-
How can variance of ETFE be decreased?
- calculating the averaged ETFE
What is the crest factor?
▪ 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.
